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Sample records for entropy yields spatial

  1. SpatEntropy: Spatial Entropy Measures in R

    OpenAIRE

    Altieri, Linda; Cocchi, Daniela; Roli, Giulia

    2018-01-01

    This article illustrates how to measure the heterogeneity of spatial data presenting a finite number of categories via computation of spatial entropy. The R package SpatEntropy contains functions for the computation of entropy and spatial entropy measures. The extension to spatial entropy measures is a unique feature of SpatEntropy. In addition to the traditional version of Shannon's entropy, the package includes Batty's spatial entropy, O'Neill's entropy, Li and Reynolds' contagion index, Ka...

  2. Spatial-dependence recurrence sample entropy

    Science.gov (United States)

    Pham, Tuan D.; Yan, Hong

    2018-03-01

    Measuring complexity in terms of the predictability of time series is a major area of research in science and engineering, and its applications are spreading throughout many scientific disciplines, where the analysis of physiological signals is perhaps the most widely reported in literature. Sample entropy is a popular measure for quantifying signal irregularity. However, the sample entropy does not take sequential information, which is inherently useful, into its calculation of sample similarity. Here, we develop a method that is based on the mathematical principle of the sample entropy and enables the capture of sequential information of a time series in the context of spatial dependence provided by the binary-level co-occurrence matrix of a recurrence plot. Experimental results on time-series data of the Lorenz system, physiological signals of gait maturation in healthy children, and gait dynamics in Huntington's disease show the potential of the proposed method.

  3. Monte Carlo power iteration: Entropy and spatial correlations

    International Nuclear Information System (INIS)

    Nowak, Michel; Miao, Jilang; Dumonteil, Eric; Forget, Benoit; Onillon, Anthony; Smith, Kord S.; Zoia, Andrea

    2016-01-01

    Highlights: • We show that the entropy function might be misleading in criticality simulations. • We interpret the spatial fluctuations of the fission chains in terms of the key parameters of the simulated system. • We show that the behavior of the entropy function is related to the theory of neutron clustering. - Abstract: The behavior of Monte Carlo criticality simulations is often assessed by examining the convergence of the so-called entropy function. In this work, we shall show that the entropy function may lead to a misleading interpretation, and that potential issues occur when spatial correlations induced by fission events are important. We will support our analysis by examining the higher-order moments of the entropy function and the center of mass of the neutron population. Within the framework of a simplified model based on branching processes, we will relate the behavior of the spatial fluctuations of the fission chains to the key parameters of the simulated system, namely, the number of particles per generation, the reactor size and the migration area. Numerical simulations of a fuel rod and of a whole core suggest that the obtained results are quite general and hold true also for real-world applications.

  4. Spatial data modelling and maximum entropy theory

    Czech Academy of Sciences Publication Activity Database

    Klimešová, Dana; Ocelíková, E.

    2005-01-01

    Roč. 51, č. 2 (2005), s. 80-83 ISSN 0139-570X Institutional research plan: CEZ:AV0Z10750506 Keywords : spatial data classification * distribution function * error distribution Subject RIV: BD - Theory of Information

  5. Maximum and minimum entropy states yielding local continuity bounds

    Science.gov (United States)

    Hanson, Eric P.; Datta, Nilanjana

    2018-04-01

    Given an arbitrary quantum state (σ), we obtain an explicit construction of a state ρɛ * ( σ ) [respectively, ρ * , ɛ ( σ ) ] which has the maximum (respectively, minimum) entropy among all states which lie in a specified neighborhood (ɛ-ball) of σ. Computing the entropy of these states leads to a local strengthening of the continuity bound of the von Neumann entropy, i.e., the Audenaert-Fannes inequality. Our bound is local in the sense that it depends on the spectrum of σ. The states ρɛ * ( σ ) and ρ * , ɛ (σ) depend only on the geometry of the ɛ-ball and are in fact optimizers for a larger class of entropies. These include the Rényi entropy and the minimum- and maximum-entropies, providing explicit formulas for certain smoothed quantities. This allows us to obtain local continuity bounds for these quantities as well. In obtaining this bound, we first derive a more general result which may be of independent interest, namely, a necessary and sufficient condition under which a state maximizes a concave and Gâteaux-differentiable function in an ɛ-ball around a given state σ. Examples of such a function include the von Neumann entropy and the conditional entropy of bipartite states. Our proofs employ tools from the theory of convex optimization under non-differentiable constraints, in particular Fermat's rule, and majorization theory.

  6. Redefining yield gaps at various spatial scales

    Science.gov (United States)

    Meng, K.; Fishman, R.; Norstrom, A. V.; Diekert, F. K.; Engstrom, G.; Gars, J.; McCarney, G. R.; Sjostedt, M.

    2013-12-01

    Recent research has highlighted the prevalence of 'yield gaps' around the world and the importance of closing them for global food security. However, the traditional concept of yield gap -defined as the difference between observed and optimal yield under biophysical conditions - omit relevant socio-economic and ecological constraints and thus offer limited guidance on potential policy interventions. This paper proposes alternative definitions of yield gaps by incorporating rich, high resolution, national and sub-national agricultural datasets. We examine feasible efforts to 'close yield gaps' at various spatial scales and across different socio-economic and ecological domains.

  7. Joint entropy for space and spatial frequency domains estimated from psychometric functions of achromatic discrimination.

    Science.gov (United States)

    Silveira, Vladímir de Aquino; Souza, Givago da Silva; Gomes, Bruno Duarte; Rodrigues, Anderson Raiol; Silveira, Luiz Carlos de Lima

    2014-01-01

    We used psychometric functions to estimate the joint entropy for space discrimination and spatial frequency discrimination. Space discrimination was taken as discrimination of spatial extent. Seven subjects were tested. Gábor functions comprising unidimensionalsinusoidal gratings (0.4, 2, and 10 cpd) and bidimensionalGaussian envelopes (1°) were used as reference stimuli. The experiment comprised the comparison between reference and test stimulithat differed in grating's spatial frequency or envelope's standard deviation. We tested 21 different envelope's standard deviations around the reference standard deviation to study spatial extent discrimination and 19 different grating's spatial frequencies around the reference spatial frequency to study spatial frequency discrimination. Two series of psychometric functions were obtained for 2%, 5%, 10%, and 100% stimulus contrast. The psychometric function data points for spatial extent discrimination or spatial frequency discrimination were fitted with Gaussian functions using the least square method, and the spatial extent and spatial frequency entropies were estimated from the standard deviation of these Gaussian functions. Then, joint entropy was obtained by multiplying the square root of space extent entropy times the spatial frequency entropy. We compared our results to the theoretical minimum for unidimensional Gábor functions, 1/4π or 0.0796. At low and intermediate spatial frequencies and high contrasts, joint entropy reached levels below the theoretical minimum, suggesting non-linear interactions between two or more visual mechanisms. We concluded that non-linear interactions of visual pathways, such as the M and P pathways, could explain joint entropy values below the theoretical minimum at low and intermediate spatial frequencies and high contrasts. These non-linear interactions might be at work at intermediate and high contrasts at all spatial frequencies once there was a substantial decrease in joint

  8. Impact parameter dependence of the specific entropy and the light particle yield in relativistic heavy ion collisions

    International Nuclear Information System (INIS)

    Gudima, K.K.; Toneev, V.D.

    1986-01-01

    The connection between the fragment yield and the associated specific entropy of particles produced in the course of a relativistic heavy ion collision is studied within the cascade approach. The essential impact parameter dependence of the fragment yield indicates that the specific entropy increases with impact parameter and that the critical density of the system decay is the larger the more central the collision process is. The results show that the thermodynamical equilibrium limit for the entropy production is not reached for such heavy systems as Nb+Nb at 400 MeV/nucleon and that the finite size effects and the dynamical freeze-out process are dominant factors in determining the cluster yield

  9. Spatial Decomposition of Translational Water–Water Correlation Entropy in Binding Pockets

    Science.gov (United States)

    2015-01-01

    A number of computational tools available today compute the thermodynamic properties of water at surfaces and in binding pockets by using inhomogeneous solvation theory (IST) to analyze explicit-solvent simulations. Such methods enable qualitative spatial mappings of both energy and entropy around a solute of interest and can also be applied quantitatively. However, the entropy estimates of existing methods have, to date, been almost entirely limited to the first-order terms in the IST’s entropy expansion. These first-order terms account for localization and orientation of water molecules in the field of the solute but not for the modification of water–water correlations by the solute. Here, we present an extension of the Grid Inhomogeneous Solvation Theory (GIST) approach which accounts for water–water translational correlations. The method involves rewriting the two-point density of water in terms of a conditional density and utilizes the efficient nearest-neighbor entropy estimation approach. Spatial maps of this second order term, for water in and around the synthetic host cucurbit[7]uril and in the binding pocket of the enzyme Factor Xa, reveal mainly negative contributions, indicating solute-induced water–water correlations relative to bulk water; particularly strong signals are obtained for sites at the entrances of cavities or pockets. This second-order term thus enters with the same, negative, sign as the first order translational and orientational terms. Numerical and convergence properties of the methodology are examined. PMID:26636620

  10. Spatially-Explicit Bayesian Information Entropy Metrics for Calibrating Landscape Transformation Models

    Directory of Open Access Journals (Sweden)

    Kostas Alexandridis

    2013-06-01

    Full Text Available Assessing spatial model performance often presents challenges related to the choice and suitability of traditional statistical methods in capturing the true validity and dynamics of the predicted outcomes. The stochastic nature of many of our contemporary spatial models of land use change necessitate the testing and development of new and innovative methodologies in statistical spatial assessment. In many cases, spatial model performance depends critically on the spatially-explicit prior distributions, characteristics, availability and prevalence of the variables and factors under study. This study explores the statistical spatial characteristics of statistical model assessment of modeling land use change dynamics in a seven-county study area in South-Eastern Wisconsin during the historical period of 1963–1990. The artificial neural network-based Land Transformation Model (LTM predictions are used to compare simulated with historical land use transformations in urban/suburban landscapes. We introduce a range of Bayesian information entropy statistical spatial metrics for assessing the model performance across multiple simulation testing runs. Bayesian entropic estimates of model performance are compared against information-theoretic stochastic entropy estimates and theoretically-derived accuracy assessments. We argue for the critical role of informational uncertainty across different scales of spatial resolution in informing spatial landscape model assessment. Our analysis reveals how incorporation of spatial and landscape information asymmetry estimates can improve our stochastic assessments of spatial model predictions. Finally our study shows how spatially-explicit entropic classification accuracy estimates can work closely with dynamic modeling methodologies in improving our scientific understanding of landscape change as a complex adaptive system and process.

  11. Spatial Sampling of Weather Data for Regional Crop Yield Simulations

    Science.gov (United States)

    Van Bussel, Lenny G. J.; Ewert, Frank; Zhao, Gang; Hoffmann, Holger; Enders, Andreas; Wallach, Daniel; Asseng, Senthold; Baigorria, Guillermo A.; Basso, Bruno; Biernath, Christian; hide

    2016-01-01

    Field-scale crop models are increasingly applied at spatio-temporal scales that range from regions to the globe and from decades up to 100 years. Sufficiently detailed data to capture the prevailing spatio-temporal heterogeneity in weather, soil, and management conditions as needed by crop models are rarely available. Effective sampling may overcome the problem of missing data but has rarely been investigated. In this study the effect of sampling weather data has been evaluated for simulating yields of winter wheat in a region in Germany over a 30-year period (1982-2011) using 12 process-based crop models. A stratified sampling was applied to compare the effect of different sizes of spatially sampled weather data (10, 30, 50, 100, 500, 1000 and full coverage of 34,078 sampling points) on simulated wheat yields. Stratified sampling was further compared with random sampling. Possible interactions between sample size and crop model were evaluated. The results showed differences in simulated yields among crop models but all models reproduced well the pattern of the stratification. Importantly, the regional mean of simulated yields based on full coverage could already be reproduced by a small sample of 10 points. This was also true for reproducing the temporal variability in simulated yields but more sampling points (about 100) were required to accurately reproduce spatial yield variability. The number of sampling points can be smaller when a stratified sampling is applied as compared to a random sampling. However, differences between crop models were observed including some interaction between the effect of sampling on simulated yields and the model used. We concluded that stratified sampling can considerably reduce the number of required simulations. But, differences between crop models must be considered as the choice for a specific model can have larger effects on simulated yields than the sampling strategy. Assessing the impact of sampling soil and crop management

  12. Simulating the influence of crop spatial patterns on canola yield

    DEFF Research Database (Denmark)

    Griepentrog, H.W.; Nielsen, J.; Olsen, Jannie Maj

    2011-01-01

    plant uniformity on the yield of oil seed rape. Voronoi polygons (tessellations) which define the area closer to an individual than to any other individual were used as a measure of the area available to each plant, and corrections were included for extreme polygon shape and eccentricity of the plant...... location within the polygon. These adjusted polygon areas were used to investigate the potential influence of two of the most important determinants of crop sowing spatial uniformity: row width and longitudinal spacing accuracy, on yield per unit area, and to ask how changes in seeding technology would...

  13. Spatial correlation in matter-wave interference as a measure of decoherence, dephasing, and entropy

    Science.gov (United States)

    Chen, Zilin; Beierle, Peter; Batelaan, Herman

    2018-04-01

    The loss of contrast in double-slit electron diffraction due to dephasing and decoherence processes is studied. It is shown that the spatial intensity correlation function of diffraction patterns can be used to distinguish between dephasing and decoherence. This establishes a measure of time reversibility that does not require the determination of coherence terms of the density matrix, while von Neumann entropy, another measure of time reversibility, does require coherence terms. This technique is exciting in view of the need to understand and control the detrimental experimental effect of contrast loss and for fundamental studies on the transition from the classical to the quantum regime.

  14. Ethiopian Wheat Yield and Yield Gap Estimation: A Spatial Small Area Integrated Data Approach

    Science.gov (United States)

    Mann, M.; Warner, J.

    2015-12-01

    Despite the collection of routine annual agricultural surveys and significant advances in GIS and remote sensing products, little econometric research has been undertaken in predicting developing nation's agricultural yields. In this paper, we explore the determinants of wheat output per hectare in Ethiopia during the 2011-2013 Meher crop seasons aggregated to the woreda administrative area. Using a panel data approach, combining national agricultural field surveys with relevant GIS and remote sensing products, the model explains nearly 40% of the total variation in wheat output per hectare across the country. The model also identifies specific contributors to wheat yields that include farm management techniques (eg. area planted, improved seed, fertilizer, irrigation), weather (eg. rainfall), water availability (vegetation and moisture deficit indexes) and policy intervention. Our findings suggest that woredas produce between 9.8 and 86.5% of their potential wheat output per hectare given their altitude, weather conditions, terrain, and plant health. At the median, Amhara, Oromiya, SNNP, and Tigray produce 48.6, 51.5, 49.7, and 61.3% of their local attainable yields, respectively. This research has a broad range of applications, especially from a public policy perspective: identifying causes of yield fluctuations, remotely evaluating larger agricultural intervention packages, and analyzing relative yield potential. Overall, the combination of field surveys with spatial data can be used to identify management priorities for improving production at a variety of administrative levels.

  15. Nonequilibrium entropies

    International Nuclear Information System (INIS)

    Maes, Christian

    2012-01-01

    In contrast to the quite unique entropy concept useful for systems in (local) thermodynamic equilibrium, there is a variety of quite distinct nonequilibrium entropies, reflecting different physical points. We disentangle these entropies as they relate to heat, fluctuations, response, time asymmetry, variational principles, monotonicity, volume contraction or statistical forces. However, not all of those extensions yield state quantities as understood thermodynamically. At the end we sketch how aspects of dynamical activity can take over for obtaining an extended Clausius relation.

  16. Density responses and spatial distribution of cotton yield and yield components in jujube (Zizyphus jujube)/cotton (Gossypium hirsutum) agroforestry

    NARCIS (Netherlands)

    Wang, Qi; Han, Shuo; Zhang, Lizhen; Zhang, Dongsheng; Werf, van der Wopke; Evers, Jochem B.; Sun, Hongquan; Su, Zhicheng; Zhang, Siping

    2016-01-01

    Trees are the dominant species in agroforestry systems, profoundly affecting the performance of understory crops. Proximity to trees is a key factor in crop performance, but rather little information is available on the spatial distribution of yield and yield components of crop species under the

  17. On the Conditional Entropy of Wireless Networks

    DEFF Research Database (Denmark)

    Coon, Justin P.; Badiu, Mihai Alin; Gündüz, Deniz

    2018-01-01

    The characterization of topological uncertainty in wireless networks using the formalism of graph entropy has received interest in the spatial networks community. In this paper, we develop lower bounds on the entropy of a wireless network by conditioning on potential network observables. Two...... approaches are considered: 1) conditioning on subgraphs, and 2) conditioning on node positions. The first approach is shown to yield a relatively tight bound on the network entropy. The second yields a loose bound, in general, but it provides insight into the dependence between node positions (modelled using...

  18. The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems

    KAUST Repository

    Di Francesco, M.

    2008-12-08

    We study the long-time asymptotics of reaction-diffusion-type systems that feature a monotone decaying entropy (Lyapunov, free energy) functional. We consider both bounded domains and confining potentials on the whole space for arbitrary space dimensions. Our aim is to derive quantitative expressions for (or estimates of) the rates of convergence towards an (entropy minimizing) equilibrium state in terms of the constants of diffusion and reaction and with respect to conserved quantities. Our method, the so-called entropy approach, seeks to quantify convergence to equilibrium by using functional inequalities, which relate quantitatively the entropy and its dissipation in time. The entropy approach is well suited to nonlinear problems and known to be quite robust with respect to model variations. It has already been widely applied to scalar diffusion-convection equations, and the main goal of this paper is to study its generalization to systems of partial differential equations that contain diffusion and reaction terms and admit fewer conservation laws than the size of the system. In particular, we successfully apply the entropy approach to general linear systems and to a nonlinear example of a reaction-diffusion-convection system arising in solid-state physics as a paradigm for general nonlinear systems. © 2008 The Royal Society.

  19. Temporal and spatial evolution characteristics of disturbance wave in a hypersonic boundary layer due to single-frequency entropy disturbance.

    Science.gov (United States)

    Wang, Zhenqing; Tang, Xiaojun; Lv, Hongqing; Shi, Jianqiang

    2014-01-01

    By using a high-order accurate finite difference scheme, direct numerical simulation of hypersonic flow over an 8° half-wedge-angle blunt wedge under freestream single-frequency entropy disturbance is conducted; the generation and the temporal and spatial nonlinear evolution of boundary layer disturbance waves are investigated. Results show that, under the freestream single-frequency entropy disturbance, the entropy state of boundary layer is changed sharply and the disturbance waves within a certain frequency range are induced in the boundary layer. Furthermore, the amplitudes of disturbance waves in the period phase are larger than that in the response phase and ablation phase and the frequency range in the boundary layer in the period phase is narrower than that in these two phases. In addition, the mode competition, dominant mode transformation, and disturbance energy transfer exist among different modes both in temporal and in spatial evolution. The mode competition changes the characteristics of nonlinear evolution of the unstable waves in the boundary layer. The development of the most unstable mode along streamwise relies more on the motivation of disturbance waves in the upstream than that of other modes on this motivation.

  20. The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems

    KAUST Repository

    Di Francesco, M.; Fellner, K.; Markowich, P. A

    2008-01-01

    and reaction terms and admit fewer conservation laws than the size of the system. In particular, we successfully apply the entropy approach to general linear systems and to a nonlinear example of a reaction-diffusion-convection system arising in solid

  1. Variability of effects of spatial climate data aggregation on regional yield simulation by crop models

    NARCIS (Netherlands)

    Hoffmann, H.; Zhao, G.; Bussel, van L.G.J.

    2015-01-01

    Field-scale crop models are often applied at spatial resolutions coarser than that of the arable field. However, little is known about the response of the models to spatially aggregated climate input data and why these responses can differ across models. Depending on the model, regional yield

  2. Integrating Entropy-Based Naïve Bayes and GIS for Spatial Evaluation of Flood Hazard.

    Science.gov (United States)

    Liu, Rui; Chen, Yun; Wu, Jianping; Gao, Lei; Barrett, Damian; Xu, Tingbao; Li, Xiaojuan; Li, Linyi; Huang, Chang; Yu, Jia

    2017-04-01

    Regional flood risk caused by intensive rainfall under extreme climate conditions has increasingly attracted global attention. Mapping and evaluation of flood hazard are vital parts in flood risk assessment. This study develops an integrated framework for estimating spatial likelihood of flood hazard by coupling weighted naïve Bayes (WNB), geographic information system, and remote sensing. The north part of Fitzroy River Basin in Queensland, Australia, was selected as a case study site. The environmental indices, including extreme rainfall, evapotranspiration, net-water index, soil water retention, elevation, slope, drainage proximity, and density, were generated from spatial data representing climate, soil, vegetation, hydrology, and topography. These indices were weighted using the statistics-based entropy method. The weighted indices were input into the WNB-based model to delineate a regional flood risk map that indicates the likelihood of flood occurrence. The resultant map was validated by the maximum inundation extent extracted from moderate resolution imaging spectroradiometer (MODIS) imagery. The evaluation results, including mapping and evaluation of the distribution of flood hazard, are helpful in guiding flood inundation disaster responses for the region. The novel approach presented consists of weighted grid data, image-based sampling and validation, cell-by-cell probability inferring and spatial mapping. It is superior to an existing spatial naive Bayes (NB) method for regional flood hazard assessment. It can also be extended to other likelihood-related environmental hazard studies. © 2016 Society for Risk Analysis.

  3. The Temporal and Spatial Evolution of Water Yield in Dali County

    Directory of Open Access Journals (Sweden)

    Jing Yu

    2015-05-01

    Full Text Available Water yield is of great importance to the balance between supply and demand of water resources. The provision of freshwater for Dali is estimated and mapped in 1988, 1995, 2000, 2005 and 2008, using the Integrated Valuation of Environmental Services and Tradeoffs (InVEST modeling toolset. The stability of water yield’s spatial variation is analyzed by a sorting method. The factors are explored which lead to the change in the relative water yield capacity. The yields at five points in time are compared, and the result of which shows a sharp fluctuation. The water yield curve is of a similar waveform as precipitation. An obvious and relatively stable spatial variation appears for water yield. The highest water yield areas are mainly located in the area where the elevation is high and both the elevation and the slope changes are large, and the main land uses are Shrub Land and High Coverage Grassland. The lowest areas are mainly in the eastern part of Erhai or the surrounding area. Precipitation, construction land expansion and the implementation of policy on land use are the three main factors which contribute to the change of the relative water yield capacity during 1988–2008 in Dali. In the study area, the water yield appears highly sensitive to the change in precipitation. The elasticity coefficient is calculated to illustrate the sensitivity of the water yield to the precipitation. When the elasticity index is larger, the risk of natural disaster will be higher.

  4. Spatial-temporal variability of leaf chlorophyll and its relationship with cocoa yield

    Directory of Open Access Journals (Sweden)

    Caique C. Medauar

    Full Text Available ABSTRACT The objective of this study was to evaluate the spatial-temporal variability of leaf chlorophyll index and its relationship with cocoa yield. The experiment was carried out in an experimental area of cocoa production located in Ilhéus, Bahia State, Brazil. Leaf chlorophyll content was measured in September, October, January, February, March and April in the 2014/2015 season, at each sampling point of a regular grid by using a portable chlorophyll meter. Under the same conditions, yield was evaluated and the data were submitted to descriptive statistics and a linear correlation study. Geostatistical analysis was used to determine and quantify the spatial and temporal variability of leaf chlorophyll index and yield. Leaf chlorophyll index varied over the period evaluated, but the months of February, March and April showed no spatial dependence in the study area, indicating absence of temporal stability. Cocoa monthly yield, except in January, presented high spatial variability. Under the conditions of this study, it was not possible to establish a relationship between leaf chlorophyll index and cocoa yield.

  5. Improving Estimations of Spatial Distribution of Soil Respiration Using the Bayesian Maximum Entropy Algorithm and Soil Temperature as Auxiliary Data.

    Directory of Open Access Journals (Sweden)

    Junguo Hu

    Full Text Available Soil respiration inherently shows strong spatial variability. It is difficult to obtain an accurate characterization of soil respiration with an insufficient number of monitoring points. However, it is expensive and cumbersome to deploy many sensors. To solve this problem, we proposed employing the Bayesian Maximum Entropy (BME algorithm, using soil temperature as auxiliary information, to study the spatial distribution of soil respiration. The BME algorithm used the soft data (auxiliary information effectively to improve the estimation accuracy of the spatiotemporal distribution of soil respiration. Based on the functional relationship between soil temperature and soil respiration, the BME algorithm satisfactorily integrated soil temperature data into said spatial distribution. As a means of comparison, we also applied the Ordinary Kriging (OK and Co-Kriging (Co-OK methods. The results indicated that the root mean squared errors (RMSEs and absolute values of bias for both Day 1 and Day 2 were the lowest for the BME method, thus demonstrating its higher estimation accuracy. Further, we compared the performance of the BME algorithm coupled with auxiliary information, namely soil temperature data, and the OK method without auxiliary information in the same study area for 9, 21, and 37 sampled points. The results showed that the RMSEs for the BME algorithm (0.972 and 1.193 were less than those for the OK method (1.146 and 1.539 when the number of sampled points was 9 and 37, respectively. This indicates that the former method using auxiliary information could reduce the required number of sampling points for studying spatial distribution of soil respiration. Thus, the BME algorithm, coupled with soil temperature data, can not only improve the accuracy of soil respiration spatial interpolation but can also reduce the number of sampling points.

  6. Improving Estimations of Spatial Distribution of Soil Respiration Using the Bayesian Maximum Entropy Algorithm and Soil Temperature as Auxiliary Data.

    Science.gov (United States)

    Hu, Junguo; Zhou, Jian; Zhou, Guomo; Luo, Yiqi; Xu, Xiaojun; Li, Pingheng; Liang, Junyi

    2016-01-01

    Soil respiration inherently shows strong spatial variability. It is difficult to obtain an accurate characterization of soil respiration with an insufficient number of monitoring points. However, it is expensive and cumbersome to deploy many sensors. To solve this problem, we proposed employing the Bayesian Maximum Entropy (BME) algorithm, using soil temperature as auxiliary information, to study the spatial distribution of soil respiration. The BME algorithm used the soft data (auxiliary information) effectively to improve the estimation accuracy of the spatiotemporal distribution of soil respiration. Based on the functional relationship between soil temperature and soil respiration, the BME algorithm satisfactorily integrated soil temperature data into said spatial distribution. As a means of comparison, we also applied the Ordinary Kriging (OK) and Co-Kriging (Co-OK) methods. The results indicated that the root mean squared errors (RMSEs) and absolute values of bias for both Day 1 and Day 2 were the lowest for the BME method, thus demonstrating its higher estimation accuracy. Further, we compared the performance of the BME algorithm coupled with auxiliary information, namely soil temperature data, and the OK method without auxiliary information in the same study area for 9, 21, and 37 sampled points. The results showed that the RMSEs for the BME algorithm (0.972 and 1.193) were less than those for the OK method (1.146 and 1.539) when the number of sampled points was 9 and 37, respectively. This indicates that the former method using auxiliary information could reduce the required number of sampling points for studying spatial distribution of soil respiration. Thus, the BME algorithm, coupled with soil temperature data, can not only improve the accuracy of soil respiration spatial interpolation but can also reduce the number of sampling points.

  7. Impact of Spatial Soil and Climate Input Data Aggregation on Regional Yield Simulations

    Science.gov (United States)

    Hoffmann, Holger; Zhao, Gang; Asseng, Senthold; Bindi, Marco; Biernath, Christian; Constantin, Julie; Coucheney, Elsa; Dechow, Rene; Doro, Luca; Eckersten, Henrik; Gaiser, Thomas; Grosz, Balázs; Heinlein, Florian; Kassie, Belay T.; Kersebaum, Kurt-Christian; Klein, Christian; Kuhnert, Matthias; Lewan, Elisabet; Moriondo, Marco; Nendel, Claas; Priesack, Eckart; Raynal, Helene; Roggero, Pier P.; Rötter, Reimund P.; Siebert, Stefan; Specka, Xenia; Tao, Fulu; Teixeira, Edmar; Trombi, Giacomo; Wallach, Daniel; Weihermüller, Lutz; Yeluripati, Jagadeesh; Ewert, Frank

    2016-01-01

    We show the error in water-limited yields simulated by crop models which is associated with spatially aggregated soil and climate input data. Crop simulations at large scales (regional, national, continental) frequently use input data of low resolution. Therefore, climate and soil data are often generated via averaging and sampling by area majority. This may bias simulated yields at large scales, varying largely across models. Thus, we evaluated the error associated with spatially aggregated soil and climate data for 14 crop models. Yields of winter wheat and silage maize were simulated under water-limited production conditions. We calculated this error from crop yields simulated at spatial resolutions from 1 to 100 km for the state of North Rhine-Westphalia, Germany. Most models showed yields biased by data. The relative mean absolute error (rMAE) of most models using aggregated soil data was in the range or larger than the inter-annual or inter-model variability in yields. This error increased further when both climate and soil data were aggregated. Distinct error patterns indicate that the rMAE may be estimated from few soil variables. Illustrating the range of these aggregation effects across models, this study is a first step towards an ex-ante assessment of aggregation errors in large-scale simulations. PMID:27055028

  8. Impact of Spatial Soil and Climate Input Data Aggregation on Regional Yield Simulations.

    Science.gov (United States)

    Hoffmann, Holger; Zhao, Gang; Asseng, Senthold; Bindi, Marco; Biernath, Christian; Constantin, Julie; Coucheney, Elsa; Dechow, Rene; Doro, Luca; Eckersten, Henrik; Gaiser, Thomas; Grosz, Balázs; Heinlein, Florian; Kassie, Belay T; Kersebaum, Kurt-Christian; Klein, Christian; Kuhnert, Matthias; Lewan, Elisabet; Moriondo, Marco; Nendel, Claas; Priesack, Eckart; Raynal, Helene; Roggero, Pier P; Rötter, Reimund P; Siebert, Stefan; Specka, Xenia; Tao, Fulu; Teixeira, Edmar; Trombi, Giacomo; Wallach, Daniel; Weihermüller, Lutz; Yeluripati, Jagadeesh; Ewert, Frank

    2016-01-01

    We show the error in water-limited yields simulated by crop models which is associated with spatially aggregated soil and climate input data. Crop simulations at large scales (regional, national, continental) frequently use input data of low resolution. Therefore, climate and soil data are often generated via averaging and sampling by area majority. This may bias simulated yields at large scales, varying largely across models. Thus, we evaluated the error associated with spatially aggregated soil and climate data for 14 crop models. Yields of winter wheat and silage maize were simulated under water-limited production conditions. We calculated this error from crop yields simulated at spatial resolutions from 1 to 100 km for the state of North Rhine-Westphalia, Germany. Most models showed yields biased by <15% when aggregating only soil data. The relative mean absolute error (rMAE) of most models using aggregated soil data was in the range or larger than the inter-annual or inter-model variability in yields. This error increased further when both climate and soil data were aggregated. Distinct error patterns indicate that the rMAE may be estimated from few soil variables. Illustrating the range of these aggregation effects across models, this study is a first step towards an ex-ante assessment of aggregation errors in large-scale simulations.

  9. Impact of Spatial Soil and Climate Input Data Aggregation on Regional Yield Simulations.

    Directory of Open Access Journals (Sweden)

    Holger Hoffmann

    Full Text Available We show the error in water-limited yields simulated by crop models which is associated with spatially aggregated soil and climate input data. Crop simulations at large scales (regional, national, continental frequently use input data of low resolution. Therefore, climate and soil data are often generated via averaging and sampling by area majority. This may bias simulated yields at large scales, varying largely across models. Thus, we evaluated the error associated with spatially aggregated soil and climate data for 14 crop models. Yields of winter wheat and silage maize were simulated under water-limited production conditions. We calculated this error from crop yields simulated at spatial resolutions from 1 to 100 km for the state of North Rhine-Westphalia, Germany. Most models showed yields biased by <15% when aggregating only soil data. The relative mean absolute error (rMAE of most models using aggregated soil data was in the range or larger than the inter-annual or inter-model variability in yields. This error increased further when both climate and soil data were aggregated. Distinct error patterns indicate that the rMAE may be estimated from few soil variables. Illustrating the range of these aggregation effects across models, this study is a first step towards an ex-ante assessment of aggregation errors in large-scale simulations.

  10. Effect of Spatial Arrangement on Growth and Yield of Cowpea in a Cowpea-maize Intercrop

    Directory of Open Access Journals (Sweden)

    Ocaya, CP.

    2001-01-01

    Full Text Available Cowpea growth and yield performance when intercropped with maize was studied for 3 consecutive seasons under three spatial arrangements, i. e., maize planted at 90 x 30, 100 x 27, and 120 x 22.5 cm, with 2 rows of cowpea between the maize rows. Growth and yield of cowpea was improved significantly by widening maize intra-row distances as compared to the 90 x 30 cm spacing. Hence, intercropped cowpea needs to be sown where maize rows are wide apart, but the maize rows should not be too wide as this would lower the grain yield of maize.

  11. Analysis of the spatial variability of crop yield and soil properties in small agricultural plots

    Directory of Open Access Journals (Sweden)

    Vieira Sidney Rosa

    2003-01-01

    Full Text Available The objective of this study was to assess spatial variability of soil properties and crop yield under no tillage as a function of time, in two soil/climate conditions in São Paulo State, Brazil. The two sites measured approximately one hectare each and were cultivated with crop sequences which included corn, soybean, cotton, oats, black oats, wheat, rye, rice and green manure. Soil fertility, soil physical properties and crop yield were measured in a 10-m grid. The soils were a Dusky Red Latossol (Oxisol and a Red Yellow Latossol (Ultisol. Soil sampling was performed in each field every two years after harvesting of the summer crop. Crop yield was measured at the end of each crop cycle, in 2 x 2.5 m sub plots. Data were analysed using semivariogram analysis and kriging interpolation for contour map generation. Yield maps were constructed in order to visually compare the variability of yields, the variability of the yield components and related soil properties. The results show that the factors affecting the variability of crop yield varies from one crop to another. The changes in yield from one year to another suggest that the causes of variability may change with time. The changes with time for the cross semivariogram between phosphorus in leaves and soybean yield is another evidence of this result.

  12. Satellite-based studies of maize yield spatial variations and their causes in China

    Science.gov (United States)

    Zhao, Y.

    2013-12-01

    Maize production in China has been expanding significantly in the past two decades, but yield has become relatively stagnant in the past few years, and needs to be improved to meet increasing demand. Multiple studies found that the gap between potential and actual yield of maize is as large as 40% to 60% of yield potential. Although a few major causes of yield gap have been qualitatively identified with surveys, there has not been spatial analysis aimed at quantifying relative importance of specific biophysical and socio-economic causes, information which would be useful for targeting interventions. This study analyzes the causes of yield variation at field and village level in Quzhou county of North China Plain (NCP). We combine remote sensing and crop modeling to estimate yields in 2009-2012, and identify fields that are consistently high or low yielding. To establish the relationship between yield and potential factors, we gather data on those factors through a household survey. We select targeted survey fields such that not only both extremes of yield distribution but also all soil texture categories in the county is covered. Our survey assesses management and biophysical factors as well as social factors such as farmers' access to agronomic knowledge, which is approximated by distance to the closest demonstration plot or 'Science and technology backyard'. Our survey covers 10 townships, 53 villages and 180 fields. Three to ten farmers are surveyed depending on the amount of variation present among sub pixels of each field. According to survey results, we extract the amount of variation within as well as between villages and or soil type. The higher within village or within field variation, the higher importance of management factors. Factors such as soil type and access to knowledge are more represented by between village variation. Through regression and analysis of variance, we gain more quantitative and thorough understanding of causes to yield variation at

  13. Spatial distribution of the chemical properties of the soil and of soybean yield in the field

    Directory of Open Access Journals (Sweden)

    Alexandre Gazolla-Neto

    2016-06-01

    Full Text Available ABSTRACT The aim of this study was to evaluate the spatial dependence between chemical properties of the soil and yield components in the soybean using precision farming techniques. Samples of the soil and plants were taken from georeferenced points to determine the chemical properties of the soil and the yield components. The results were submitted to Pearson correlation analysis, descriptive statistics and geostatistics. The coefficient of variation showed a wide range of distribution for the chemical attributes of the soil, with the highest indices being found for the levels of available phosphorus (102% and potassium (72.65%. Soil pH and organic matter showed a coefficient of variation of 5.96 and 15.93% respectively. Semivariogram analysis of the yield components (productivity, 1,000-seed weight and number of seeds and the chemical properties of the soil (organic matter, pH, phosphorus, potassium, calcium, magnesium, boron, manganese and zinc fitted the spherical model with moderate spatial dependence, with values ranging from 200 to 700 m. Spatial distribution by means of map interpolation was efficient in evaluating spatial variability, allowing the identification and quantification of regions of low and high productivity in the production area, together with the distribution of soil attributes and their respective levels of availability to the soybean plants.

  14. STRUCTURE, SPATIAL DISTRIBUTION AND SEED YIELD FOR ANDIROBA (Carapa guianensis Aubl. IN SOUTH RORAIMA

    Directory of Open Access Journals (Sweden)

    Helio Tonini

    2009-10-01

    Full Text Available Andiroba is one of the Amazon species with great potential of exploration for timber and non-timber forest products (NFTPs. This work was carried out with the objective of studying the population structure, spatial distribution and seed yield in a native forest of andiroba in the south of Roraima state. A permanent sample plot of 300 x 300 m (9 ha was installed and all the trees with DBH equal or superior to 10 cm were identified, mapped and measured. In each tree, the light climate, crown form and lianas load were appraised. To identify the spatial distribution, the medium variance/average rate and the Morisita’s Index were used. The seed yield data were obtained by the seed weighing, being 145 trees monitored during 2006. The population presented a diametric distribution of the j inverted type, and a seed yield of 65,4 kg.ha-1 with average of 8,3 kg.tree-1 was observed. DBH ≥ 30 cm was considered as borderline for commercial seed yield, allowing stratifying the population in juveniles (DBH ≤ 30 cm and adults (DBH > 30 cm. The spatial distribution analysis showed that adult individuals presented random distribution and the juveniles tendency of grouping.

  15. Effect of Spatial Arrangement on Growth and Yield of Cowpea in a Cowpea-maize Intercrop

    OpenAIRE

    Ocaya, CP.; Adipala, E.; Osiru, DSO.

    2001-01-01

    Cowpea growth and yield performance when intercropped with maize was studied for 3 consecutive seasons under three spatial arrangements, i. e., maize planted at 90 x 30, 100 x 27, and 120 x 22.5 cm, with 2 rows of cowpea between the maize rows. Growth and yield of cowpea was improved significantly by widening maize intra-row distances as compared to the 90 x 30 cm spacing. Hence, intercropped cowpea needs to be sown where maize rows are wide apart, but the maize rows should not be too wide as...

  16. A New Scrambling Evaluation Scheme Based on Spatial Distribution Entropy and Centroid Difference of Bit-Plane

    Science.gov (United States)

    Zhao, Liang; Adhikari, Avishek; Sakurai, Kouichi

    Watermarking is one of the most effective techniques for copyright protection and information hiding. It can be applied in many fields of our society. Nowadays, some image scrambling schemes are used as one part of the watermarking algorithm to enhance the security. Therefore, how to select an image scrambling scheme and what kind of the image scrambling scheme may be used for watermarking are the key problems. Evaluation method of the image scrambling schemes can be seen as a useful test tool for showing the property or flaw of the image scrambling method. In this paper, a new scrambling evaluation system based on spatial distribution entropy and centroid difference of bit-plane is presented to obtain the scrambling degree of image scrambling schemes. Our scheme is illustrated and justified through computer simulations. The experimental results show (in Figs. 6 and 7) that for the general gray-scale image, the evaluation degree of the corresponding cipher image for the first 4 significant bit-planes selection is nearly the same as that for the 8 bit-planes selection. That is why, instead of taking 8 bit-planes of a gray-scale image, it is sufficient to take only the first 4 significant bit-planes for the experiment to find the scrambling degree. This 50% reduction in the computational cost makes our scheme efficient.

  17. [Spatial-temporal variations of spring maize potential yields in a changing climate in Northeast China.

    Science.gov (United States)

    Liu, Zhi Juan; Yang, Xiao Guang; Lyu, Shuo; Wang, Jing; Lin, Xiao Mao

    2018-01-01

    Based on meteorological data, agro-meteorological observations, and agricultural statistical data in Northeast China (NEC), by using the validated Agricultural Production System sIMulator (APSIM-maize), the potential, attainable, potential farmers' and actual farmers' yields of spring maize during the period 1961 to 2015 were analyzed, and the effects of climate variation on maize potential yield in NEC were quantified. Results indicated that the potential yield of spring maize was 12.2 t·hm -2 during the period 1961 to 2015, with those in northeast being lower than southwest within the study region. The attainable yield of spring maize was 11.3 t·hm -2 , and showed a similar spatial distribution with potential yield. Under the current farmers' management practices, mean simulated potential and actual farmers' yields were 6.5 and 4.5 t·hm -2 , respectively. Assuming there were no changes in cultivars and management practices in NEC, the mean potential, attainable, and potential farmers' yields of spring maize would decrease by 0.34, 0.25 and 0.10 t·hm -2 per decade in NEC. However, the actual farmers' yields increased with the value of 1.27 t·hm -2 per decade averaged over NEC. Due to climate variation, year-to-year variations of spring maize potential, attainable, and potential farmers' yields were significant, ranging from 10.0 to 14.4, 9.8 to 13.3, 4.4 to 8.5 t·hm -2 , respectively.

  18. STRUCTURE, SPATIAL DISTRIBUTION AND SEED YIELD FOR ANDIROBA (Carapa guianensis Aubl. IN SOUTH RORAIMA

    Directory of Open Access Journals (Sweden)

    Ademir R. Ruschel

    2009-09-01

    Full Text Available Andiroba is one of the Amazon species with great potential of exploration for timber and non-timberforest products (NFTPs. This work was carried out with the objective of studying the population structure,spatial distribution and seed yield in a native forest of andiroba in the south of Roraima state. A permanentsample plot of 300 x 300 m (9 ha was installed and all the trees with DBH equal or superior to 10 cm wereidentified, mapped and measured. In each tree, the light climate, crown form and lianas load were appraised.To identify the spatial distribution, the medium variance/average rate and the Morisita’s Index were used.The seed yield data were obtained by the seed weighing, being 145 trees monitored during 2006. Thepopulation presented a diametric distribution of the j inverted type, and a seed yield of 65,4 kg.ha-1 withaverage of 8,3 kg.tree-1 was observed. DBH ≥ 30 cm was considered as borderline for commercial seed yield,allowing stratifying the population in juveniles (DBH ≤ 30 cm and adults (DBH > 30 cm. The spatialdistribution analysis showed that adult individuals presented random distribution and the juveniles tendencyof grouping.

  19. Simulating maize yield and bomass with spatial variability of soil field capacity

    Science.gov (United States)

    Ma, Liwang; Ahuja, Lajpat; Trout, Thomas; Nolan, Bernard T.; Malone, Robert W.

    2015-01-01

    Spatial variability in field soil properties is a challenge for system modelers who use single representative values, such as means, for model inputs, rather than their distributions. In this study, the root zone water quality model (RZWQM2) was first calibrated for 4 yr of maize (Zea mays L.) data at six irrigation levels in northern Colorado and then used to study spatial variability of soil field capacity (FC) estimated in 96 plots on maize yield and biomass. The best results were obtained when the crop parameters were fitted along with FCs, with a root mean squared error (RMSE) of 354 kg ha–1 for yield and 1202 kg ha–1 for biomass. When running the model using each of the 96 sets of field-estimated FC values, instead of calibrating FCs, the average simulated yield and biomass from the 96 runs were close to measured values with a RMSE of 376 kg ha–1 for yield and 1504 kg ha–1 for biomass. When an average of the 96 FC values for each soil layer was used, simulated yield and biomass were also acceptable with a RMSE of 438 kg ha–1 for yield and 1627 kg ha–1 for biomass. Therefore, when there are large numbers of FC measurements, an average value might be sufficient for model inputs. However, when the ranges of FC measurements were known for each soil layer, a sampled distribution of FCs using the Latin hypercube sampling (LHS) might be used for model inputs.

  20. More dimensions: Less entropy

    International Nuclear Information System (INIS)

    Kolb, E.W.; Lindley, D.; Seckel, D.

    1984-01-01

    For a cosmological model with d noncompact and D compact spatial dimensions and symmetry R 1 x S/sup d/ x S/sup D/, we calculate the entropy produced in d dimensions due to the compactification of D dimensions and show it too small to be of cosmological interest. Although insufficient entropy is produced in the model we study, the contraction of extra dimensions does lead to entropy production. We discuss modifications of our assumptions, including changing our condition for decoupling of the extra dimensions, which may lead to a large entropy production and change our conclusions

  1. Interannual and spatial variability of maple syrup yield as related to climatic factors

    Science.gov (United States)

    Houle, Daniel

    2014-01-01

    Sugar maple syrup production is an important economic activity for eastern Canada and the northeastern United States. Since annual variations in syrup yield have been related to climate, there are concerns about the impacts of climatic change on the industry in the upcoming decades. Although the temporal variability of syrup yield has been studied for specific sites on different time scales or for large regions, a model capable of accounting for both temporal and regional differences in yield is still lacking. In the present study, we studied the factors responsible for interregional and interannual variability in maple syrup yield over the 2001–2012 period, by combining the data from 8 Quebec regions (Canada) and 10 U.S. states. The resulting model explained 44.5% of the variability in yield. It includes the effect of climatic conditions that precede the sapflow season (variables from the previous growing season and winter), the effect of climatic conditions during the current sapflow season, and terms accounting for intercountry and temporal variability. Optimal conditions for maple syrup production appear to be spatially restricted by less favourable climate conditions occurring during the growing season in the north, and in the south, by the warmer winter and earlier spring conditions. This suggests that climate change may favor maple syrup production northwards, while southern regions are more likely to be negatively affected by adverse spring conditions. PMID:24949244

  2. Modelling spatial and temporal variations of annual suspended sediment yields from small agricultural catchments.

    Science.gov (United States)

    Rymszewicz, A; Bruen, M; O'Sullivan, J J; Turner, J N; Lawler, D M; Harrington, J R; Conroy, E; Kelly-Quinn, M

    2018-04-01

    Estimates of sediment yield are important for ecological and geomorphological assessment of fluvial systems and for assessment of soil erosion within a catchment. Many regulatory frameworks, such as the Convention for the Protection of the Marine Environment of the North-East Atlantic, derived from the Oslo and Paris Commissions (OSPAR) require reporting of annual sediment fluxes. While they may be measured in large rivers, sediment flux is rarely measured in smaller rivers. Measurements of sediment transport at a national scale can be also challenging and therefore, sediment yield models are often utilised by water resource managers for the predictions of sediment yields in the ungauged catchments. Regression based models, calibrated to field measurements, can offer an advantage over complex and computational models due to their simplicity, easy access to input data and due to the additional insights into factors controlling sediment export in the study sites. While traditionally calibrated to long-term average values of sediment yields such predictions cannot represent temporal variations. This study addresses this issue in a novel way by taking account of the variation from year to year in hydrological variables in the developed models (using annual mean runoff, annual mean flow, flows exceeded in five percentage of the time (Q5) and seasonal rainfall estimated separately for each year of observations). Other parameters included in the models represent spatial differences influenced by factors such as soil properties (% poorly drained soils and % peaty soils), land-use (% pasture or % arable lands), channel slope (S1085) and drainage network properties (drainage density). Catchment descriptors together with year-specific hydrological variables can explain both spatial differences and inter-annual variability of suspended sediment yields. The methodology is demonstrated by deriving equations from Irish data-sets (compiled in this study) with the best model

  3. Improved Satellite-based Crop Yield Mapping by Spatially Explicit Parameterization of Crop Phenology

    Science.gov (United States)

    Jin, Z.; Azzari, G.; Lobell, D. B.

    2016-12-01

    Field-scale mapping of crop yields with satellite data often relies on the use of crop simulation models. However, these approaches can be hampered by inaccuracies in the simulation of crop phenology. Here we present and test an approach to use dense time series of Landsat 7 and 8 acquisitions data to calibrate various parameters related to crop phenology simulation, such as leaf number and leaf appearance rates. These parameters are then mapped across the Midwestern United States for maize and soybean, and for two different simulation models. We then implement our recently developed Scalable satellite-based Crop Yield Mapper (SCYM) with simulations reflecting the improved phenology parameterizations, and compare to prior estimates based on default phenology routines. Our preliminary results show that the proposed method can effectively alleviate the underestimation of early-season LAI by the default Agricultural Production Systems sIMulator (APSIM), and that spatially explicit parameterization for the phenology model substantially improves the SCYM performance in capturing the spatiotemporal variation in maize and soybean yield. The scheme presented in our study thus preserves the scalability of SCYM, while significantly reducing its uncertainty.

  4. Adjoint entropy vs topological entropy

    OpenAIRE

    Giordano Bruno, Anna

    2012-01-01

    Recently the adjoint algebraic entropy of endomorphisms of abelian groups was introduced and studied. We generalize the notion of adjoint entropy to continuous endomorphisms of topological abelian groups. Indeed, the adjoint algebraic entropy is defined using the family of all finite-index subgroups, while we take only the subfamily of all open finite-index subgroups to define the topological adjoint entropy. This allows us to compare the (topological) adjoint entropy with the known topologic...

  5. Solution of the spatial neutral model yields new bounds on the Amazonian species richness

    Science.gov (United States)

    Shem-Tov, Yahav; Danino, Matan; Shnerb, Nadav M.

    2017-02-01

    Neutral models, in which individual agents with equal fitness undergo a birth-death-mutation process, are very popular in population genetics and community ecology. Usually these models are applied to populations and communities with spatial structure, but the analytic results presented so far are limited to well-mixed or mainland-island scenarios. Here we combine analytic results and numerics to obtain an approximate solution for the species abundance distribution and the species richness for the neutral model on continuous landscape. We show how the regional diversity increases when the recruitment length decreases and the spatial segregation of species grows. Our results are supported by extensive numerical simulations and allow one to probe the numerically inaccessible regime of large-scale systems with extremely small mutation/speciation rates. Model predictions are compared with the findings of recent large-scale surveys of tropical trees across the Amazon basin, yielding new bounds for the species richness (between 13100 and 15000) and the number of singleton species (between 455 and 690).

  6. A Spatially Distributed Conceptual Model for Estimating Suspended Sediment Yield in Alpine catchments

    Science.gov (United States)

    Costa, Anna; Molnar, Peter; Anghileri, Daniela

    2017-04-01

    Suspended sediment is associated with nutrient and contaminant transport in water courses. Estimating suspended sediment load is relevant for water-quality assessment, recreational activities, reservoir sedimentation issues, and ecological habitat assessment. Suspended sediment concentration (SSC) along channels is usually reproduced by suspended sediment rating curves, which relate SSC to discharge with a power law equation. Large uncertainty characterizes rating curves based only on discharge, because sediment supply is not explicitly accounted for. The aim of this work is to develop a source-oriented formulation of suspended sediment dynamics and to estimate suspended sediment yield at the outlet of a large Alpine catchment (upper Rhône basin, Switzerland). We propose a novel modelling approach for suspended sediment which accounts for sediment supply by taking into account the variety of sediment sources in an Alpine environment, i.e. the spatial location of sediment sources (e.g. distance from the outlet and lithology) and the different processes of sediment production and transport (e.g. by rainfall, overland flow, snowmelt). Four main sediment sources, typical of Alpine environments, are included in our model: glacial erosion, hillslope erosion, channel erosion and erosion by mass wasting processes. The predictive model is based on gridded datasets of precipitation and air temperature which drive spatially distributed degree-day models to simulate snowmelt and ice-melt, and determine erosive rainfall. A mass balance at the grid scale determines daily runoff. Each cell belongs to a different sediment source (e.g. hillslope, channel, glacier cell). The amount of sediment entrained and transported in suspension is simulated through non-linear functions of runoff, specific for sediment production and transport processes occurring at the grid scale (e.g. rainfall erosion, snowmelt-driven overland flow). Erodibility factors identify different lithological units

  7. Nonsymmetric entropy and maximum nonsymmetric entropy principle

    International Nuclear Information System (INIS)

    Liu Chengshi

    2009-01-01

    Under the frame of a statistical model, the concept of nonsymmetric entropy which generalizes the concepts of Boltzmann's entropy and Shannon's entropy, is defined. Maximum nonsymmetric entropy principle is proved. Some important distribution laws such as power law, can be derived from this principle naturally. Especially, nonsymmetric entropy is more convenient than other entropy such as Tsallis's entropy in deriving power laws.

  8. Symplectic entropy

    International Nuclear Information System (INIS)

    De Nicola, Sergio; Fedele, Renato; Man'ko, Margarita A; Man'ko, Vladimir I

    2007-01-01

    The tomographic-probability description of quantum states is reviewed. The symplectic tomography of quantum states with continuous variables is studied. The symplectic entropy of the states with continuous variables is discussed and its relation to Shannon entropy and information is elucidated. The known entropic uncertainty relations of the probability distribution in position and momentum of a particle are extended and new uncertainty relations for symplectic entropy are obtained. The partial case of symplectic entropy, which is optical entropy of quantum states, is considered. The entropy associated to optical tomogram is shown to satisfy the new entropic uncertainty relation. The example of Gaussian states of harmonic oscillator is studied and the entropic uncertainty relations for optical tomograms of the Gaussian state are shown to minimize the uncertainty relation

  9. Entropy and transverse section reconstruction

    International Nuclear Information System (INIS)

    Gullberg, G.T.

    1976-01-01

    A new approach to the reconstruction of a transverse section using projection data from multiple views incorporates the concept of maximum entropy. The principle of maximizing information entropy embodies the assurance of minimizing bias or prejudice in the reconstruction. Using maximum entropy is a necessary condition for the reconstructed image. This entropy criterion is most appropriate for 3-D reconstruction of objects from projections where the system is underdetermined or the data are limited statistically. This is the case in nuclear medicine time limitations in patient studies do not yield sufficient projections

  10. Multi-approach assessment of the spatial distribution of the specific yield: application to the Crau plain aquifer, France

    Science.gov (United States)

    Seraphin, Pierre; Gonçalvès, Julio; Vallet-Coulomb, Christine; Champollion, Cédric

    2018-03-01

    Spatially distributed values of the specific yield, a fundamental parameter for transient groundwater mass balance calculations, were obtained by means of three independent methods for the Crau plain, France. In contrast to its traditional use to assess recharge based on a given specific yield, the water-table fluctuation (WTF) method, applied using major recharging events, gave a first set of reference values. Then, large infiltration processes recorded by monitored boreholes and caused by major precipitation events were interpreted in terms of specific yield by means of a one-dimensional vertical numerical model solving Richards' equations within the unsaturated zone. Finally, two gravity field campaigns, at low and high piezometric levels, were carried out to assess the groundwater mass variation and thus alternative specific yield values. The range obtained by the WTF method for this aquifer made of alluvial detrital material was 2.9- 26%, in line with the scarce data available so far. The average spatial value of specific yield by the WTF method (9.1%) is consistent with the aquifer scale value from the hydro-gravimetric approach. In this investigation, an estimate of the hitherto unknown spatial distribution of the specific yield over the Crau plain was obtained using the most reliable method (the WTF method). A groundwater mass balance calculation over the domain using this distribution yielded similar results to an independent quantification based on a stable isotope-mixing model. This agreement reinforces the relevance of such estimates, which can be used to build a more accurate transient hydrogeological model.

  11. Spatial Rice Yield Estimation Based on MODIS and Sentinel-1 SAR Data and ORYZA Crop Growth Model

    Directory of Open Access Journals (Sweden)

    Tri D. Setiyono

    2018-02-01

    Full Text Available Crop insurance is a viable solution to reduce the vulnerability of smallholder farmers to risks from pest and disease outbreaks, extreme weather events, and market shocks that threaten their household food and income security. In developing and emerging countries, the implementation of area yield-based insurance, the form of crop insurance preferred by clients and industry, is constrained by the limited availability of detailed historical yield records. Remote-sensing technology can help to fill this gap by providing an unbiased and replicable source of the needed data. This study is dedicated to demonstrating and validating the methodology of remote sensing and crop growth model-based rice yield estimation with the intention of historical yield data generation for application in crop insurance. The developed system combines MODIS and SAR-based remote-sensing data to generate spatially explicit inputs for rice using a crop growth model. MODIS reflectance data were used to generate multitemporal LAI maps using the inverted Radiative Transfer Model (RTM. SAR data were used to generate rice area maps using MAPScape-RICE to mask LAI map products for further processing, including smoothing with logistic function and running yield simulation using the ORYZA crop growth model facilitated by the Rice Yield Estimation System (Rice-YES. Results from this study indicate that the approach of assimilating MODIS and SAR data into a crop growth model can generate well-adjusted yield estimates that adequately describe spatial yield distribution in the study area while reliably replicating official yield data with root mean square error, RMSE, of 0.30 and 0.46 t ha−1 (normalized root mean square error, NRMSE of 5% and 8% for the 2016 spring and summer seasons, respectively, in the Red River Delta of Vietnam, as evaluated at district level aggregation. The information from remote-sensing technology was also useful for identifying geographic locations with

  12. Simple, spatial and predictive approach for cereal yield prediction in the semi-arid areas

    Science.gov (United States)

    Toumi, Jihad; Khabba, Said; Er-Raki, Salah; Le page, Michel; Chahbi Bellakanji, Aicha; Lili Chabaane, Zohra; Ezzahar, Jamal; Zribi, Mehrez; Jarlan, Lionel

    2016-04-01

    The objective is to develop a simple, spatial and predictive approach of dry matter (DM) and grain yield (GY) of cereal in the semi-arid areas. The proposed method is based on the three efficiencies model of Monteith (1972). This approach summarizes the transformation of solar radiation to the dry matter (DM) by the climate (ɛc), interception (ɛi) and conversion (ɛconv) efficiencies. The method combines the maximum of ɛi and ɛconv (noted ɛimax and ɛconvmax) into a single parameter denoted ɛmax, calculating as a function of cumulating growing degree day (CGDD). Also, the stress coefficient ks, which affects the conversion of solar radiation to the biomass was calculated by the surface temperature or the water balance at the root zone. In addition, the expression of ks has been improved by the consideration of the results achieved by deficit irrigation (AquaCrop and STICS models) which showed that the value of ks from 0.7 to 1 didn't affect significantly the cereal production. For the partitioning of the dry matter developed, between straw and grain, the method proposed calculates a variable Harvest Index coefficient (HI). HI is deducted from CGDD and HI0max (maximal final harvest Index in the region of study). Finally, the approach calculates DM depending Satellite Information (NDVI and surface temperature Ts) and climatic data (solar radiation and air temperature). In the case of no availability of Ts, the amount of irrigation is required to calculate ks. Until now, the developed model has been calibrated and validated on the irrigated area R3, located 40 Km east of Marrakech. The evolutions of DM and GY were reproduced satisfactorily. R2 and RMSE are respectively 0.98 and 0.35 t/ha and 0.98 and 0.19 t/ha, respectively. Currently, additional tests are in progress on data relating to the Kairouan plain of Tunisia.

  13. Spatial resolution of precipitation and radiation: the effect on regional crop yield forecasts

    NARCIS (Netherlands)

    Wit, de A.J.W.; Boogaard, H.L.; Diepen, van C.A.

    2005-01-01

    This paper explores the effect of uncertainty in precipitation and radiation on crop simulation results at local (50 × 50 km grids) and regional scale (NUTS1 regions) and on the crop yield forecasts for Germany and France. Two experiments were carried out where crop yields for winter-wheat and grain

  14. Estimating the spatial distribution of soil moisture based on Bayesian maximum entropy method with auxiliary data from remote sensing

    Science.gov (United States)

    Gao, Shengguo; Zhu, Zhongli; Liu, Shaomin; Jin, Rui; Yang, Guangchao; Tan, Lei

    2014-10-01

    Soil moisture (SM) plays a fundamental role in the land-atmosphere exchange process. Spatial estimation based on multi in situ (network) data is a critical way to understand the spatial structure and variation of land surface soil moisture. Theoretically, integrating densely sampled auxiliary data spatially correlated with soil moisture into the procedure of spatial estimation can improve its accuracy. In this study, we present a novel approach to estimate the spatial pattern of soil moisture by using the BME method based on wireless sensor network data and auxiliary information from ASTER (Terra) land surface temperature measurements. For comparison, three traditional geostatistic methods were also applied: ordinary kriging (OK), which used the wireless sensor network data only, regression kriging (RK) and ordinary co-kriging (Co-OK) which both integrated the ASTER land surface temperature as a covariate. In Co-OK, LST was linearly contained in the estimator, in RK, estimator is expressed as the sum of the regression estimate and the kriged estimate of the spatially correlated residual, but in BME, the ASTER land surface temperature was first retrieved as soil moisture based on the linear regression, then, the t-distributed prediction interval (PI) of soil moisture was estimated and used as soft data in probability form. The results indicate that all three methods provide reasonable estimations. Co-OK, RK and BME can provide a more accurate spatial estimation by integrating the auxiliary information Compared to OK. RK and BME shows more obvious improvement compared to Co-OK, and even BME can perform slightly better than RK. The inherent issue of spatial estimation (overestimation in the range of low values and underestimation in the range of high values) can also be further improved in both RK and BME. We can conclude that integrating auxiliary data into spatial estimation can indeed improve the accuracy, BME and RK take better advantage of the auxiliary

  15. A novel segmentation method for uneven lighting image with noise injection based on non-local spatial information and intuitionistic fuzzy entropy

    Science.gov (United States)

    Yu, Haiyan; Fan, Jiulun

    2017-12-01

    Local thresholding methods for uneven lighting image segmentation always have the limitations that they are very sensitive to noise injection and that the performance relies largely upon the choice of the initial window size. This paper proposes a novel algorithm for segmenting uneven lighting images with strong noise injection based on non-local spatial information and intuitionistic fuzzy theory. We regard an image as a gray wave in three-dimensional space, which is composed of many peaks and troughs, and these peaks and troughs can divide the image into many local sub-regions in different directions. Our algorithm computes the relative characteristic of each pixel located in the corresponding sub-region based on fuzzy membership function and uses it to replace its absolute characteristic (its gray level) to reduce the influence of uneven light on image segmentation. At the same time, the non-local adaptive spatial constraints of pixels are introduced to avoid noise interference with the search of local sub-regions and the computation of local characteristics. Moreover, edge information is also taken into account to avoid false peak and trough labeling. Finally, a global method based on intuitionistic fuzzy entropy is employed on the wave transformation image to obtain the segmented result. Experiments on several test images show that the proposed method has excellent capability of decreasing the influence of uneven illumination on images and noise injection and behaves more robustly than several classical global and local thresholding methods.

  16. Spatiotemporal Scaling Effect on Rainfall Network Design Using Entropy

    Directory of Open Access Journals (Sweden)

    Chiang Wei

    2014-08-01

    Full Text Available Because of high variation in mountainous areas, rainfall data at different spatiotemporal scales may yield potential uncertainty for network design. However, few studies focus on the scaling effect on both the spatial and the temporal scale. By calculating the maximum joint entropy of hourly typhoon events, monthly, six dry and wet months and annual rainfall between 1992 and 2012 for 1-, 3-, and 5-km grids, the relocated candidate rain gauges in the National Taiwan University Experimental Forest of Central Taiwan are prioritized. The results show: (1 the network exhibits different locations for first prioritized candidate rain gauges for different spatiotemporal scales; (2 the effect of spatial scales is insignificant compared to temporal scales; and (3 a smaller number and a lower percentage of required stations (PRS reach stable joint entropy for a long duration at finer spatial scale. Prioritized candidate rain gauges provide key reference points for adjusting the network to capture more accurate information and minimize redundancy.

  17. Analysis of complex time series using refined composite multiscale entropy

    International Nuclear Information System (INIS)

    Wu, Shuen-De; Wu, Chiu-Wen; Lin, Shiou-Gwo; Lee, Kung-Yen; Peng, Chung-Kang

    2014-01-01

    Multiscale entropy (MSE) is an effective algorithm for measuring the complexity of a time series that has been applied in many fields successfully. However, MSE may yield an inaccurate estimation of entropy or induce undefined entropy because the coarse-graining procedure reduces the length of a time series considerably at large scales. Composite multiscale entropy (CMSE) was recently proposed to improve the accuracy of MSE, but it does not resolve undefined entropy. Here we propose a refined composite multiscale entropy (RCMSE) to improve CMSE. For short time series analyses, we demonstrate that RCMSE increases the accuracy of entropy estimation and reduces the probability of inducing undefined entropy.

  18. Effect of spatial arrangement and density on weed infestation and yield of maize (zea mays l.)

    International Nuclear Information System (INIS)

    Saeed, M.; Huang, Z.; Huang, H.; Wei, S.

    2016-01-01

    Field experiments were conducted during summer season 2012 and consequently repeated in 2013 to assess the efficacy of row and plant spacing on weed infestation and yield of maize crop. The experiments were carried out in Randomized Complete Block (RCB) design with split plot arrangements. Three row spacings i.e. 60, 75 and 90 cm were assigned to main plots while different plant spacings i.e. 10, 15, 20, 25 and 30 cm were allotted to subplots, respectively. The results showed that for both the years narrow row and plant spacing effectively suppressed weeds while wider row and plant spacing resulted in higher weed density. The data showed that the maximum weed density (202.07 and 218.70 m-2) was recorded in 90 cm row spacing in 2012 and 2013, respectively. However, among plant spacing highest weed density of 214.89 m-2 and 219.83 m-2 was recorded in 30 cm plant spacing during 2012 and 2013, respectively. The data regarding biological yield showed maximum biological yield in 60 cm row spacing while among plant spacing the highest biological yield was resulted in narrow plant spacing of 10 cm during both years. Furthermore, highest grain yield of 4928.9 kg ha-1 in 2012 and 5063.9 kg ha-1 in 2013 was recorded in 75 cm row spacing while lowest grain yield of 3026 kg ha-1 in 2012 and 3989 kg ha-1 in 2013 was observed for 90 cm row spacing. Among plant spacing highest grain yield of 4474.8 kg ha-1 and 5228.5 kg ha-1 was recorded in 15 cm plant spacing whereas lowest grain yield of 3554 kg ha-1 and 4010.6 kg ha-1 was observed for 30 cm row spacing in 2012 and 2013, respectively. The regression analysis also showed highest grain yield form 15-20 cm plant spacing during both years. Similarly the correlation data showed that with increase in weed density the grain yield decreases accordingly. The two years of research showed that narrow spacing (15-20 x 75 cm) enhanced the competitive ability of maize crop and suppressed weed growth. (author)

  19. Investigating dynamical complexity in the magnetosphere using various entropy measures

    Science.gov (United States)

    Balasis, Georgios; Daglis, Ioannis A.; Papadimitriou, Constantinos; Kalimeri, Maria; Anastasiadis, Anastasios; Eftaxias, Konstantinos

    2009-09-01

    The complex system of the Earth's magnetosphere corresponds to an open spatially extended nonequilibrium (input-output) dynamical system. The nonextensive Tsallis entropy has been recently introduced as an appropriate information measure to investigate dynamical complexity in the magnetosphere. The method has been employed for analyzing Dst time series and gave promising results, detecting the complexity dissimilarity among different physiological and pathological magnetospheric states (i.e., prestorm activity and intense magnetic storms, respectively). This paper explores the applicability and effectiveness of a variety of computable entropy measures (e.g., block entropy, Kolmogorov entropy, T complexity, and approximate entropy) to the investigation of dynamical complexity in the magnetosphere. We show that as the magnetic storm approaches there is clear evidence of significant lower complexity in the magnetosphere. The observed higher degree of organization of the system agrees with that inferred previously, from an independent linear fractal spectral analysis based on wavelet transforms. This convergence between nonlinear and linear analyses provides a more reliable detection of the transition from the quiet time to the storm time magnetosphere, thus showing evidence that the occurrence of an intense magnetic storm is imminent. More precisely, we claim that our results suggest an important principle: significant complexity decrease and accession of persistency in Dst time series can be confirmed as the magnetic storm approaches, which can be used as diagnostic tools for the magnetospheric injury (global instability). Overall, approximate entropy and Tsallis entropy yield superior results for detecting dynamical complexity changes in the magnetosphere in comparison to the other entropy measures presented herein. Ultimately, the analysis tools developed in the course of this study for the treatment of Dst index can provide convenience for space weather

  20. Entropy maximization

    Indian Academy of Sciences (India)

    Abstract. It is shown that (i) every probability density is the unique maximizer of relative entropy in an appropriate class and (ii) in the class of all pdf f that satisfy. ∫ fhi dμ = λi for i = 1, 2,...,...k the maximizer of entropy is an f0 that is pro- portional to exp(. ∑ ci hi ) for some choice of ci . An extension of this to a continuum of.

  1. Entropy Maximization

    Indian Academy of Sciences (India)

    It is shown that (i) every probability density is the unique maximizer of relative entropy in an appropriate class and (ii) in the class of all pdf that satisfy ∫ f h i d = i for i = 1 , 2 , … , … k the maximizer of entropy is an f 0 that is proportional to exp ⁡ ( ∑ c i h i ) for some choice of c i . An extension of this to a continuum of ...

  2. Entropy? Honest!

    Directory of Open Access Journals (Sweden)

    Tommaso Toffoli

    2016-06-01

    Full Text Available Here we deconstruct, and then in a reasoned way reconstruct, the concept of “entropy of a system”, paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a count associated with a description; this count (traditionally expressed in logarithmic form for a number of good reasons is in essence the number of possibilities—specific instances or “scenarios”—that match that description. Very natural (and virtually inescapable generalizations of the idea of description are the probability distribution and its quantum mechanical counterpart, the density operator. We track the process of dynamically updating entropy as a system evolves. Three factors may cause entropy to change: (1 the system’s internal dynamics; (2 unsolicited external influences on it; and (3 the approximations one has to make when one tries to predict the system’s future state. The latter task is usually hampered by hard-to-quantify aspects of the original description, limited data storage and processing resource, and possibly algorithmic inadequacy. Factors 2 and 3 introduce randomness—often huge amounts of it—into one’s predictions and accordingly degrade them. When forecasting, as long as the entropy bookkeping is conducted in an honest fashion, this degradation will always lead to an entropy increase. To clarify the above point we introduce the notion of honest entropy, which coalesces much of what is of course already done, often tacitly, in responsible entropy-bookkeping practice. This notion—we believe—will help to fill an expressivity gap in scientific discourse. With its help, we shall prove that any dynamical system—not just our physical universe—strictly obeys Clausius’s original formulation of the second law of thermodynamics if and only if it is invertible. Thus this law is a tautological property of invertible systems!

  3. Multivariate refined composite multiscale entropy analysis

    International Nuclear Information System (INIS)

    Humeau-Heurtier, Anne

    2016-01-01

    Multiscale entropy (MSE) has become a prevailing method to quantify signals complexity. MSE relies on sample entropy. However, MSE may yield imprecise complexity estimation at large scales, because sample entropy does not give precise estimation of entropy when short signals are processed. A refined composite multiscale entropy (RCMSE) has therefore recently been proposed. Nevertheless, RCMSE is for univariate signals only. The simultaneous analysis of multi-channel (multivariate) data often over-performs studies based on univariate signals. We therefore introduce an extension of RCMSE to multivariate data. Applications of multivariate RCMSE to simulated processes reveal its better performances over the standard multivariate MSE. - Highlights: • Multiscale entropy quantifies data complexity but may be inaccurate at large scale. • A refined composite multiscale entropy (RCMSE) has therefore recently been proposed. • Nevertheless, RCMSE is adapted to univariate time series only. • We herein introduce an extension of RCMSE to multivariate data. • It shows better performances than the standard multivariate multiscale entropy.

  4. Analysis of factors which limited the spatial variation of barley yield on the forest-steppe chernozems of Kursk region

    Science.gov (United States)

    Belik, Anton; Vasenev, Ivan; Jablonskikh, Lidia; Bozhko, Svetlana

    2017-04-01

    The crop yield is the most important indicator of the efficiency of agricultural production. It is the function that depends on a large number of groups of independent variables, such as the weather, soil fertility and overall culture agriculture. A huge number of combinations of these factors contribute to the formation of high spatial variety of crop yields within small areas, includes the slope agrolandscapes in Kursk region. Spatial variety of yield leads to a significant reduction in the efficiency of agriculture. In this connection, evaluation and analysis of the factors, which limits the yield of field crops is a very urgent proble in agroecology. The research was conducted in the period of 2003-2004 on a representative field. The typical and leached chernozems with the varying thickness and of erosion degree are dominated in soil cover. At the time of field research studied areas were busy by barley. The reseached soils have an average and increased fertility level. Chernozem typical full-face, and the leached contain an average of 4.5-6% humus, close to neutral pH, favorable values of physico-chemical parameters, medium and high content of nutrients. The eroded chernozems differs agrogenic marked declining in fertility parameters. The diversity of meso- and micro-relief in the fields and soil cover influence to significant spatial variety of fertility. For example the content of nutrients in the soil variation can be up to 5-fold level. High spatial heterogeneity of soils fertility ifluence to barley yield variety. During research on the productivity of the field varied in the range of 20-43 c/ha, and 7-44 c/ha (2004). Analysis of the factors, which limited the yield of barley, showed that the first priorities occupy unregulated characterises: slope angle and the classification of soils (subtype and race of chernozem and the difference in the degree of erosion), which determines the development of erosion processes and redistribution available to plants

  5. Simulated optimization of crop yield through irrigation system design and operation based on the spatial variability of soil hydrodynamic properties

    International Nuclear Information System (INIS)

    Gurovich, L.; Stern, J.; Ramos, R.

    1983-01-01

    Spatial autocorrelation and kriging techniques were applied to soil infiltrability data from a 20 hectare field, to separate homogeneous irrigation units. Border irrigation systems were designed for each unit and combinations of units by using DESIGN, a computer model based on soil infiltrability and hydraulics of surface water flow, which enables optimal irrigation systems to be designed. Water depths effectively infiltrated at different points along the irrigation run were determined, and the agronomic irrigation efficiency of the unit evaluated. A modification of Hanks' evapotranspiration model, PLANTGRO, was used to evaluate plant growth, relative crop yield and soil-water economy throughout the growing season, at several points along each irrigation unit. The effect of different irrigation designs on total field yield and total water used for irrigation was evaluated by integrating yield values corresponding to each point, volume and inflow time during each irrigation. For relevant data from winter wheat grown in the central area of Chile during 1981, simulation by an interactive and sequentially recurrent use of DESIGN and PLANTGRO models, was carried out. The results obtained indicate that, when a field is separated into homogeneous irrigation units on the basis of the spatial variability of soil infiltrability and the border irrigation systems are designed according to soil characteristics, both a significant yield increase and less water use can be obtained by comparison with other criteria of field zonification for irrigation management. The use of neutrometric determinations to assess soil-water content during the growing season, as a validation of the results obtained in this work, is discussed. (author)

  6. Spatial distribution of overland flow and sediment yield in semi-arid rangelands

    International Nuclear Information System (INIS)

    Sarah, P.; Lavee, H.

    2009-01-01

    Feedbacks and mutual links exist among soil, vegetation and water; they enable co-evolution of these features within eco-geomorphic systems, These relations are fragile, especially in semi-arid areas where grazing is the main land use. The simples subdivision of the surface of many semi-arid rangelands is into a two-component mosaic pattern comprising shrub patches interspersed with open spaces, with the former acting s skinks for water and other resources, and the latter as sources. However close observations in areas under grazing in the northern Negev region of Israel suggested that the spatial patterns of surface components is more complicated, and that the open space between shrubs consists of two components: herbaceous areas, separated by trampling routes that support no vegetation. (Author)

  7. Dynamic Cross-Entropy.

    Science.gov (United States)

    Aur, Dorian; Vila-Rodriguez, Fidel

    2017-01-01

    Complexity measures for time series have been used in many applications to quantify the regularity of one dimensional time series, however many dynamical systems are spatially distributed multidimensional systems. We introduced Dynamic Cross-Entropy (DCE) a novel multidimensional complexity measure that quantifies the degree of regularity of EEG signals in selected frequency bands. Time series generated by discrete logistic equations with varying control parameter r are used to test DCE measures. Sliding window DCE analyses are able to reveal specific period doubling bifurcations that lead to chaos. A similar behavior can be observed in seizures triggered by electroconvulsive therapy (ECT). Sample entropy data show the level of signal complexity in different phases of the ictal ECT. The transition to irregular activity is preceded by the occurrence of cyclic regular behavior. A significant increase of DCE values in successive order from high frequencies in gamma to low frequencies in delta band reveals several phase transitions into less ordered states, possible chaos in the human brain. To our knowledge there are no reliable techniques able to reveal the transition to chaos in case of multidimensional times series. In addition, DCE based on sample entropy appears to be robust to EEG artifacts compared to DCE based on Shannon entropy. The applied technique may offer new approaches to better understand nonlinear brain activity. Copyright © 2016 Elsevier B.V. All rights reserved.

  8. Upper entropy axioms and lower entropy axioms

    International Nuclear Information System (INIS)

    Guo, Jin-Li; Suo, Qi

    2015-01-01

    The paper suggests the concepts of an upper entropy and a lower entropy. We propose a new axiomatic definition, namely, upper entropy axioms, inspired by axioms of metric spaces, and also formulate lower entropy axioms. We also develop weak upper entropy axioms and weak lower entropy axioms. Their conditions are weaker than those of Shannon–Khinchin axioms and Tsallis axioms, while these conditions are stronger than those of the axiomatics based on the first three Shannon–Khinchin axioms. The subadditivity and strong subadditivity of entropy are obtained in the new axiomatics. Tsallis statistics is a special case of satisfying our axioms. Moreover, different forms of information measures, such as Shannon entropy, Daroczy entropy, Tsallis entropy and other entropies, can be unified under the same axiomatics

  9. Spatially distinct response of rice yield to autonomous adaptation under the CMIP5 multi-model projections

    Science.gov (United States)

    Shin, Yonghee; Lee, Eun-Jeong; Im, Eun-Soon; Jung, Il-Won

    2017-02-01

    Rice ( Oryza sativa L.) is a very important staple crop, as it feeds more than half of the world's population. Numerous studies have focused on the negative impacts of climate change on rice production. However, there is little debate on which region of the world is more vulnerable to climate change and how adaptation to this change can mitigate the negative impacts on rice production. We investigated the impacts of climate change on rice yield, based on simulations combining a global crop model, M-GAZE, and Coupled Model Intercomparison Project Phase 5 (CMIP5) multi-model projections. Our focus was the impact of mitigating emission forcings (representative concentration pathway RCP 4.5 vs. RCP 8.5) and autonomous adaptation (i.e., changing crop variety and planting date) on rice yield. In general, our results showed that climate change due to anthropogenic warming leads to a significant reduction in rice yield. However, autonomous adaptation provides the potential to reduce the negative impact of global warming on rice yields in a spatially distinct manner. The adaptation was less beneficial for countries located at a low latitude (e.g., Cambodia, Thailand, Brazil) compared to mid-latitude countries (e.g., USA, China, Pakistan), as regional climates at the lower latitudes are already near the upper temperature thresholds for acceptable rice growth. These findings suggest that the socioeconomic effects from rice production in lowlatitude countries can be highly vulnerable to anthropogenic global warming. Therefore, these countries need to be accountable to develop transformative adaptation strategies, such as adopting (or developing) heat-tolerant varieties, and/or improve irrigation systems and fertilizer use efficiency.

  10. Impacts of ozone air pollution and temperature extremes on crop yields: Spatial variability, adaptation and implications for future food security

    Science.gov (United States)

    Tai, Amos P. K.; Val Martin, Maria

    2017-11-01

    Ozone air pollution and climate change pose major threats to global crop production, with ramifications for future food security. Previous studies of ozone and warming impacts on crops typically do not account for the strong ozone-temperature correlation when interpreting crop-ozone or crop-temperature relationships, or the spatial variability of crop-to-ozone sensitivity arising from varietal and environmental differences, leading to potential biases in their estimated crop losses. Here we develop an empirical model, called the partial derivative-linear regression (PDLR) model, to estimate the spatial variations in the sensitivities of wheat, maize and soybean yields to ozone exposures and temperature extremes in the US and Europe using a composite of multidecadal datasets, fully correcting for ozone-temperature covariation. We find generally larger and more spatially varying sensitivities of all three crops to ozone exposures than are implied by experimentally derived concentration-response functions used in most previous studies. Stronger ozone tolerance is found in regions with high ozone levels and high consumptive crop water use, reflecting the existence of spatial adaptation and effect of water constraints. The spatially varying sensitivities to temperature extremes also indicate stronger heat tolerance in crops grown in warmer regions. The spatial adaptation of crops to ozone and temperature we find can serve as a surrogate for future adaptation. Using the PDLR-derived sensitivities and 2000-2050 ozone and temperature projections by the Community Earth System Model, we estimate that future warming and unmitigated ozone pollution can combine to cause an average decline in US wheat, maize and soybean production by 13%, 43% and 28%, respectively, and a smaller decline for European crops. Aggressive ozone regulation is shown to offset such decline to various extents, especially for wheat. Our findings demonstrate the importance of considering ozone regulation

  11. Temporal and Spatial Variation of Water Yield Modulus in the Yangtze River Basin in Recent 60 Years

    Science.gov (United States)

    Shi, Xiaoqing; Weng, Baisha; Qin, Tianling

    2018-01-01

    The Yangtze River Basin is the largest river basin of Asia and the third largest river basin of the world, the gross water resources amount ranks first in the river basins of the country, and it occupies an important position in the national water resources strategic layout. Under the influence of climate change and human activities, the water cycle has changed. The temporal and spatial distribution of precipitation in the basin is more uneven and the floods are frequent. In order to explore the water yield condition in the Yangtze River Basin, we selected the Water Yield Modulus (WYM) as the evaluation index, then analyzed the temporal and spatial evolution characteristics of the WYM in the Yangtze River Basin by using the climate tendency method and the M-K trend test method. The results showed that the average WYM of the Yangtze River Basin in 1956-2015 are between 103,600 and 1,262,900 m3/km2, with an average value of 562,300 m3/km2, which is greater than the national average value of 295,000 m3/km2. The minimum value appeared in the northwestern part of the Tongtian River district, the maximum value appeared in the northeastern of Dongting Lake district. The rate of change in 1956-2015 is between -0.68/a and 0.79/a, it showed a downward trend in the western part but not significantly, an upward trend in the eastern part reached a significance level of α=0.01. The minimum value appeared in the Tongtian River district, the largest value appeared in the Hangjia Lake district, and the average tendency rate is 0.04/a in the whole basin.

  12. On the Conditional Entropy of Wireless Networks

    DEFF Research Database (Denmark)

    Coon, Justin P.; Badiu, Mihai Alin; Gündüz, Deniz

    2018-01-01

    The characterization of topological uncertainty in wireless networks using the formalism of graph entropy has received interest in the spatial networks community. In this paper, we develop lower bounds on the entropy of a wireless network by conditioning on potential network observables. Two appr...... a homogeneous binomial point process in this work) and the network topology....

  13. Spatial variability of forage yield and soil physical attributes of a Brachiaria decumbens pasture in the Brazilian Cerrado

    Directory of Open Access Journals (Sweden)

    Cristiano Magalhães Pariz

    2011-10-01

    Full Text Available The objective of this study was to analyze variability, linear and spatial correlations of forage dry mass yield (FDM and dry matter percentage (DM% of Brachiaria decumbens with the bulk density (BD, gravimetric (GM and volumetric (VM moisture, mechanical resistance to penetration (RP and organic matter content (OM, at depths 1 (0-0.10 m and 2 (0.10-0.20 m, in a Red Latosol (Oxisol, in order to select an indicator of soil physical quality and identify possible causes of pasture degradation. The geostatistical grid was installed to collect soil and plant data, with 121 sampling points, over an area of 2.56 ha. The linear correlation between FDM × DM% and FDM × BD2 was low, but highly significant. Spatial correlations varied inversely and positively, respectively. Except for DM% and BD, at both depths, the other attributes showed average to high variability, indicating a heterogeneous environment. Thus, geostatistics emerges as an important tool in understanding the interactions in pasture ecosystems, in order to minimize possible causes of degradation and indicate better alternatives for soil-plant-animal management. The decrease in FDM and increased BD1 are indicators of physical degradation (compaction of Red Latosol (Oxisol, particularly in the places with the highest concentration of animals and excessive trampling, in Cerrado conditions, in the municipality of Selvíria, Mato Grosso do Sul State, Brazil.

  14. Entropy of the system formed in heavy ion collision

    International Nuclear Information System (INIS)

    Gudima, K.K.; Schulz, H.; Toneev, V.D.

    1985-01-01

    In frames of a cascade model the entropy evolution in a system producted in heavy ion collisions is investigated. Entropy calculation is based on smoothing of the distribution function over the momentum space by the temperature field introduction. The resulting entropy per one nucleon is shown to be rather sensitive to phase space subdivision into cells at the stage of free scattering of reaction products. Compared to recent experimental results for specific entropy values inferred from the composite particle yield of 4π measurements, it is found that cascade calculations do not favour some particular entropy model treatments and suggest smaller entropy values than following from consideration within equilibrium statistics

  15. Excess Entropy and Diffusivity

    Indian Academy of Sciences (India)

    First page Back Continue Last page Graphics. Excess Entropy and Diffusivity. Excess entropy scaling of diffusivity (Rosenfeld,1977). Analogous relationships also exist for viscosity and thermal conductivity.

  16. A Theoretical Basis for Entropy-Scaling Effects in Human Mobility Patterns.

    Science.gov (United States)

    Osgood, Nathaniel D; Paul, Tuhin; Stanley, Kevin G; Qian, Weicheng

    2016-01-01

    Characterizing how people move through space has been an important component of many disciplines. With the advent of automated data collection through GPS and other location sensing systems, researchers have the opportunity to examine human mobility at spatio-temporal resolution heretofore impossible. However, the copious and complex data collected through these logging systems can be difficult for humans to fully exploit, leading many researchers to propose novel metrics for encapsulating movement patterns in succinct and useful ways. A particularly salient proposed metric is the mobility entropy rate of the string representing the sequence of locations visited by an individual. However, mobility entropy rate is not scale invariant: entropy rate calculations based on measurements of the same trajectory at varying spatial or temporal granularity do not yield the same value, limiting the utility of mobility entropy rate as a metric by confounding inter-experimental comparisons. In this paper, we derive a scaling relationship for mobility entropy rate of non-repeating straight line paths from the definition of Lempel-Ziv compression. We show that the resulting formulation predicts the scaling behavior of simulated mobility traces, and provides an upper bound on mobility entropy rate under certain assumptions. We further show that this formulation has a maximum value for a particular sampling rate, implying that optimal sampling rates for particular movement patterns exist.

  17. Explaining the entropy concept and entropy components

    Directory of Open Access Journals (Sweden)

    Marko Popovic

    2018-04-01

    Full Text Available Total entropy of a thermodynamic system consists of two components: thermal entropy due to energy, and residual entropy due to molecular orientation. In this article, a three-step method for explaining entropy is suggested. Step one is to use a classical method to introduce thermal entropy STM as a function of temperature T and heat capacity at constant pressure Cp: STM = ∫(Cp/T dT. Thermal entropy is the entropy due to uncertainty in motion of molecules and vanishes at absolute zero (zero-point energy state. It is also the measure of useless thermal energy that cannot be converted into useful work. The next step is to introduce residual entropy S0 as a function of the number of molecules N and the number of distinct orientations available to them in a crystal m: S0 = N kB ln m, where kB is the Boltzmann constant. Residual entropy quantifies the uncertainty in molecular orientation. Residual entropy, unlike thermal entropy, is independent of temperature and remains present at absolute zero. The third step is to show that thermal entropy and residual entropy add up to the total entropy of a thermodynamic system S: S = S0 + STM. This method of explanation should result in a better comprehension of residual entropy and thermal entropy, as well as of their similarities and differences. The new method was tested in teaching at Faculty of Chemistry University of Belgrade, Serbia. The results of the test show that the new method has a potential to improve the quality of teaching.

  18. Text mining by Tsallis entropy

    Science.gov (United States)

    Jamaati, Maryam; Mehri, Ali

    2018-01-01

    Long-range correlations between the elements of natural languages enable them to convey very complex information. Complex structure of human language, as a manifestation of natural languages, motivates us to apply nonextensive statistical mechanics in text mining. Tsallis entropy appropriately ranks the terms' relevance to document subject, taking advantage of their spatial correlation length. We apply this statistical concept as a new powerful word ranking metric in order to extract keywords of a single document. We carry out an experimental evaluation, which shows capability of the presented method in keyword extraction. We find that, Tsallis entropy has reliable word ranking performance, at the same level of the best previous ranking methods.

  19. Maximum Entropy in Drug Discovery

    Directory of Open Access Journals (Sweden)

    Chih-Yuan Tseng

    2014-07-01

    Full Text Available Drug discovery applies multidisciplinary approaches either experimentally, computationally or both ways to identify lead compounds to treat various diseases. While conventional approaches have yielded many US Food and Drug Administration (FDA-approved drugs, researchers continue investigating and designing better approaches to increase the success rate in the discovery process. In this article, we provide an overview of the current strategies and point out where and how the method of maximum entropy has been introduced in this area. The maximum entropy principle has its root in thermodynamics, yet since Jaynes’ pioneering work in the 1950s, the maximum entropy principle has not only been used as a physics law, but also as a reasoning tool that allows us to process information in hand with the least bias. Its applicability in various disciplines has been abundantly demonstrated. We give several examples of applications of maximum entropy in different stages of drug discovery. Finally, we discuss a promising new direction in drug discovery that is likely to hinge on the ways of utilizing maximum entropy.

  20. The maximum entropy production and maximum Shannon information entropy in enzyme kinetics

    Science.gov (United States)

    Dobovišek, Andrej; Markovič, Rene; Brumen, Milan; Fajmut, Aleš

    2018-04-01

    We demonstrate that the maximum entropy production principle (MEPP) serves as a physical selection principle for the description of the most probable non-equilibrium steady states in simple enzymatic reactions. A theoretical approach is developed, which enables maximization of the density of entropy production with respect to the enzyme rate constants for the enzyme reaction in a steady state. Mass and Gibbs free energy conservations are considered as optimization constraints. In such a way computed optimal enzyme rate constants in a steady state yield also the most uniform probability distribution of the enzyme states. This accounts for the maximal Shannon information entropy. By means of the stability analysis it is also demonstrated that maximal density of entropy production in that enzyme reaction requires flexible enzyme structure, which enables rapid transitions between different enzyme states. These results are supported by an example, in which density of entropy production and Shannon information entropy are numerically maximized for the enzyme Glucose Isomerase.

  1. The pigeon's discrimination of visual entropy: a logarithmic function.

    Science.gov (United States)

    Young, Michael E; Wasserman, Edward A

    2002-11-01

    We taught 8 pigeons to discriminate 16-icon arrays that differed in their visual variability or "entropy" to see whether the relationship between entropy and discriminative behavior is linear (in which equivalent differences in entropy should produce equivalent changes in behavior) or logarithmic (in which higher entropy values should be less discriminable from one another than lower entropy values). Pigeons received a go/no-go task in which the lower entropy arrays were reinforced for one group and the higher entropy arrays were reinforced for a second group. The superior discrimination of the second group was predicted by a theoretical analysis in which excitatory and inhibitory stimulus generalization gradients fall along a logarithmic, but not a linear scale. Reanalysis of previously published data also yielded results consistent with a logarithmic relationship between entropy and discriminative behavior.

  2. Combined Spectral and Spatial Modeling of Corn Yield Based on Aerial Images and Crop Surface Models Acquired with an Unmanned Aircraft System

    Directory of Open Access Journals (Sweden)

    Jakob Geipel

    2014-10-01

    Full Text Available Precision Farming (PF management strategies are commonly based on estimations of within-field yield potential, often derived from remotely-sensed products, e.g., Vegetation Index (VI maps. These well-established means, however, lack important information, like crop height. Combinations of VI-maps and detailed 3D Crop Surface Models (CSMs enable advanced methods for crop yield prediction. This work utilizes an Unmanned Aircraft System (UAS to capture standard RGB imagery datasets for corn grain yield prediction at three early- to mid-season growth stages. The imagery is processed into simple VI-orthoimages for crop/non-crop classification and 3D CSMs for crop height determination at different spatial resolutions. Three linear regression models are tested on their prediction ability using site-specific (i unclassified mean heights, (ii crop-classified mean heights and (iii a combination of crop-classified mean heights with according crop coverages. The models show determination coefficients \\({R}^{2}\\ of up to 0.74, whereas model (iii performs best with imagery captured at the end of stem elongation and intermediate spatial resolution (0.04m\\(\\cdot\\px\\(^{-1}\\.Following these results, combined spectral and spatial modeling, based on aerial images and CSMs, proves to be a suitable method for mid-season corn yield prediction.

  3. Gravitational entropies in LTB dust models

    International Nuclear Information System (INIS)

    Sussman, Roberto A; Larena, Julien

    2014-01-01

    We consider generic Lemaître–Tolman–Bondi (LTB) dust models to probe the gravitational entropy proposals of Clifton, Ellis and Tavakol (CET) and of Hosoya and Buchert (HB). We also consider a variant of the HB proposal based on a suitable quasi-local scalar weighted average. We show that the conditions for entropy growth for all proposals are directly related to a negative correlation of similar fluctuations of the energy density and Hubble scalar. While this correlation is evaluated locally for the CET proposal, it must be evaluated in a non-local domain dependent manner for the two HB proposals. By looking at the fulfilment of these conditions at the relevant asymptotic limits we are able to provide a well grounded qualitative description of the full time evolution and radial asymptotic scaling of the three entropies in generic models. The following rigorous analytic results are obtained for the three proposals: (i) entropy grows when the density growing mode is dominant, (ii) all ever-expanding hyperbolic models reach a stable terminal equilibrium characterized by an inhomogeneous entropy maximum in their late time evolution; (iii) regions with decaying modes and collapsing elliptic models exhibit unstable equilibria associated with an entropy minimum (iv) near singularities the CET entropy diverges while the HB entropies converge; (v) the CET entropy converges for all models in the radial asymptotic range, whereas the HB entropies only converge for models asymptotic to a Friedmann–Lemaître–Robertson–Walker background. The fact that different independent proposals yield fairly similar conditions for entropy production, time evolution and radial scaling in generic LTB models seems to suggest that their common notion of a ‘gravitational entropy’ may be a theoretically robust concept applicable to more general spacetimes. (paper)

  4. Quantum dynamical entropy revisited

    International Nuclear Information System (INIS)

    Hudetz, T.

    1996-10-01

    We define a new quantum dynamical entropy, which is a 'hybrid' of the closely related, physically oriented entropy introduced by Alicki and Fannes in 1994, and of the mathematically well-developed, single-argument entropy introduced by Connes, Narnhofer and Thirring in 1987. We show that this new quantum dynamical entropy has many properties similar to the ones of the Alicki-Fannes entropy, and also inherits some additional properties from the CNT entropy. In particular, the 'hybrid' entropy interpolates between the two different ways in which both the AF and the CNT entropy of the shift automorphism on the quantum spin chain agree with the usual quantum entropy density, resulting in even better agreement. Also, the new quantum dynamical entropy generalizes the classical dynamical entropy of Kolmogorov and Sinai in the same way as does the AF entropy. Finally, we estimate the 'hybrid' entropy both for the Powers-Price shift systems and for the noncommutative Arnold map on the irrational rotation C * -algebra, leaving some interesting open problems. (author)

  5. ENTROPY - OUR BEST FRIEND

    Directory of Open Access Journals (Sweden)

    Urban Kordes

    2005-10-01

    Full Text Available The paper tries to tackle the question of connection between entropy and the living. Definitions of life as the phenomenon that defies entropy are overviewed and the conclusion is reached that life is in a way dependant on entropy - it couldn't exist without it. Entropy is a sort of medium, a fertile soil, that gives life possibility to blossom. Paper ends with presenting some consequences for the field of artificial intelligence.

  6. Entropy of Baker's Transformation

    Institute of Scientific and Technical Information of China (English)

    栾长福

    2003-01-01

    Four theorems about four different kinds of entropies for Baker's transformation are presented. The Kolmogorov entropy of Baker's transformation is sensitive to the initial flips by the time. The topological entropy of Baker's transformation is found to be log k. The conditions for the state of Baker's transformation to be forbidden are also derived. The relations among the Shanonn, Kolmogorov, topological and Boltzmann entropies are discussed in details.

  7. Physical entropy, information entropy and their evolution equations

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    Inspired by the evolution equation of nonequilibrium statistical physics entropy and the concise statistical formula of the entropy production rate, we develop a theory of the dynamic information entropy and build a nonlinear evolution equation of the information entropy density changing in time and state variable space. Its mathematical form and physical meaning are similar to the evolution equation of the physical entropy: The time rate of change of information entropy density originates together from drift, diffusion and production. The concise statistical formula of information entropy production rate is similar to that of physical entropy also. Furthermore, we study the similarity and difference between physical entropy and information entropy and the possible unification of the two statistical entropies, and discuss the relationship among the principle of entropy increase, the principle of equilibrium maximum entropy and the principle of maximum information entropy as well as the connection between them and the entropy evolution equation.

  8. Entropy generation of nanofluid flow in a microchannel heat sink

    Science.gov (United States)

    Manay, Eyuphan; Akyürek, Eda Feyza; Sahin, Bayram

    2018-06-01

    Present study aims to investigate the effects of the presence of nano sized TiO2 particles in the base fluid on entropy generation rate in a microchannel heat sink. Pure water was chosen as base fluid, and TiO2 particles were suspended into the pure water in five different particle volume fractions of 0.25%, 0.5%, 1.0%, 1.5% and 2.0%. Under laminar, steady state flow and constant heat flux boundary conditions, thermal, frictional, total entropy generation rates and entropy generation number ratios of nanofluids were experimentally analyzed in microchannel flow for different channel heights of 200 μm, 300 μm, 400 μm and 500 μm. It was observed that frictional and total entropy generation rates increased as thermal entropy generation rate were decreasing with an increase in particle volume fraction. In microchannel flows, thermal entropy generation could be neglected due to its too low rate smaller than 1.10e-07 in total entropy generation. Higher channel heights caused higher thermal entropy generation rates, and increasing channel height yielded an increase from 30% to 52% in thermal entropy generation. When channel height decreased, an increase of 66%-98% in frictional entropy generation was obtained. Adding TiO2 nanoparticles into the base fluid caused thermal entropy generation to decrease about 1.8%-32.4%, frictional entropy generation to increase about 3.3%-21.6%.

  9. Entropy: Order or Information

    Science.gov (United States)

    Ben-Naim, Arieh

    2011-01-01

    Changes in entropy can "sometimes" be interpreted in terms of changes in disorder. On the other hand, changes in entropy can "always" be interpreted in terms of changes in Shannon's measure of information. Mixing and demixing processes are used to highlight the pitfalls in the association of entropy with disorder. (Contains 3 figures.)

  10. Entropy of uremia and dialysis technology.

    Science.gov (United States)

    Ronco, Claudio

    2013-01-01

    The second law of thermodynamics applies with local exceptions to patient history and therapy interventions. Living things preserve their low level of entropy throughout time because they receive energy from their surroundings in the form of food. They gain their order at the expense of disordering the nutrients they consume. Death is the thermodynamically favored state: it represents a large increase in entropy as molecular structure yields to chaos. The kidney is an organ dissipating large amounts of energy to maintain the level of entropy of the organism as low as possible. Diseases, and in particular uremia, represent conditions of rapid increase in entropy. Therapeutic strategies are oriented towards a reduction in entropy or at least a decrease in the speed of entropy increase. Uremia is a process accelerating the trend towards randomness and disorder (increase in entropy). Dialysis is a factor external to the patient that tends to reduce the level of entropy caused by kidney disease. Since entropy can only increase in closed systems, energy and work must be spent to limit the entropy of uremia. This energy should be adapted to the system (patient) and be specifically oriented and personalized. This includes a multidimensional effort to achieve an adequate dialysis that goes beyond small molecular weight solute clearance. It includes a biological plan for recovery of homeostasis and a strategy towards long-term rehabilitation of the patient. Such objectives can be achieved with a combination of technology and innovation to answer specific questions that are still present after 60 years of dialysis history. This change in the individual bioentropy may represent a local exception to natural trends as the patient could be considered an isolated universe responding to the classic laws of thermodynamics. Copyright © 2013 S. Karger AG, Basel.

  11. Quantum chaos: entropy signatures

    International Nuclear Information System (INIS)

    Miller, P.A.; Sarkar, S.; Zarum, R.

    1998-01-01

    A definition of quantum chaos is given in terms of entropy production rates for a quantum system coupled weakly to a reservoir. This allows the treatment of classical and quantum chaos on the same footing. In the quantum theory the entropy considered is the von Neumann entropy and in classical systems it is the Gibbs entropy. The rate of change of the coarse-grained Gibbs entropy of the classical system with time is given by the Kolmogorov-Sinai (KS) entropy. The relation between KS entropy and the rate of change of von Neumann entropy is investigated for the kicked rotator. For a system which is classically chaotic there is a linear relationship between these two entropies. Moreover it is possible to construct contour plots for the local KS entropy and compare it with the corresponding plots for the rate of change of von Neumann entropy. The quantitative and qualitative similarities of these plots are discussed for the standard map (kicked rotor) and the generalised cat maps. (author)

  12. Entropy and information

    CERN Document Server

    Volkenstein, Mikhail V

    2009-01-01

    The book "Entropy and Information" deals with the thermodynamical concept of entropy and its relationship to information theory. It is successful in explaining the universality of the term "Entropy" not only as a physical phenomenon, but reveals its existence also in other domains. E.g., Volkenstein discusses the "meaning" of entropy in a biological context and shows how entropy is related to artistic activities. Written by the renowned Russian bio-physicist Mikhail V. Volkenstein, this book on "Entropy and Information" surely serves as a timely introduction to understand entropy from a thermodynamic perspective and is definitely an inspiring and thought-provoking book that should be read by every physicist, information-theorist, biologist, and even artist.

  13. Spatial and harvesting influence on growth, yield, quality and economic potential of Kalmegh (Andrographis paniculata Wall Ex. Nees

    Directory of Open Access Journals (Sweden)

    Sanjeev Kumar

    2013-08-01

    Full Text Available Andrographis paniculata, commonly known as Kalmegh, is used both in Ayurvedic and Unani system of medicines because of its immunological, antibacterial and hepatoprotective properties. This study was carried out to investigate the influence of four harvesting times (120,135,150 days after planting and at seed maturity and four planting distances (30×15, 30×10, 20×15 and 20×10 cm on growth, dry herbage biomass, seed yield and quality traits of Andrographis paniculata at CCS Haryana Agricultural University, Hisar, India in the two years 2005 and 2006. The treatments were laid out in a split plot design with three replications. The maximum values for dry herbage biomass yield (5.14 t ha^(-1, net returns (760.00 EUR ha^(-1, B:C ratio (2.59, andrographolide content (2.63% and total yield (135.00 kg ha^(-1 were detected 135 days after planting with an optimum planting distance of 30×15 cm. However, the maximum iron content was estimated 120 days after planting. The highest dry herbage (4.58 t ha^(-1 and maximum seed yield (19.7 kg ha^(-1 were registered at plants that were lined out with a distance of 20×10 cm.

  14. RNA Thermodynamic Structural Entropy.

    Science.gov (United States)

    Garcia-Martin, Juan Antonio; Clote, Peter

    2015-01-01

    Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe the first two accurate and efficient algorithms to compute the conformational entropy for RNA secondary structures, with respect to the Turner energy model, where free energy parameters are determined from UV absorption experiments. An algorithm to compute the derivational entropy for RNA secondary structures had previously been introduced, using stochastic context free grammars (SCFGs). However, the numerical value of derivational entropy depends heavily on the chosen context free grammar and on the training set used to estimate rule probabilities. Using data from the Rfam database, we determine that both of our thermodynamic methods, which agree in numerical value, are substantially faster than the SCFG method. Thermodynamic structural entropy is much smaller than derivational entropy, and the correlation between length-normalized thermodynamic entropy and derivational entropy is moderately weak to poor. In applications, we plot the structural entropy as a function of temperature for known thermoswitches, such as the repression of heat shock gene expression (ROSE) element, we determine that the correlation between hammerhead ribozyme cleavage activity and total free energy is improved by including an additional free energy term arising from conformational entropy, and we plot the structural entropy of windows of the HIV-1 genome. Our software RNAentropy can compute structural entropy for any user-specified temperature, and supports both the Turner'99 and Turner'04 energy parameters. It follows that RNAentropy is state-of-the-art software to compute RNA secondary structure conformational entropy. Source code is available at https://github.com/clotelab/RNAentropy/; a full web server is available at http

  15. RNA Thermodynamic Structural Entropy.

    Directory of Open Access Journals (Sweden)

    Juan Antonio Garcia-Martin

    Full Text Available Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe the first two accurate and efficient algorithms to compute the conformational entropy for RNA secondary structures, with respect to the Turner energy model, where free energy parameters are determined from UV absorption experiments. An algorithm to compute the derivational entropy for RNA secondary structures had previously been introduced, using stochastic context free grammars (SCFGs. However, the numerical value of derivational entropy depends heavily on the chosen context free grammar and on the training set used to estimate rule probabilities. Using data from the Rfam database, we determine that both of our thermodynamic methods, which agree in numerical value, are substantially faster than the SCFG method. Thermodynamic structural entropy is much smaller than derivational entropy, and the correlation between length-normalized thermodynamic entropy and derivational entropy is moderately weak to poor. In applications, we plot the structural entropy as a function of temperature for known thermoswitches, such as the repression of heat shock gene expression (ROSE element, we determine that the correlation between hammerhead ribozyme cleavage activity and total free energy is improved by including an additional free energy term arising from conformational entropy, and we plot the structural entropy of windows of the HIV-1 genome. Our software RNAentropy can compute structural entropy for any user-specified temperature, and supports both the Turner'99 and Turner'04 energy parameters. It follows that RNAentropy is state-of-the-art software to compute RNA secondary structure conformational entropy. Source code is available at https://github.com/clotelab/RNAentropy/; a full web server is available at http

  16. Spatially-explicit modeling of multi-scale drivers of aboveground forest biomass and water yield in watersheds of the Southeastern United States.

    Science.gov (United States)

    Ajaz Ahmed, Mukhtar Ahmed; Abd-Elrahman, Amr; Escobedo, Francisco J; Cropper, Wendell P; Martin, Timothy A; Timilsina, Nilesh

    2017-09-01

    Understanding ecosystem processes and the influence of regional scale drivers can provide useful information for managing forest ecosystems. Examining more local scale drivers of forest biomass and water yield can also provide insights for identifying and better understanding the effects of climate change and management on forests. We used diverse multi-scale datasets, functional models and Geographically Weighted Regression (GWR) to model ecosystem processes at the watershed scale and to interpret the influence of ecological drivers across the Southeastern United States (SE US). Aboveground forest biomass (AGB) was determined from available geospatial datasets and water yield was estimated using the Water Supply and Stress Index (WaSSI) model at the watershed level. Our geostatistical model examined the spatial variation in these relationships between ecosystem processes, climate, biophysical, and forest management variables at the watershed level across the SE US. Ecological and management drivers at the watershed level were analyzed locally to identify whether drivers contribute positively or negatively to aboveground forest biomass and water yield ecosystem processes and thus identifying potential synergies and tradeoffs across the SE US region. Although AGB and water yield drivers varied geographically across the study area, they were generally significantly influenced by climate (rainfall and temperature), land-cover factor1 (Water and barren), land-cover factor2 (wetland and forest), organic matter content high, rock depth, available water content, stand age, elevation, and LAI drivers. These drivers were positively or negatively associated with biomass or water yield which significantly contributes to ecosystem interactions or tradeoff/synergies. Our study introduced a spatially-explicit modelling framework to analyze the effect of ecosystem drivers on forest ecosystem structure, function and provision of services. This integrated model approach facilitates

  17. Applications of quantum entropy to statistics

    International Nuclear Information System (INIS)

    Silver, R.N.; Martz, H.F.

    1994-01-01

    This paper develops two generalizations of the maximum entropy (ME) principle. First, Shannon classical entropy is replaced by von Neumann quantum entropy to yield a broader class of information divergences (or penalty functions) for statistics applications. Negative relative quantum entropy enforces convexity, positivity, non-local extensivity and prior correlations such as smoothness. This enables the extension of ME methods from their traditional domain of ill-posed in-verse problems to new applications such as non-parametric density estimation. Second, given a choice of information divergence, a combination of ME and Bayes rule is used to assign both prior and posterior probabilities. Hyperparameters are interpreted as Lagrange multipliers enforcing constraints. Conservation principles are proposed to act statistical regularization and other hyperparameters, such as conservation of information and smoothness. ME provides an alternative to heirarchical Bayes methods

  18. Spatial model of land use change related to sediment yield (case study: Cipeles and Cilutung watershed, West Java)

    Science.gov (United States)

    Wulandari, D. W.; Kusratmoko, E.; Indra, T. L.

    2018-05-01

    Land use changes (LUC) as a result of increasing human need for space are likely to destroy the hydrological function of the watershed, increase land degradation, stimulate erosion and drive the process of sedimentation. This study aimed to predict LUC during the period 1990 to 2030 in relation to sediment yield in Cilutung and Cipeles Watershed, West Java. LUC were simulated following the model of Cellular Automata-Marcov Chain, whereas land use composition in 2030 was predicted using Land Change Modeler on Idrisi Selva Software. Elevation, slope, distance from road, distance from river, and distance from settlement were selected as driving factors for LUC in this study. Erosion and sediment yield were predicted using WATEM/SEDEM model based on land use, rainfall, soil texture and topography. The results showed that the areas of forest and shrub have slightly declined up to 5% during the period 1990 to 2016, generally being converted into rice fields, settlements, non-irrigated fields and plantations. In addition, rice fields, settlements, and plantations were expected to substantially increase up to 50% in 2030. Furthermore, the study also revealed that erosion and sediment yield tend to increase every year. This is likely associated with LUC occurring in Cipeles and Cilutung Watershed.

  19. Impact of the spatial resolution of climatic data and soil physical properties on regional corn yield predictions using the STICS crop model

    Science.gov (United States)

    Jégo, Guillaume; Pattey, Elizabeth; Mesbah, S. Morteza; Liu, Jiangui; Duchesne, Isabelle

    2015-09-01

    The assimilation of Earth observation (EO) data into crop models has proven to be an efficient way to improve yield prediction at a regional scale by estimating key unknown crop management practices. However, the efficiency of prediction depends on the uncertainty associated with the data provided to crop models, particularly climatic data and soil physical properties. In this study, the performance of the STICS (Simulateur mulTIdisciplinaire pour les Cultures Standard) crop model for predicting corn yield after assimilation of leaf area index derived from EO data was evaluated under different scenarios. The scenarios were designed to examine the impact of using fine-resolution soil physical properties, as well as the impact of using climatic data from either one or four weather stations across the region of interest. The results indicate that when only one weather station was used, the average annual yield by producer was predicted well (absolute error <5%), but the spatial variability lacked accuracy (root mean square error = 1.3 t ha-1). The model root mean square error for yield prediction was highly correlated with the distance between the weather stations and the fields, for distances smaller than 10 km, and reached 0.5 t ha-1 for a 5-km distance when fine-resolution soil properties were used. When four weather stations were used, no significant improvement in model performance was observed. This was because of a marginal decrease (30%) in the average distance between fields and weather stations (from 10 to 7 km). However, the yield predictions were improved by approximately 15% with fine-resolution soil properties regardless of the number of weather stations used. The impact of the uncertainty associated with the EO-derived soil textures and the impact of alterations in rainfall distribution were also evaluated. A variation of about 10% in any of the soil physical textures resulted in a change in dry yield of 0.4 t ha-1. Changes in rainfall distribution

  20. A comparison of EEG spectral entropy with conventional quantitative ...

    African Journals Online (AJOL)

    Adele

    and decrease with increasing depth of anaesthesia. Spectral en- tropy yields two scales: Response Entropy (RE), ranging between. 0 to100, is an amalgam of EEG and frontal muscle activity while. State Entropy (SE), consisting mainly of EEG activity in a lower frequency band, ranges from 0 to 91.2 Initial reports have pro-.

  1. Spatial mapping of cadmium zinc telluride materials properties and electrical response to improve device yield and performance

    CERN Document Server

    Van Scyoc, J M; Yoon, H; Gilbert, T S; Hilton, N R; Lund, J C; James, R B

    1999-01-01

    Cadmium zinc telluride has experienced tremendous growth in its application to various radiation sensing problems over the last five years. However, there are still issues with yield, particularly of the large volume devices needed for imaging and sensitivity-critical applications. Inhomogeneities of various types and on various length scales currently prevent the fabrication of large devices of high spectral performance. This paper discusses the development of a set of characterization tools for quantifying these inhomogeneities, in order to develop improvement strategies to achieve the desired cadmium zinc telluride crystals for detector fabrication.

  2. Use of remote sensing, geographic information systems, and spatial statistics to assess spatio-temporal population dynamics of Heterodera glycines and soybean yield quantity and quality

    Science.gov (United States)

    Moreira, Antonio Jose De Araujo

    Soybean, Glycine max (L.) Merr., is an important source of oil and protein worldwide, and soybean cyst nematode (SCN), Heterodera glycines, is among the most important yield-limiting factors in soybean production worldwide. Early detection of SCN is difficult because soybean plants infected by SCN often do not exhibit visible symptoms. It was hypothesized, however, that reflectance data obtained by remote sensing from soybean canopies may be used to detect plant stress caused by SCN infection. Moreover, reflectance measurements may be related to soybean growth and yield. Two field experiments were conducted from 2000 to 2002 to study the relationships among reflectance data, quantity and quality of soybean yield, and SCN population densities. The best relationships between reflectance and the quantity of soybean grain yield occurred when reflectance data were obtained late August to early September. Similarly, reflectance was best related to seed oil and seed protein content and seed size when measured during late August/early September. Grain quality-reflectance relationships varied spatially and temporally. Reflectance measured early or late in the season had the best relationships with SCN population densities measured at planting. Soil properties likely affected reflectance measurements obtained at the beginning of the season and somehow may have been related to SCN population densities at planting. Reflectance data obtained at the end of the growing season likely was affected by early senescence of SCN-infected soybeans. Spatio-temporal aspects of SCN population densities in both experiments were assessed using spatial statistics and regression analyses. In the 2000 and 2001 growing seasons, spring-to-fall changes in SCN population densities were best related to SCN population densities at planting for both experiments. However, within-season changes in SCN population densities were best related to SCN population densities at harvest for both experiments in

  3. Maximum Quantum Entropy Method

    OpenAIRE

    Sim, Jae-Hoon; Han, Myung Joon

    2018-01-01

    Maximum entropy method for analytic continuation is extended by introducing quantum relative entropy. This new method is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input matrix. As a result, the continuation of off-diagonal elements becomes straightforward. Without introducing any further ambiguity, the Bayesian probabilistic interpretation is maintained just as in the conventional maximum entropy method. The applications o...

  4. Transplanckian entanglement entropy

    International Nuclear Information System (INIS)

    Chang, Darwin; Chu, C.-S.; Lin Fengli

    2004-01-01

    The entanglement entropy of the event horizon is known to be plagued by the UV divergence due to the infinitely blue-shifted near horizon modes. In this Letter we calculate the entanglement entropy using the transplanckian dispersion relation, which has been proposed to model the quantum gravity effects. We show that, very generally, the entropy is rendered UV finite due to the suppression of high energy modes effected by the transplanckian dispersion relation

  5. Entropy-Stabilized Oxides

    Science.gov (United States)

    2015-09-29

    antiferroelectrics. Phys. Rev. Lett. 110, 017603 (2013). 22. Cantor , B., Chang, I., Knight, P. & Vincent, A. Microstructural development in equiatomic...Science 345, 1153–1158 (2014). 24. Gali, A. & George , E. Tensile properties of high- and medium-entropy alloys. Intermetallics 39, 74–78 (2013). 25...148–153 (2014). 26. Otto, F., Yang, Y., Bei, H. & George , E. Relative effects of enthalpy and entropy on the phase stability of equiatomic high-entropy

  6. ENTROPY FUNCTIONAL FOR CONTINUOUS SYSTEMS OF FINITE ENTROPY

    Institute of Scientific and Technical Information of China (English)

    M. Rahimi A. Riazi

    2012-01-01

    In this article,we introduce the concept of entropy functional for continuous systems on compact metric spaces,and prove some of its properties.We also extract the Kolmogorov entropy from the entropy functional.

  7. Finite entanglement entropy and spectral dimension in quantum gravity

    Energy Technology Data Exchange (ETDEWEB)

    Arzano, Michele [Rome Univ. (Italy). Dipt. di Fisica; INFN, Rome (Italy); Calcagni, Gianluca [CSIC, Madrid (Spain). Inst. de Estructura de la Materia

    2017-12-15

    What are the conditions on a field theoretic model leading to a finite entanglement entropy density? We prove two very general results: (1) Ultraviolet finiteness of a theory does not guarantee finiteness of the entropy density; (2) If the spectral dimension of the spatial boundary across which the entropy is calculated is non-negative at all scales, then the entanglement entropy cannot be finite. These conclusions, which we verify in several examples, negatively affect all quantum-gravity models, since their spectral dimension is always positive. Possible ways out are considered, including abandoning the definition of the entanglement entropy in terms of the boundary return probability or admitting an analytic continuation (not a regularization) of the usual definition. In the second case, one can get a finite entanglement entropy density in multi-fractional theories and causal dynamical triangulations. (orig.)

  8. Finite entanglement entropy and spectral dimension in quantum gravity

    International Nuclear Information System (INIS)

    Arzano, Michele; Calcagni, Gianluca

    2017-01-01

    What are the conditions on a field theoretic model leading to a finite entanglement entropy density? We prove two very general results: (1) Ultraviolet finiteness of a theory does not guarantee finiteness of the entropy density; (2) If the spectral dimension of the spatial boundary across which the entropy is calculated is non-negative at all scales, then the entanglement entropy cannot be finite. These conclusions, which we verify in several examples, negatively affect all quantum-gravity models, since their spectral dimension is always positive. Possible ways out are considered, including abandoning the definition of the entanglement entropy in terms of the boundary return probability or admitting an analytic continuation (not a regularization) of the usual definition. In the second case, one can get a finite entanglement entropy density in multi-fractional theories and causal dynamical triangulations. (orig.)

  9. Finite entanglement entropy and spectral dimension in quantum gravity

    Science.gov (United States)

    Arzano, Michele; Calcagni, Gianluca

    2017-12-01

    What are the conditions on a field theoretic model leading to a finite entanglement entropy density? We prove two very general results: (1) Ultraviolet finiteness of a theory does not guarantee finiteness of the entropy density; (2) If the spectral dimension of the spatial boundary across which the entropy is calculated is non-negative at all scales, then the entanglement entropy cannot be finite. These conclusions, which we verify in several examples, negatively affect all quantum-gravity models, since their spectral dimension is always positive. Possible ways out are considered, including abandoning the definition of the entanglement entropy in terms of the boundary return probability or admitting an analytic continuation (not a regularization) of the usual definition. In the second case, one can get a finite entanglement entropy density in multi-fractional theories and causal dynamical triangulations.

  10. Topological entropy of autonomous flows

    Energy Technology Data Exchange (ETDEWEB)

    Badii, R. [Paul Scherrer Inst. (PSI), Villigen (Switzerland)

    1997-06-01

    When studying fluid dynamics, especially in a turbulent regime, it is crucial to estimate the number of active degrees of freedom or of localized structures in the system. The topological entropy quantifies the exponential growth of the number of `distinct` orbits in a dynamical system as a function of their length, in the infinite spatial resolution limit. Here, I illustrate a novel method for its evaluation, which extends beyond maps and is applicable to any system, including autonomous flows: these are characterized by lack of a definite absolute time scale for the orbit lengths. (author) 8 refs.

  11. Prediction of Protein Configurational Entropy (Popcoen).

    Science.gov (United States)

    Goethe, Martin; Gleixner, Jan; Fita, Ignacio; Rubi, J Miguel

    2018-03-13

    A knowledge-based method for configurational entropy prediction of proteins is presented; this methodology is extremely fast, compared to previous approaches, because it does not involve any type of configurational sampling. Instead, the configurational entropy of a query fold is estimated by evaluating an artificial neural network, which was trained on molecular-dynamics simulations of ∼1000 proteins. The predicted entropy can be incorporated into a large class of protein software based on cost-function minimization/evaluation, in which configurational entropy is currently neglected for performance reasons. Software of this type is used for all major protein tasks such as structure predictions, proteins design, NMR and X-ray refinement, docking, and mutation effect predictions. Integrating the predicted entropy can yield a significant accuracy increase as we show exemplarily for native-state identification with the prominent protein software FoldX. The method has been termed Popcoen for Prediction of Protein Configurational Entropy. An implementation is freely available at http://fmc.ub.edu/popcoen/ .

  12. Entropy of Mixing of Distinguishable Particles

    Science.gov (United States)

    Kozliak, Evguenii I.

    2014-01-01

    The molar entropy of mixing yields values that depend only on the number of mixing components rather than on their chemical nature. To explain this phenomenon using the logic of chemistry, this article considers mixing of distinguishable particles, thus complementing the well-known approach developed for nondistinguishable particles, for example,…

  13. Entanglement entropy in causal set theory

    Science.gov (United States)

    Sorkin, Rafael D.; Yazdi, Yasaman K.

    2018-04-01

    Entanglement entropy is now widely accepted as having deep connections with quantum gravity. It is therefore desirable to understand it in the context of causal sets, especially since they provide in a natural manner the UV cutoff needed to render entanglement entropy finite. Formulating a notion of entanglement entropy in a causal set is not straightforward because the type of canonical hypersurface-data on which its definition typically relies is not available. Instead, we appeal to the more global expression given in Sorkin (2012 (arXiv:1205.2953)) which, for a Gaussian scalar field, expresses the entropy of a spacetime region in terms of the field’s correlation function within that region (its ‘Wightman function’ W(x, x') ). Carrying this formula over to the causal set, one obtains an entropy which is both finite and of a Lorentz invariant nature. We evaluate this global entropy-expression numerically for certain regions (primarily order-intervals or ‘causal diamonds’) within causal sets of 1  +  1 dimensions. For the causal-set counterpart of the entanglement entropy, we obtain, in the first instance, a result that follows a (spacetime) volume law instead of the expected (spatial) area law. We find, however, that one obtains an area law if one truncates the commutator function (‘Pauli–Jordan operator’) and the Wightman function by projecting out the eigenmodes of the Pauli–Jordan operator whose eigenvalues are too close to zero according to a geometrical criterion which we describe more fully below. In connection with these results and the questions they raise, we also study the ‘entropy of coarse-graining’ generated by thinning out the causal set, and we compare it with what one obtains by similarly thinning out a chain of harmonic oscillators, finding the same, ‘universal’ behaviour in both cases.

  14. Spatial variability of sorghum forage yield and physical attributes of an Planosol = Variabilidade espacial da produtividade de sorgo e atributos físicos em um Planossolo.

    Directory of Open Access Journals (Sweden)

    Rafael Montanari

    2013-12-01

    Full Text Available The cultivation of sorghum (Sorghum bicolor L. Moench is increasing in the Midwest region of Brazil with the aim of expanding the production of silage to be used in animal feed, with good adaptability to climatic conditions of the arid and semi-arid brazilian. The productive capacity of sorghum is influenced by soil physical properties (RP, UG, UV e DS, with these values appropriate to the development of the root system positively affect the productivity. In order to study the spatial and linear correlations between the yield of sorghum for forage and soil physical properties, an experiment was conducted in the Miranda city, MS, in an Planosol. The data were obtained by analysis of samples of plant (MVF and soil (RP, UG, UV e DS collected at random, having been demarcated using a GPS receiver 51 points in the cultivation area with irregular spacing. The attributes studied (plant and soil, and have spatial correlation, the variability between medium and high and well-defined spatial patterns, with a range between 130.0 and 352.0 m. The RP and UG were good indicators of soil physical quality, as for the productivity of green biomass forage sorghum. =

  15. Measurement of fluorophore concentrations and fluorescence quantum yield in tissue-simulating phantoms using three diffusion models of steady-state spatially resolved fluorescence

    Energy Technology Data Exchange (ETDEWEB)

    Diamond, Kevin R; Farrell, Thomas J; Patterson, Michael S [Department of Medical Physics, Juravinski Cancer Centre and McMaster University, 699 Concession Street, Hamilton, Ontario L8V 5C2 (Canada)

    2003-12-21

    Steady-state diffusion theory models of fluorescence in tissue have been investigated for recovering fluorophore concentrations and fluorescence quantum yield. Spatially resolved fluorescence, excitation and emission reflectance were calculated by diffusion theory and Monte Carlo simulations, and measured using a multi-fibre probe on tissue-simulating phantoms containing either aluminium phthalocyanine tetrasulfonate (AlPcS{sub 4}), Photofrin or meso-tetra-(4-sulfonatophenyl)-porphine dihydrochloride (TPPS{sub 4}). The accuracy of the fluorophore concentration and fluorescence quantum yield recovered by three different models of spatially resolved fluorescence were compared. The models were based on: (a) weighted difference of the excitation and emission reflectance, (b) fluorescence due to a point excitation source or (c) fluorescence due to a pencil beam excitation source. When literature values for the fluorescence quantum yield were used for each of the fluorophores, the fluorophore absorption coefficient (and hence concentration) at the excitation wavelengthwas recovered with a root-mean-square accuracy of 11.4% using the point source model of fluorescence and 8.0% using the more complicated pencil beam excitation model. The accuracy was calculated over a broad range of optical properties and fluorophore concentrations. The weighted difference of reflectance model performed poorly, with a root-mean-square error in concentration of about 50%. Monte Carlo simulations suggest that there are some situations where the weighted difference of reflectance is as accurate as the other two models, although this was not confirmed experimentally. Estimates of the fluorescence quantum yield in multiple scattering media were also made by determining independently from the fitted absorption spectrum and applying the various diffusion theory models. The fluorescence quantum yields for AlPcS{sub 4} and TPPS{sub 4} were calculated to be 0.59 {+-} 0.03 and 0.121 {+-} 0

  16. Measurement of fluorophore concentrations and fluorescence quantum yield in tissue-simulating phantoms using three diffusion models of steady-state spatially resolved fluorescence

    International Nuclear Information System (INIS)

    Diamond, Kevin R; Farrell, Thomas J; Patterson, Michael S

    2003-01-01

    Steady-state diffusion theory models of fluorescence in tissue have been investigated for recovering fluorophore concentrations and fluorescence quantum yield. Spatially resolved fluorescence, excitation and emission reflectance were calculated by diffusion theory and Monte Carlo simulations, and measured using a multi-fibre probe on tissue-simulating phantoms containing either aluminium phthalocyanine tetrasulfonate (AlPcS 4 ), Photofrin or meso-tetra-(4-sulfonatophenyl)-porphine dihydrochloride (TPPS 4 ). The accuracy of the fluorophore concentration and fluorescence quantum yield recovered by three different models of spatially resolved fluorescence were compared. The models were based on: (a) weighted difference of the excitation and emission reflectance, (b) fluorescence due to a point excitation source or (c) fluorescence due to a pencil beam excitation source. When literature values for the fluorescence quantum yield were used for each of the fluorophores, the fluorophore absorption coefficient (and hence concentration) at the excitation wavelengthwas recovered with a root-mean-square accuracy of 11.4% using the point source model of fluorescence and 8.0% using the more complicated pencil beam excitation model. The accuracy was calculated over a broad range of optical properties and fluorophore concentrations. The weighted difference of reflectance model performed poorly, with a root-mean-square error in concentration of about 50%. Monte Carlo simulations suggest that there are some situations where the weighted difference of reflectance is as accurate as the other two models, although this was not confirmed experimentally. Estimates of the fluorescence quantum yield in multiple scattering media were also made by determining independently from the fitted absorption spectrum and applying the various diffusion theory models. The fluorescence quantum yields for AlPcS 4 and TPPS 4 were calculated to be 0.59 ± 0.03 and 0.121 ± 0.001 respectively using the point

  17. Enthalpy–entropy compensation

    Indian Academy of Sciences (India)

    Enthalpy–entropy compensation is the name given to the correlation sometimes observed between the estimates of the enthalpy and entropy of a reaction obtained from temperature-dependence data. Although the mainly artefactual nature of this correlation has been known for many years, the subject enjoys periodical ...

  18. Entropy in Biology

    Indian Academy of Sciences (India)

    During the process of ageing, the balance shifts in the direction of anarchy. Death is ... tion of life and the laws of statistieal physics and entropy, both of which ... capable of doing work. ... defined by Ludwig Boltzmann in 1877, the entropy of the.

  19. The holographic entropy cone

    Energy Technology Data Exchange (ETDEWEB)

    Bao, Ning [Institute for Quantum Information and Matter, California Institute of Technology,Pasadena, CA 91125 (United States); Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Nezami, Sepehr [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States); Ooguri, Hirosi [Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo,Kashiwa 277-8583 (Japan); Stoica, Bogdan [Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Sully, James [Theory Group, SLAC National Accelerator Laboratory, Stanford University,Menlo Park, CA 94025 (United States); Walter, Michael [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States)

    2015-09-21

    We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.

  20. The holographic entropy cone

    International Nuclear Information System (INIS)

    Bao, Ning; Nezami, Sepehr; Ooguri, Hirosi; Stoica, Bogdan; Sully, James; Walter, Michael

    2015-01-01

    We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.

  1. Entropy and Digital Installation

    Directory of Open Access Journals (Sweden)

    Susan Ballard

    2005-01-01

    Full Text Available This paper examines entropy as a process which introduces ideas of distributed materiality to digital installation. Beginning from an analysis of entropy as both force and probability measure within information theory and it’s extension in Ruldof Arnheim’s text ‘Entropy and Art” it develops an argument for the positive rather thannegative forces of entropy. The paper centres on a discussion of two recent works by New Zealand artists Ronnie van Hout (“On the Run”, Wellington City Gallery, NZ, 2004 and Alex Monteith (“Invisible Cities”, Physics Room Contemporary Art Space, Christchurch, NZ, 2004. Ballard suggests that entropy, rather than being a hindrance to understanding or a random chaotic force, discloses a necessary and material politics of noise present in digital installation.

  2. Nonsymmetric entropy I: basic concepts and results

    OpenAIRE

    Liu, Chengshi

    2006-01-01

    A new concept named nonsymmetric entropy which generalizes the concepts of Boltzman's entropy and shannon's entropy, was introduced. Maximal nonsymmetric entropy principle was proven. Some important distribution laws were derived naturally from maximal nonsymmetric entropy principle.

  3. Linear and spatial correlation of the yield components and soybean yieldCorrelação linear e espacial dos componentes de produção e produtividade da soja

    Directory of Open Access Journals (Sweden)

    Morel de Passos e Carvalho

    2012-05-01

    Full Text Available The soybean is the crop most cultivated in Brazil, with great socioeconomic importance. In the agriculture year 2008/09 in Selvíria County, Mato Grosso do Sul State, in the Brazilian Savannah, was analyzed the production components and the soybean yield cultivated in a Typic Acrustox on no-tillage. The main purpose objective was select among the production components number of pods per plant, number of grains per pod, number of grains per plant, mass of a thousand grains, mass of grains per plant and population of plants, which of the best linear and spatial correlation aiming explain the soybean yield variability. The irregular geostatistical grid was installed to collect of data, with 120 sampling points, in an area of 8.34 ha. The values of spatial dependence range to be utilized should be among 38.1 and 114.7 meters. The model of the adjusted semivariograma was predominantly the spherical. Of the lineal and spatial point of view, the number of pods per plant and the mass of grains per plant they were correlated in a direct way with the soybean yield, demonstrating be the best components to esteem her. A soja é a cultura de grãos mais cultivada no Brasil, com enorme importância socioeconômica. No ano agrícola de 2008/09, no município de Selvíria (MS, no Cerrado Brasileiro, foram analisados os componentes de produção e a produtividade da soja cultivada em Latossolo Vermelho distroférrico em sistema plantio direto. O objetivo foi selecionar entre os componentes de produção número de vagens por planta, número de grãos por vagem, número de grãos por planta, massa de mil grãos, massa de grãos por planta e população de plantas, aquele com a melhor correlação, linear e espacial, visando explicar a variabilidade da produtividade da soja. Foi instalada a malha geoestatística irregular, para a coleta de dados, com 120 pontos amostrais, numa área de 8,34 ha. Os valores dos alcances da dependência espacial a serem empregados

  4. Entropy of the Mixture of Sources and Entropy Dimension

    OpenAIRE

    Smieja, Marek; Tabor, Jacek

    2011-01-01

    We investigate the problem of the entropy of the mixture of sources. There is given an estimation of the entropy and entropy dimension of convex combination of measures. The proof is based on our alternative definition of the entropy based on measures instead of partitions.

  5. Entropy coherent and entropy convex measures of risk

    NARCIS (Netherlands)

    Laeven, Roger; Stadje, M.A.

    2010-01-01

    We introduce entropy coherent and entropy convex measures of risk and prove a collection of axiomatic characterization and duality results. We show in particular that entropy coherent and entropy convex measures of risk emerge as negative certainty equivalents in (the regular and a generalized

  6. Entropy coherent and entropy convex measures of risk

    NARCIS (Netherlands)

    Laeven, R.J.A.; Stadje, M.

    2013-01-01

    We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. Entropy coherent and entropy convex measures of risk are special cases of φ-coherent and φ-convex measures of risk. Contrary to the classical use of coherent and convex

  7. Entropy Coherent and Entropy Convex Measures of Risk

    NARCIS (Netherlands)

    Laeven, R.J.A.; Stadje, M.A.

    2011-01-01

    We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. We prove that convex, entropy convex and entropy coherent measures of risk emerge as certainty equivalents under variational, homothetic and multiple priors preferences,

  8. Spatial analysis of the dairy yield using a conditional autoregressive model / Análise espacial da produção leiteira usando um modelo autoregressivo condicional

    Directory of Open Access Journals (Sweden)

    João Domingos Scalon

    2010-07-01

    Full Text Available The dairy yield is one of the most important activities for the Brazilian economy and the use of statistical models may improve the decision making in this productive sector. The aim of this paper was to compare the performance of both the traditional linear regression model and the spatial regression model called conditional autoregressive (CAR to explain how some covariates may contribute for the dairy yield. This work used a database on dairy yield supplied by the Brazilian Institute of Geography and Statistics (IBGE and another database on geographical information of the state of Minas Gerais provided by the Integrated Program of Technological Use of Geographical Information (GEOMINAS. The results showed the superiority of the CAR model over the traditional linear regression model to explain the dairy yield. The CAR model allowed the identification of two different spatial clusters of counties related to the dairy yield in the state of Minas Gerais. The first cluster represents the region where one observes the biggest levels of dairy yield. It is formed by the counties of the Triângulo Mineiro. The second cluster is formed by the northern counties of the state that present the lesser levels of dairy yield. A produção de leite é uma das atividades mais importantes para a economia brasileira e o uso de modelos estatísticos pode auxiliar a tomada de decisão neste setor produtivo. O objetivo deste artigo foi comparar o desempenho do modelo de regressão linear tradicional e do modelo de regressão espacial, denominado de autoregressivo condicional (CAR, para explicar como algumas variáveis preditoras contribuem para a quantidade de leite produzido. Este trabalho usou uma base de dados sobre a produção de leite fornecida pelo Instituto Brasileiro de Geografia e Estatística (IBGE e outra base de dados sobre informações geográficas do estado de Minas Gerais, fornecida pelo Programa Integrado de Uso da Tecnologia de Geoprocessamento

  9. Infinite Shannon entropy

    International Nuclear Information System (INIS)

    Baccetti, Valentina; Visser, Matt

    2013-01-01

    Even if a probability distribution is properly normalizable, its associated Shannon (or von Neumann) entropy can easily be infinite. We carefully analyze conditions under which this phenomenon can occur. Roughly speaking, this happens when arbitrarily small amounts of probability are dispersed into an infinite number of states; we shall quantify this observation and make it precise. We develop several particularly simple, elementary, and useful bounds, and also provide some asymptotic estimates, leading to necessary and sufficient conditions for the occurrence of infinite Shannon entropy. We go to some effort to keep technical computations as simple and conceptually clear as possible. In particular, we shall see that large entropies cannot be localized in state space; large entropies can only be supported on an exponentially large number of states. We are for the time being interested in single-channel Shannon entropy in the information theoretic sense, not entropy in a stochastic field theory or quantum field theory defined over some configuration space, on the grounds that this simple problem is a necessary precursor to understanding infinite entropy in a field theoretic context. (paper)

  10. Black hole thermodynamical entropy

    International Nuclear Information System (INIS)

    Tsallis, Constantino; Cirto, Leonardo J.L.

    2013-01-01

    As early as 1902, Gibbs pointed out that systems whose partition function diverges, e.g. gravitation, lie outside the validity of the Boltzmann-Gibbs (BG) theory. Consistently, since the pioneering Bekenstein-Hawking results, physically meaningful evidence (e.g., the holographic principle) has accumulated that the BG entropy S BG of a (3+1) black hole is proportional to its area L 2 (L being a characteristic linear length), and not to its volume L 3 . Similarly it exists the area law, so named because, for a wide class of strongly quantum-entangled d-dimensional systems, S BG is proportional to lnL if d=1, and to L d-1 if d>1, instead of being proportional to L d (d ≥ 1). These results violate the extensivity of the thermodynamical entropy of a d-dimensional system. This thermodynamical inconsistency disappears if we realize that the thermodynamical entropy of such nonstandard systems is not to be identified with the BG additive entropy but with appropriately generalized nonadditive entropies. Indeed, the celebrated usefulness of the BG entropy is founded on hypothesis such as relatively weak probabilistic correlations (and their connections to ergodicity, which by no means can be assumed as a general rule of nature). Here we introduce a generalized entropy which, for the Schwarzschild black hole and the area law, can solve the thermodynamic puzzle. (orig.)

  11. Entropy Production of Stars

    Directory of Open Access Journals (Sweden)

    Leonid M. Martyushev

    2015-06-01

    Full Text Available The entropy production (inside the volume bounded by a photosphere of main-sequence stars, subgiants, giants, and supergiants is calculated based on B–V photometry data. A non-linear inverse relationship of thermodynamic fluxes and forces as well as an almost constant specific (per volume entropy production of main-sequence stars (for 95% of stars, this quantity lies within 0.5 to 2.2 of the corresponding solar magnitude is found. The obtained results are discussed from the perspective of known extreme principles related to entropy production.

  12. Some remarks on conditional entropy

    NARCIS (Netherlands)

    Nijst, A.G.P.M.

    1969-01-01

    Using a definition of conditional entropy given by Hanen and Neveu [5, 10, 11] we discuss in this paper some properties of conditional entropy and mean entropy, in particular an integral representation of conditional entropy (§ 2), and the decomposition theorem of the KolmogorovSina¯i invariant (§

  13. Evaluation of a spatialized agronomic model in predicting yield and N leaching at the scale of the Seine-Normandie Basin.

    Science.gov (United States)

    Beaudoin, N; Gallois, N; Viennot, P; Le Bas, C; Puech, T; Schott, C; Buis, S; Mary, B

    2016-09-22

    The EU directive has addressed ambitious targets concerning the quality of water bodies. Predicting water quality as affected by land use and management requires using dynamic agro-hydrogeological models. In this study, an agronomic model (STICS) and a hydrogeological model (MODCOU) have been associated in order to simulate nitrogen fluxes in the Seine-Normandie Basin, which is affected by nitrate pollution of groundwater due to intensive farming systems. This modeling platform was used to predict and understand the spatial and temporal evolution of water quality over the 1971-2013 period. A quality assurance protocol (Refsgaard et al. Environ Model Softw 20: 1201-1215, 2005) was used to qualify the reliability of STICS outputs. Four iterative runs of the model were carried out with improved parameterization of soils and crop management without any change in the model. Improving model inputs changed much more the spatial distribution of simulated N losses than their mean values. STICS slightly underestimated the crop yields compared to the observed values at the administrative district scale. The platform also slightly underestimated the nitrate concentration at the outlet level with a mean difference ranging from -1.4 to -9.2 mg NO 3  L -1 according to the aquifer during the last decade. This outcome should help the stakeholders in decision-making to prevent nitrate pollution and provide new specifications for STICS development.

  14. Spatial Relation of Apparent Soil Electrical Conductivity with Crop Yields and Soil Properties at Different Topographic Positions in a Small Agricultural Watershed

    Directory of Open Access Journals (Sweden)

    Gurbir Singh

    2016-11-01

    Full Text Available Use of electromagnetic induction (EMI sensors along with geospatial modeling provide a better opportunity for understanding spatial distribution of soil properties and crop yields on a landscape level and to map site-specific management zones. The first objective of this research was to evaluate the relationship of crop yields, soil properties and apparent electrical conductivity (ECa at different topographic positions (shoulder, backslope, and deposition slope. The second objective was to examine whether the correlation of ECa with soil properties and crop yields on a watershed scale can be improved by considering topography in modeling ECa and soil properties compared to a whole field scale with no topographic separation. This study was conducted in two headwater agricultural watersheds in southern Illinois, USA. The experimental design consisted of three basins per watershed and each basin was divided into three topographic positions (shoulder, backslope and deposition using the Slope Position Classification model in ESRI ArcMap. A combine harvester equipped with a GPS-based recording system was used for yield monitoring and mapping from 2012 to 2015. Soil samples were taken at depths from 0–15 cm and 15–30 cm from 54 locations in the two watersheds in fall 2015 and analyzed for physical and chemical properties. The ECa was measured using EMI device, EM38-MK2, which provides four dipole readings ECa-H-0.5, ECa-H-1, ECa-V-0.5, and ECa-V-1. Soybean and corn yields at depositional position were 38% and 62% lower than the shoulder position in 2014 and 2015, respectively. Soil pH, total carbon (TC, total nitrogen (TN, Mehlich-3 Phosphorus (P, Bray-1 P and ECa at depositional positions were significantly higher compared to shoulder positions. Corn and soybeans yields were weakly to moderately (<±0.75 correlated with ECa. At the deposition position at the 0–15 cm depth ECa-H-0.5 was weakly correlated (r < ±0.50 with soil pH and was

  15. Entropy of international trades

    Science.gov (United States)

    Oh, Chang-Young; Lee, D.-S.

    2017-05-01

    The organization of international trades is highly complex under the collective efforts towards economic profits of participating countries given inhomogeneous resources for production. Considering the trade flux as the probability of exporting a product from a country to another, we evaluate the entropy of the world trades in the period 1950-2000. The trade entropy has increased with time, and we show that it is mainly due to the extension of trade partnership. For a given number of trade partners, the mean trade entropy is about 60% of the maximum possible entropy, independent of time, which can be regarded as a characteristic of the trade fluxes' heterogeneity and is shown to be derived from the scaling and functional behaviors of the universal trade-flux distribution. The correlation and time evolution of the individual countries' gross-domestic products and the number of trade partners show that most countries achieved their economic growth partly by extending their trade relationship.

  16. On holographic defect entropy

    International Nuclear Information System (INIS)

    Estes, John; Jensen, Kristan; O’Bannon, Andy; Tsatis, Efstratios; Wrase, Timm

    2014-01-01

    We study a number of (3+1)- and (2+1)-dimensional defect and boundary conformal field theories holographically dual to supergravity theories. In all cases the defects or boundaries are planar, and the defects are codimension-one. Using holography, we compute the entanglement entropy of a (hemi-)spherical region centered on the defect (boundary). We define defect and boundary entropies from the entanglement entropy by an appropriate background subtraction. For some (3+1)-dimensional theories we find evidence that the defect/boundary entropy changes monotonically under certain renormalization group flows triggered by operators localized at the defect or boundary. This provides evidence that the g-theorem of (1+1)-dimensional field theories generalizes to higher dimensions

  17. Minimum entropy production principle

    Czech Academy of Sciences Publication Activity Database

    Maes, C.; Netočný, Karel

    2013-01-01

    Roč. 8, č. 7 (2013), s. 9664-9677 ISSN 1941-6016 Institutional support: RVO:68378271 Keywords : MINEP Subject RIV: BE - Theoretical Physics http://www.scholarpedia.org/article/Minimum_entropy_production_principle

  18. Entropy in halide perovskites

    Science.gov (United States)

    Katan, Claudine; Mohite, Aditya D.; Even, Jacky

    2018-05-01

    Claudine Katan, Aditya D. Mohite and Jacky Even discuss the possible impact of various entropy contributions (stochastic structural fluctuations, anharmonicity and lattice softness) on the optoelectronic properties of halide perovskite materials and devices.

  19. Entropy Coding in HEVC

    OpenAIRE

    Sze, Vivienne; Marpe, Detlev

    2014-01-01

    Context-Based Adaptive Binary Arithmetic Coding (CABAC) is a method of entropy coding first introduced in H.264/AVC and now used in the latest High Efficiency Video Coding (HEVC) standard. While it provides high coding efficiency, the data dependencies in H.264/AVC CABAC make it challenging to parallelize and thus limit its throughput. Accordingly, during the standardization of entropy coding for HEVC, both aspects of coding efficiency and throughput were considered. This chapter describes th...

  20. Entropy and wigner functions

    Science.gov (United States)

    Manfredi; Feix

    2000-10-01

    The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such a definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of entanglement of a quantum state. It is shown that smoothing of the Wigner function induces an increase in entropy. This fact is used to derive some simple rules to construct positive-definite probability distributions which are also admissible Wigner functions.

  1. Entropy and Wigner Functions

    OpenAIRE

    Manfredi, G.; Feix, M. R.

    2002-01-01

    The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of entanglement of a quantum state. It is shown that smoothing of the Wigner function induces an increase in entropy. This fact is used to derive some simple rules to construct positive definite probability distributions which are also admissible Wigner functions

  2. Feasible Histories, Maximum Entropy

    International Nuclear Information System (INIS)

    Pitowsky, I.

    1999-01-01

    We consider the broadest possible consistency condition for a family of histories, which extends all previous proposals. A family that satisfies this condition is called feasible. On each feasible family of histories we choose a probability measure by maximizing entropy, while keeping the probabilities of commuting histories to their quantum mechanical values. This procedure is justified by the assumption that decoherence increases entropy. Finally, a criterion for identifying the nearly classical families is proposed

  3. Topological nearly entropy

    Science.gov (United States)

    Gulamsarwar, Syazwani; Salleh, Zabidin

    2017-08-01

    The purpose of this paper is to generalize the notions of Adler's topological entropy along with their several fundamental properties. A function f : X → Y is said to be R-map if f-1 (V) is regular open in X for every regular open set V in Y. Thus, we initiated a notion of topological nearly entropy for topological R-dynamical systems which is based on nearly compact relative to the space by using R-map.

  4. Remarks on entanglement entropy in string theory

    Science.gov (United States)

    Balasubramanian, Vijay; Parrikar, Onkar

    2018-03-01

    Entanglement entropy for spatial subregions is difficult to define in string theory because of the extended nature of strings. Here we propose a definition for bosonic open strings using the framework of string field theory. The key difference (compared to ordinary quantum field theory) is that the subregion is chosen inside a Cauchy surface in the "space of open string configurations." We first present a simple calculation of this entanglement entropy in free light-cone string field theory, ignoring subtleties related to the factorization of the Hilbert space. We reproduce the answer expected from an effective field theory point of view, namely a sum over the one-loop entanglement entropies corresponding to all the particle-excitations of the string, and further show that the full string theory regulates ultraviolet divergences in the entanglement entropy. We then revisit the question of factorization of the Hilbert space by analyzing the covariant phase-space associated with a subregion in Witten's covariant string field theory. We show that the pure gauge (i.e., BRST exact) modes in the string field become dynamical at the entanglement cut. Thus, a proper definition of the entropy must involve an extended Hilbert space, with new stringy edge modes localized at the entanglement cut.

  5. Entropy of quasiblack holes

    International Nuclear Information System (INIS)

    Lemos, Jose P. S.; Zaslavskii, Oleg B.

    2010-01-01

    We trace the origin of the black hole entropy S, replacing a black hole by a quasiblack hole. Let the boundary of a static body approach its own gravitational radius, in such a way that a quasihorizon forms. We show that if the body is thermal with the temperature taking the Hawking value at the quasihorizon limit, it follows, in the nonextremal case, from the first law of thermodynamics that the entropy approaches the Bekenstein-Hawking value S=A/4. In this setup, the key role is played by the surface stresses on the quasihorizon and one finds that the entropy comes from the quasihorizon surface. Any distribution of matter inside the surface leads to the same universal value for the entropy in the quasihorizon limit. This can be of some help in the understanding of black hole entropy. Other similarities between black holes and quasiblack holes such as the mass formulas for both objects had been found previously. We also discuss the entropy for extremal quasiblack holes, a more subtle issue.

  6. Entropy, matter, and cosmology.

    Science.gov (United States)

    Prigogine, I; Géhéniau, J

    1986-09-01

    The role of irreversible processes corresponding to creation of matter in general relativity is investigated. The use of Landau-Lifshitz pseudotensors together with conformal (Minkowski) coordinates suggests that this creation took place in the early universe at the stage of the variation of the conformal factor. The entropy production in this creation process is calculated. It is shown that these dissipative processes lead to the possibility of cosmological models that start from empty conditions and gradually build up matter and entropy. Gravitational entropy takes a simple meaning as associated to the entropy that is necessary to produce matter. This leads to an extension of the third law of thermodynamics, as now the zero point of entropy becomes the space-time structure out of which matter is generated. The theory can be put into a convenient form using a supplementary "C" field in Einstein's field equations. The role of the C field is to express the coupling between gravitation and matter leading to irreversible entropy production.

  7. On the Conditional Rényi Entropy

    NARCIS (Netherlands)

    S. Fehr (Serge); S. Berens (Stefan)

    2014-01-01

    htmlabstractThe Rényi entropy of general order unifies the well-known Shannon entropy with several other entropy notions, like the min-entropy or the collision entropy. In contrast to the Shannon entropy, there seems to be no commonly accepted definition for the conditional Rényi entropy: several

  8. EEG entropy measures in anesthesia

    Directory of Open Access Journals (Sweden)

    Zhenhu eLiang

    2015-02-01

    Full Text Available Objective: Entropy algorithms have been widely used in analyzing EEG signals during anesthesia. However, a systematic comparison of these entropy algorithms in assessing anesthesia drugs’ effect is lacking. In this study, we compare the capability of twelve entropy indices for monitoring depth of anesthesia (DoA and detecting the burst suppression pattern (BSP, in anesthesia induced by GA-BAergic agents.Methods: Twelve indices were investigated, namely Response Entropy (RE and State entropy (SE, three wavelet entropy (WE measures (Shannon WE (SWE, Tsallis WE (TWE and Renyi WE (RWE, Hilbert-Huang spectral entropy (HHSE, approximate entropy (ApEn, sample entropy (SampEn, Fuzzy entropy, and three permutation entropy (PE measures (Shannon PE (SPE, Tsallis PE (TPE and Renyi PE (RPE. Two EEG data sets from sevoflurane-induced and isoflu-rane-induced anesthesia respectively were selected to assess the capability of each entropy index in DoA monitoring and BSP detection. To validate the effectiveness of these entropy algorithms, phar-macokinetic / pharmacodynamic (PK/PD modeling and prediction probability analysis were applied. The multifractal detrended fluctuation analysis (MDFA as a non-entropy measure was compared.Results: All the entropy and MDFA indices could track the changes in EEG pattern during different anesthesia states. Three PE measures outperformed the other entropy indices, with less baseline vari-ability, higher coefficient of determination and prediction probability, and RPE performed best; ApEn and SampEn discriminated BSP best. Additionally, these entropy measures showed an ad-vantage in computation efficiency compared with MDFA.Conclusion: Each entropy index has its advantages and disadvantages in estimating DoA. Overall, it is suggested that the RPE index was a superior measure.Significance: Investigating the advantages and disadvantages of these entropy indices could help improve current clinical indices for monitoring DoA.

  9. Spatial Estimation of Losses Attributable to Meteorological Disasters in a Specific Area (105.0°E–115.0°E, 25°N–35°N Using Bayesian Maximum Entropy and Partial Least Squares Regression

    Directory of Open Access Journals (Sweden)

    F. S. Zhang

    2016-01-01

    Full Text Available The spatial mapping of losses attributable to such disasters is now well established as a means of describing the spatial patterns of disaster risk, and it has been shown to be suitable for many types of major meteorological disasters. However, few studies have been carried out by developing a regression model to estimate the effects of the spatial distribution of meteorological factors on losses associated with meteorological disasters. In this study, the proposed approach is capable of the following: (a estimating the spatial distributions of seven meteorological factors using Bayesian maximum entropy, (b identifying the four mapping methods used in this research with the best performance based on the cross validation, and (c establishing a fitted model between the PLS components and disaster losses information using partial least squares regression within a specific research area. The results showed the following: (a best mapping results were produced by multivariate Bayesian maximum entropy with probabilistic soft data; (b the regression model using three PLS components, extracted from seven meteorological factors by PLS method, was the most predictive by means of PRESS/SS test; (c northern Hunan Province sustains the most damage, and southeastern Gansu Province and western Guizhou Province sustained the least.

  10. Statistical Entropy of the Kaluza-Klein Black Hole from the Horizon Conformal Field Theory

    Institute of Scientific and Technical Information of China (English)

    JING Ji-Liang; YAN Mu-Lin

    2001-01-01

    The statistical entropy of the Kaluza-Klein black hole is studied by counting the black hole states which form an algebra of diffeomorphism at Killing horizon with a central charge. It is shown that the entropy yielded by the standard Cardy formula agrees with the Bekenstein-Hawking entropy only if we take period T of function u as the periodicity of the Euclidean black hole. On the other hand, the first-order quantum correction to the entropy is proportional to the logarithm of the Bekenstein-Hawking entropy with a factor -1/2.

  11. Entropy of network ensembles

    Science.gov (United States)

    Bianconi, Ginestra

    2009-03-01

    In this paper we generalize the concept of random networks to describe network ensembles with nontrivial features by a statistical mechanics approach. This framework is able to describe undirected and directed network ensembles as well as weighted network ensembles. These networks might have nontrivial community structure or, in the case of networks embedded in a given space, they might have a link probability with a nontrivial dependence on the distance between the nodes. These ensembles are characterized by their entropy, which evaluates the cardinality of networks in the ensemble. In particular, in this paper we define and evaluate the structural entropy, i.e., the entropy of the ensembles of undirected uncorrelated simple networks with given degree sequence. We stress the apparent paradox that scale-free degree distributions are characterized by having small structural entropy while they are so widely encountered in natural, social, and technological complex systems. We propose a solution to the paradox by proving that scale-free degree distributions are the most likely degree distribution with the corresponding value of the structural entropy. Finally, the general framework we present in this paper is able to describe microcanonical ensembles of networks as well as canonical or hidden-variable network ensembles with significant implications for the formulation of network-constructing algorithms.

  12. Entropy Production in Stochastics

    Directory of Open Access Journals (Sweden)

    Demetris Koutsoyiannis

    2017-10-01

    Full Text Available While the modern definition of entropy is genuinely probabilistic, in entropy production the classical thermodynamic definition, as in heat transfer, is typically used. Here we explore the concept of entropy production within stochastics and, particularly, two forms of entropy production in logarithmic time, unconditionally (EPLT or conditionally on the past and present having been observed (CEPLT. We study the theoretical properties of both forms, in general and in application to a broad set of stochastic processes. A main question investigated, related to model identification and fitting from data, is how to estimate the entropy production from a time series. It turns out that there is a link of the EPLT with the climacogram, and of the CEPLT with two additional tools introduced here, namely the differenced climacogram and the climacospectrum. In particular, EPLT and CEPLT are related to slopes of log-log plots of these tools, with the asymptotic slopes at the tails being most important as they justify the emergence of scaling laws of second-order characteristics of stochastic processes. As a real-world application, we use an extraordinary long time series of turbulent velocity and show how a parsimonious stochastic model can be identified and fitted using the tools developed.

  13. System Entropy Measurement of Stochastic Partial Differential Systems

    Directory of Open Access Journals (Sweden)

    Bor-Sen Chen

    2016-03-01

    Full Text Available System entropy describes the dispersal of a system’s energy and is an indication of the disorder of a physical system. Several system entropy measurement methods have been developed for dynamic systems. However, most real physical systems are always modeled using stochastic partial differential dynamic equations in the spatio-temporal domain. No efficient method currently exists that can calculate the system entropy of stochastic partial differential systems (SPDSs in consideration of the effects of intrinsic random fluctuation and compartment diffusion. In this study, a novel indirect measurement method is proposed for calculating of system entropy of SPDSs using a Hamilton–Jacobi integral inequality (HJII-constrained optimization method. In other words, we solve a nonlinear HJII-constrained optimization problem for measuring the system entropy of nonlinear stochastic partial differential systems (NSPDSs. To simplify the system entropy measurement of NSPDSs, the global linearization technique and finite difference scheme were employed to approximate the nonlinear stochastic spatial state space system. This allows the nonlinear HJII-constrained optimization problem for the system entropy measurement to be transformed to an equivalent linear matrix inequalities (LMIs-constrained optimization problem, which can be easily solved using the MATLAB LMI-toolbox (MATLAB R2014a, version 8.3. Finally, several examples are presented to illustrate the system entropy measurement of SPDSs.

  14. Entropy budget of the earth,atmosphere and ocean system

    Institute of Scientific and Technical Information of China (English)

    GAN Zijun; YAN Youfangand; QI Yiquan

    2004-01-01

    The energy budget in the system of the earth, atmosphere and ocean conforms to the first law of thermodynamics, namely the law of conservation of energy, and it is balanced when the system is in a steady-state condition. However, the entropy budget following the second law of thermodynamics is unbalanced. In this paper, we deduce the expressions of entropy flux and re-estimate the earth, atmosphere and ocean annual mean entropy budget with the updated climatologically global mean energy budget and the climatologically air-sea flux data. The calculated results show that the earth system obtains a net influx of negative entropy (-1179.3 mWm-2K-1) from its surroundings, and the atmosphere and the ocean systems obtain a net input of negative entropy at about -537.4 mWm-2K-1 and -555.6 mWm-2K-1, respectively. Calculations of the entropy budget can provide some guidance for further understanding the spatial-temporal change of the local entropy flux, and the entropy production resulting from all kinds of irreversible processes inside these systems.

  15. ENTROPY FLOW CHARACTERISTICS ANALYSIS OF TYPHOON MATSA (0509)

    Institute of Scientific and Technical Information of China (English)

    XU Hui; LIU Chong-jian

    2008-01-01

    The evolution of Typhoon Matsa (0509) is examined in terms of entropy flow through an entropy balance equation derived from the Gibbs relation, according to the second law of thermodynamics. The entropy flows in the various significant stages of (genesis, development and decaying) during its evolution are diagnosed based on the outputs of the PSU/NCAR mesoscale model (known as MM5). The results show that: (1) the vertical spatial distribution of entropy flow for Matsa is characterized by a predominantly negative entropy flow in a large portion of the troposphere and a positive flow in the upper levels; (2) the fields of entropy flows at the middle troposphere (500 hPa) show that the growth of the typhoon is greatly dependent on the negative entropy flows from its surroundings; and (3) the simulated centres of heavy rainfall associated with the typhoon match well with the zones of large negative entropy flows, suggesting that they may be a significant indicator for severe weather events.

  16. MoNbTaV Medium-Entropy Alloy

    Directory of Open Access Journals (Sweden)

    Hongwei Yao

    2016-05-01

    Full Text Available Guided by CALPHAD (Calculation of Phase Diagrams modeling, the refractory medium-entropy alloy MoNbTaV was synthesized by vacuum arc melting under a high-purity argon atmosphere. A body-centered cubic solid solution phase was experimentally confirmed in the as-cast ingot using X-ray diffraction and scanning electron microscopy. The measured lattice parameter of the alloy (3.208 Å obeys the rule of mixtures (ROM, but the Vickers microhardness (4.95 GPa and the yield strength (1.5 GPa are about 4.5 and 4.6 times those estimated from the ROM, respectively. Using a simple model on solid solution strengthening predicts a yield strength of approximately 1.5 GPa. Thermodynamic analysis shows that the total entropy of the alloy is more than three times the configurational entropy at room temperature, and the entropy of mixing exhibits a small negative departure from ideal mixing.

  17. Analysis of entropy models with equality and inequality constraints

    Energy Technology Data Exchange (ETDEWEB)

    Jefferson, T R; Scott, C H

    1979-06-01

    Entropy models are emerging as valuable tools in the study of various social problems of spatial interaction. With the development of the modeling has come diversity. Increased flexibility in the model can be obtained by allowing certain constraints to be relaxed from equality to inequality. To provide a better understanding of these entropy models they are analyzed by geometric programming. Dual mathematical programs and algorithms are obtained. 7 references.

  18. A gravitational entropy proposal

    International Nuclear Information System (INIS)

    Clifton, Timothy; Tavakol, Reza; Ellis, George F R

    2013-01-01

    We propose a thermodynamically motivated measure of gravitational entropy based on the Bel–Robinson tensor, which has a natural interpretation as the effective super-energy–momentum tensor of free gravitational fields. The specific form of this measure differs depending on whether the gravitational field is Coulomb-like or wave-like, and reduces to the Bekenstein–Hawking value when integrated over the interior of a Schwarzschild black hole. For scalar perturbations of a Robertson–Walker geometry we find that the entropy goes like the Hubble weighted anisotropy of the gravitational field, and therefore increases as structure formation occurs. This is in keeping with our expectations for the behaviour of gravitational entropy in cosmology, and provides a thermodynamically motivated arrow of time for cosmological solutions of Einstein’s field equations. It is also in keeping with Penrose’s Weyl curvature hypothesis. (paper)

  19. Microscopic entropy and nonlocality

    International Nuclear Information System (INIS)

    Karpov, E.; Ordonets, G.; Petroskij, T.; Prigozhin, I.

    2003-01-01

    We have obtained a microscopic expression for entropy in terms of H function based on nonunitary Λ transformation which leads from the time evolution as a unitary group to a Markovian dynamics and unifies the reversible and irreversible aspects of quantum mechanics. This requires a new representation outside the Hilbert space. In terms of H, we show the entropy production and the entropy flow during the emission and absorption of radiation by an atom. Analyzing the time inversion experiment, we emphasize the importance of pre- and postcollisional correlations, which break the symmetry between incoming and outgoing waves. We consider the angle dependence of the H function in a three-dimensional situation. A model including virtual transitions is discussed in a subsequent paper

  20. Parametric Bayesian Estimation of Differential Entropy and Relative Entropy

    OpenAIRE

    Gupta; Srivastava

    2010-01-01

    Given iid samples drawn from a distribution with known parametric form, we propose the minimization of expected Bregman divergence to form Bayesian estimates of differential entropy and relative entropy, and derive such estimators for the uniform, Gaussian, Wishart, and inverse Wishart distributions. Additionally, formulas are given for a log gamma Bregman divergence and the differential entropy and relative entropy for the Wishart and inverse Wishart. The results, as always with Bayesian est...

  1. EEG entropy measures in anesthesia

    Science.gov (United States)

    Liang, Zhenhu; Wang, Yinghua; Sun, Xue; Li, Duan; Voss, Logan J.; Sleigh, Jamie W.; Hagihira, Satoshi; Li, Xiaoli

    2015-01-01

    Highlights: ► Twelve entropy indices were systematically compared in monitoring depth of anesthesia and detecting burst suppression.► Renyi permutation entropy performed best in tracking EEG changes associated with different anesthesia states.► Approximate Entropy and Sample Entropy performed best in detecting burst suppression. Objective: Entropy algorithms have been widely used in analyzing EEG signals during anesthesia. However, a systematic comparison of these entropy algorithms in assessing anesthesia drugs' effect is lacking. In this study, we compare the capability of 12 entropy indices for monitoring depth of anesthesia (DoA) and detecting the burst suppression pattern (BSP), in anesthesia induced by GABAergic agents. Methods: Twelve indices were investigated, namely Response Entropy (RE) and State entropy (SE), three wavelet entropy (WE) measures [Shannon WE (SWE), Tsallis WE (TWE), and Renyi WE (RWE)], Hilbert-Huang spectral entropy (HHSE), approximate entropy (ApEn), sample entropy (SampEn), Fuzzy entropy, and three permutation entropy (PE) measures [Shannon PE (SPE), Tsallis PE (TPE) and Renyi PE (RPE)]. Two EEG data sets from sevoflurane-induced and isoflurane-induced anesthesia respectively were selected to assess the capability of each entropy index in DoA monitoring and BSP detection. To validate the effectiveness of these entropy algorithms, pharmacokinetic/pharmacodynamic (PK/PD) modeling and prediction probability (Pk) analysis were applied. The multifractal detrended fluctuation analysis (MDFA) as a non-entropy measure was compared. Results: All the entropy and MDFA indices could track the changes in EEG pattern during different anesthesia states. Three PE measures outperformed the other entropy indices, with less baseline variability, higher coefficient of determination (R2) and prediction probability, and RPE performed best; ApEn and SampEn discriminated BSP best. Additionally, these entropy measures showed an advantage in computation

  2. Absence of log correction in entropy of large black holes

    Energy Technology Data Exchange (ETDEWEB)

    Ghosh, A., E-mail: amit.ghosh@saha.ac.in; Mitra, P., E-mail: parthasarathi.mitra@saha.ac.in

    2014-06-27

    Earlier calculations of black hole entropy in loop quantum gravity led to a dominant term proportional to the area, but there was a correction involving the logarithm of the area, the Chern–Simons level being assumed to be large. We find that the calculations yield an entropy proportional to the area eigenvalue with no such correction if the Chern–Simons level is finite, so that the area eigenvalue can be relatively large.

  3. Algebraic topological entropy

    International Nuclear Information System (INIS)

    Hudetz, T.

    1989-01-01

    As a 'by-product' of the Connes-Narnhofer-Thirring theory of dynamical entropy for (originally non-Abelian) nuclear C * -algebras, the well-known variational principle for topological entropy is eqivalently reformulated in purly algebraically defined terms for (separable) Abelian C * -algebras. This 'algebraic variational principle' should not only nicely illustrate the 'feed-back' of methods developed for quantum dynamical systems to the classical theory, but it could also be proved directly by 'algebraic' methods and could thus further simplify the original proof of the variational principle (at least 'in principle'). 23 refs. (Author)

  4. Combinatorial Image Entropy

    DEFF Research Database (Denmark)

    Yuri, Shtarkov; Justesen, Jørn

    1997-01-01

    The concept of entropy for an image on a discrete two dimensional grid is introduced. This concept is used as an information theoretic bound on the coding rate for the image. It is proved that this quantity exists as a limit for arbitrary sets satisfying certain conditions.......The concept of entropy for an image on a discrete two dimensional grid is introduced. This concept is used as an information theoretic bound on the coding rate for the image. It is proved that this quantity exists as a limit for arbitrary sets satisfying certain conditions....

  5. Maximum Entropy Fundamentals

    Directory of Open Access Journals (Sweden)

    F. Topsøe

    2001-09-01

    Full Text Available Abstract: In its modern formulation, the Maximum Entropy Principle was promoted by E.T. Jaynes, starting in the mid-fifties. The principle dictates that one should look for a distribution, consistent with available information, which maximizes the entropy. However, this principle focuses only on distributions and it appears advantageous to bring information theoretical thinking more prominently into play by also focusing on the "observer" and on coding. This view was brought forward by the second named author in the late seventies and is the view we will follow-up on here. It leads to the consideration of a certain game, the Code Length Game and, via standard game theoretical thinking, to a principle of Game Theoretical Equilibrium. This principle is more basic than the Maximum Entropy Principle in the sense that the search for one type of optimal strategies in the Code Length Game translates directly into the search for distributions with maximum entropy. In the present paper we offer a self-contained and comprehensive treatment of fundamentals of both principles mentioned, based on a study of the Code Length Game. Though new concepts and results are presented, the reading should be instructional and accessible to a rather wide audience, at least if certain mathematical details are left aside at a rst reading. The most frequently studied instance of entropy maximization pertains to the Mean Energy Model which involves a moment constraint related to a given function, here taken to represent "energy". This type of application is very well known from the literature with hundreds of applications pertaining to several different elds and will also here serve as important illustration of the theory. But our approach reaches further, especially regarding the study of continuity properties of the entropy function, and this leads to new results which allow a discussion of models with so-called entropy loss. These results have tempted us to speculate over

  6. Maximum entropy methods

    International Nuclear Information System (INIS)

    Ponman, T.J.

    1984-01-01

    For some years now two different expressions have been in use for maximum entropy image restoration and there has been some controversy over which one is appropriate for a given problem. Here two further entropies are presented and it is argued that there is no single correct algorithm. The properties of the four different methods are compared using simple 1D simulations with a view to showing how they can be used together to gain as much information as possible about the original object. (orig.)

  7. Entanglement entropy and duality

    Energy Technology Data Exchange (ETDEWEB)

    Radičević, Ðorđe [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA 94305-4060 (United States)

    2016-11-22

    Using the algebraic approach to entanglement entropy, we study several dual pairs of lattice theories and show how the entropy is completely preserved across each duality. Our main result is that a maximal algebra of observables in a region typically dualizes to a non-maximal algebra in a dual region. In particular, we show how the usual notion of tracing out external degrees of freedom dualizes to a tracing out coupled to an additional summation over superselection sectors. We briefly comment on possible extensions of our results to more intricate dualities, including holographic ones.

  8. Maximum entropy tokamak configurations

    International Nuclear Information System (INIS)

    Minardi, E.

    1989-01-01

    The new entropy concept for the collective magnetic equilibria is applied to the description of the states of a tokamak subject to ohmic and auxiliary heating. The condition for the existence of steady state plasma states with vanishing entropy production implies, on one hand, the resilience of specific current density profiles and, on the other, severe restrictions on the scaling of the confinement time with power and current. These restrictions are consistent with Goldston scaling and with the existence of a heat pinch. (author)

  9. Algebraic entropy for algebraic maps

    International Nuclear Information System (INIS)

    Hone, A N W; Ragnisco, Orlando; Zullo, Federico

    2016-01-01

    We propose an extension of the concept of algebraic entropy, as introduced by Bellon and Viallet for rational maps, to algebraic maps (or correspondences) of a certain kind. The corresponding entropy is an index of the complexity of the map. The definition inherits the basic properties from the definition of entropy for rational maps. We give an example with positive entropy, as well as two examples taken from the theory of Bäcklund transformations. (letter)

  10. 2D Tsallis Entropy for Image Segmentation Based on Modified Chaotic Bat Algorithm

    Directory of Open Access Journals (Sweden)

    Zhiwei Ye

    2018-03-01

    Full Text Available Image segmentation is a significant step in image analysis and computer vision. Many entropy based approaches have been presented in this topic; among them, Tsallis entropy is one of the best performing methods. However, 1D Tsallis entropy does not consider make use of the spatial correlation information within the neighborhood results might be ruined by noise. Therefore, 2D Tsallis entropy is proposed to solve the problem, and results are compared with 1D Fisher, 1D maximum entropy, 1D cross entropy, 1D Tsallis entropy, fuzzy entropy, 2D Fisher, 2D maximum entropy and 2D cross entropy. On the other hand, due to the existence of huge computational costs, meta-heuristics algorithms like genetic algorithm (GA, particle swarm optimization (PSO, ant colony optimization algorithm (ACO and differential evolution algorithm (DE are used to accelerate the 2D Tsallis entropy thresholding method. In this paper, considering 2D Tsallis entropy as a constrained optimization problem, the optimal thresholds are acquired by maximizing the objective function using a modified chaotic Bat algorithm (MCBA. The proposed algorithm has been tested on some actual and infrared images. The results are compared with that of PSO, GA, ACO and DE and demonstrate that the proposed method outperforms other approaches involved in the paper, which is a feasible and effective option for image segmentation.

  11. A Note on Quantum Entropy

    International Nuclear Information System (INIS)

    Hansen, Frank

    2016-01-01

    Incremental information, as measured by the quantum entropy, is increasing when two ensembles are united. This result was proved by Lieb and Ruskai, and it is the foundation for the proof of strong subadditivity of quantum entropy. We present a truly elementary proof of this fact in the context of the broader family of matrix entropies introduced by Chen and Tropp.

  12. A Note on Quantum Entropy

    Energy Technology Data Exchange (ETDEWEB)

    Hansen, Frank, E-mail: frank.hansen@m.tohoku.ac.jp [Tohoku University, Institute for Excellence in Higher Education (Japan)

    2016-06-15

    Incremental information, as measured by the quantum entropy, is increasing when two ensembles are united. This result was proved by Lieb and Ruskai, and it is the foundation for the proof of strong subadditivity of quantum entropy. We present a truly elementary proof of this fact in the context of the broader family of matrix entropies introduced by Chen and Tropp.

  13. Relations Among Some Fuzzy Entropy Formulae

    Institute of Scientific and Technical Information of China (English)

    卿铭

    2004-01-01

    Fuzzy entropy has been widely used to analyze and design fuzzy systems, and many fuzzy entropy formulae have been proposed. For further in-deepth analysis of fuzzy entropy, the axioms and some important formulae of fuzzy entropy are introduced. Some equivalence results among these fuzzy entropy formulae are proved, and it is shown that fuzzy entropy is a special distance measurement.

  14. Entropie analysis of floating car data systems

    Directory of Open Access Journals (Sweden)

    F. Gössel

    2004-01-01

    Full Text Available The knowledge of the actual traffic state is a basic prerequisite of modern traffic telematic systems. Floating Car Data (FCD systems are becoming more and more important for the provision of actual and reliable traffic data. In these systems the vehicle velocity is the original variable for the evaluation of the current traffic condition. As real FCDsystems are operating under conditions of limited transmission and processing capacity the analysis of the original variable vehicle speed is of special interest. Entropy considerations are especially useful for the deduction of fundamental restrictions and limitations. The paper analyses velocity-time profiles by means of information entropy. It emphasises in quantification of the information content of velocity-time profiles and the discussion of entropy dynamic in velocity-time profiles. Investigations are based on empirical data derived during field trials. The analysis of entropy dynamic is carried out in two different ways. On one hand velocity differences within a certain interval of time are used, on the other hand the transinformation between velocities in certain time distances was evaluated. One important result is an optimal sample-rate for the detection of velocity data in FCD-systems. The influence of spatial segmentation and of different states of traffic was discussed.

  15. Dynamical maximum entropy approach to flocking.

    Science.gov (United States)

    Cavagna, Andrea; Giardina, Irene; Ginelli, Francesco; Mora, Thierry; Piovani, Duccio; Tavarone, Raffaele; Walczak, Aleksandra M

    2014-04-01

    We derive a new method to infer from data the out-of-equilibrium alignment dynamics of collectively moving animal groups, by considering the maximum entropy model distribution consistent with temporal and spatial correlations of flight direction. When bird neighborhoods evolve rapidly, this dynamical inference correctly learns the parameters of the model, while a static one relying only on the spatial correlations fails. When neighbors change slowly and the detailed balance is satisfied, we recover the static procedure. We demonstrate the validity of the method on simulated data. The approach is applicable to other systems of active matter.

  16. Entropy à la Boltzmann

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 9. Entropy à la Boltzmann. Jayanta K Bhattacharjee. General Article Volume 6 Issue 9 September 2001 pp 19-34. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/006/09/0019-0034 ...

  17. Entropy in Physics

    Indian Academy of Sciences (India)

    Consider the integral. taken over a reversible transformation. We shall call this function the entropy of state A.” 'Thermodynamics' by Enrico Fermi. “Let Γ be the volume of the region of motion of the states, and. This is the basic assumption of ...

  18. Rescaling Temperature and Entropy

    Science.gov (United States)

    Olmsted, John, III

    2010-01-01

    Temperature and entropy traditionally are expressed in units of kelvin and joule/kelvin. These units obscure some important aspects of the natures of these thermodynamic quantities. Defining a rescaled temperature using the Boltzmann constant, T' = k[subscript B]T, expresses temperature in energy units, thereby emphasizing the close relationship…

  19. Optimized Kernel Entropy Components.

    Science.gov (United States)

    Izquierdo-Verdiguier, Emma; Laparra, Valero; Jenssen, Robert; Gomez-Chova, Luis; Camps-Valls, Gustau

    2017-06-01

    This brief addresses two main issues of the standard kernel entropy component analysis (KECA) algorithm: the optimization of the kernel decomposition and the optimization of the Gaussian kernel parameter. KECA roughly reduces to a sorting of the importance of kernel eigenvectors by entropy instead of variance, as in the kernel principal components analysis. In this brief, we propose an extension of the KECA method, named optimized KECA (OKECA), that directly extracts the optimal features retaining most of the data entropy by means of compacting the information in very few features (often in just one or two). The proposed method produces features which have higher expressive power. In particular, it is based on the independent component analysis framework, and introduces an extra rotation to the eigen decomposition, which is optimized via gradient-ascent search. This maximum entropy preservation suggests that OKECA features are more efficient than KECA features for density estimation. In addition, a critical issue in both the methods is the selection of the kernel parameter, since it critically affects the resulting performance. Here, we analyze the most common kernel length-scale selection criteria. The results of both the methods are illustrated in different synthetic and real problems. Results show that OKECA returns projections with more expressive power than KECA, the most successful rule for estimating the kernel parameter is based on maximum likelihood, and OKECA is more robust to the selection of the length-scale parameter in kernel density estimation.

  20. On Using Entropy for Enhancing Handwriting Preprocessing

    Directory of Open Access Journals (Sweden)

    Bernhard Peischl

    2012-11-01

    Full Text Available Handwriting is an important modality for Human-Computer Interaction. For medical professionals, handwriting is (still the preferred natural method of documentation. Handwriting recognition has long been a primary research area in Computer Science. With the tremendous ubiquity of smartphones, along with the renaissance of the stylus, handwriting recognition has become a new impetus. However, recognition rates are still not 100% perfect, and researchers still are constantly improving handwriting algorithms. In this paper we evaluate the performance of entropy based slant- and skew-correction, and compare the results to other methods. We selected 3700 words of 23 writers out of the Unipen-ICROW-03 benchmark set, which we annotated with their associated error angles by hand. Our results show that the entropy-based slant correction method outperforms a window based approach with an average precision of 6:02 for the entropy-based method, compared with the 7:85 for the alternative. On the other hand, the entropy-based skew correction yields a lower average precision of 2:86, compared with the average precision of 2:13 for the alternative LSM based approach.

  1. Entropy and cosmology.

    Science.gov (United States)

    Zucker, M. H.

    This paper is a critical analysis and reassessment of entropic functioning as it applies to the question of whether the ultimate fate of the universe will be determined in the future to be "open" (expanding forever to expire in a big chill), "closed" (collapsing to a big crunch), or "flat" (balanced forever between the two). The second law of thermodynamics declares that entropy can only increase and that this principle extends, inevitably, to the universe as a whole. This paper takes the position that this extension is an unwarranted projection based neither on experience nonfact - an extrapolation that ignores the powerful effect of a gravitational force acting within a closed system. Since it was originally presented by Clausius, the thermodynamic concept of entropy has been redefined in terms of "order" and "disorder" - order being equated with a low degree of entropy and disorder with a high degree. This revised terminology more subjective than precise, has generated considerable confusion in cosmology in several critical instances. For example - the chaotic fireball of the big bang, interpreted by Stephen Hawking as a state of disorder (high entropy), is infinitely hot and, thermally, represents zero entropy (order). Hawking, apparently focusing on the disorderly "chaotic" aspect, equated it with a high degree of entropy - overlooking the fact that the universe is a thermodynamic system and that the key factor in evaluating the big-bang phenomenon is the infinitely high temperature at the early universe, which can only be equated with zero entropy. This analysis resolves this confusion and reestablishes entropy as a cosmological function integrally linked to temperature. The paper goes on to show that, while all subsystems contained within the universe require external sources of energization to have their temperatures raised, this requirement does not apply to the universe as a whole. The universe is the only system that, by itself can raise its own

  2. Temporal Correlations and Neural Spike Train Entropy

    International Nuclear Information System (INIS)

    Schultz, Simon R.; Panzeri, Stefano

    2001-01-01

    Sampling considerations limit the experimental conditions under which information theoretic analyses of neurophysiological data yield reliable results. We develop a procedure for computing the full temporal entropy and information of ensembles of neural spike trains, which performs reliably for limited samples of data. This approach also yields insight to the role of correlations between spikes in temporal coding mechanisms. The method, when applied to recordings from complex cells of the monkey primary visual cortex, results in lower rms error information estimates in comparison to a 'brute force' approach

  3. Entropy equilibrium equation and dynamic entropy production in environment liquid

    Institute of Scientific and Technical Information of China (English)

    2002-01-01

    The entropy equilibrium equation is the basis of the nonequilibrium state thermodynamics. But the internal energy implies the kinetic energy of the fluid micelle relative to mass center in the classical entropy equilibrium equation at present. This internal energy is not the mean kinetic energy of molecular movement in thermodynamics. Here a modified entropy equilibrium equation is deduced, based on the concept that the internal energy is just the mean kinetic energy of the molecular movement. A dynamic entropy production is introduced into the entropy equilibrium equation to describe the dynamic process distinctly. This modified entropy equilibrium equation can describe not only the entropy variation of the irreversible processes but also the reversible processes in a thermodynamic system. It is more reasonable and suitable for wider applications.

  4. Entropy, neutro-entropy and anti-entropy for neutrosophic information

    OpenAIRE

    Vasile Patrascu

    2017-01-01

    This approach presents a multi-valued representation of the neutrosophic information. It highlights the link between the bifuzzy information and neutrosophic one. The constructed deca-valued structure shows the neutrosophic information complexity. This deca-valued structure led to construction of two new concepts for the neutrosophic information: neutro-entropy and anti-entropy. These two concepts are added to the two existing: entropy and non-entropy. Thus, we obtained the following triad: e...

  5. Calculation of von Neumann entropy for hydrogen and positronium negative ions

    International Nuclear Information System (INIS)

    Lin, Chien-Hao; Ho, Yew Kam

    2014-01-01

    In the present work, we carry out calculations of von Neumann entropies and linear entropies for the hydrogen negative ion and the positronium negative ion. We concentrate on the spatial (electron–electron orbital) entanglement in these ions by using highly correlated Hylleraas functions to represent their ground states, and to take care of correlation effects. We apply the Schmidt decomposition method on the partial-wave expanded two-electron wave functions, and from which the one-particle reduced density matrix can be obtained, leading to the quantifications of linear entropy and von Neumann entropy in the H − and Ps − ions. - Highlights: • We calculate von Neumann entropies and linear entropies for hydrogen and positronium negative ions. • We employ highly correlated Hylleraas functions to take into account of correlation effects. • Spatial (electron–electron orbital) entanglement is quantified using the Schmidt decomposition method. • The eigenvalues of the one-particle reduced density matrix are calculated

  6. Entropy, neutro-entropy and anti-entropy for neutrosophic information

    OpenAIRE

    Vasile Patrascu

    2017-01-01

    This article shows a deca-valued representation of neutrosophic information in which are defined the following features: truth, falsity, weak truth, weak falsity, ignorance, contradiction, saturation, neutrality, ambiguity and hesitation. Using these features, there are constructed computing formulas for entropy, neutro-entropy and anti-entropy.

  7. The different paths to entropy

    International Nuclear Information System (INIS)

    Benguigui, L

    2013-01-01

    In order to understand how the complex concept of entropy emerged, we propose a trip into the past, reviewing the works of Clausius, Boltzmann, Gibbs and Planck. In particular, since Gibbs's work is not very well known we present a detailed analysis, recalling the three definitions of entropy that Gibbs gives. The introduction of entropy in quantum mechanics gives in a compact form all the classical definitions of entropy. Perhaps one of the most important aspects of entropy is to see it as a thermodynamic potential like the others proposed by Callen. The calculation of fluctuations in thermodynamic quantities is thus naturally related to entropy. We close with some remarks on entropy and irreversibility. (paper)

  8. Entropies from Markov Models as Complexity Measures of Embedded Attractors

    Directory of Open Access Journals (Sweden)

    Julián D. Arias-Londoño

    2015-06-01

    Full Text Available This paper addresses the problem of measuring complexity from embedded attractors as a way to characterize changes in the dynamical behavior of different types of systems with a quasi-periodic behavior by observing their outputs. With the aim of measuring the stability of the trajectories of the attractor along time, this paper proposes three new estimations of entropy that are derived from a Markov model of the embedded attractor. The proposed estimators are compared with traditional nonparametric entropy measures, such as approximate entropy, sample entropy and fuzzy entropy, which only take into account the spatial dimension of the trajectory. The method proposes the use of an unsupervised algorithm to find the principal curve, which is considered as the “profile trajectory”, that will serve to adjust the Markov model. The new entropy measures are evaluated using three synthetic experiments and three datasets of physiological signals. In terms of consistency and discrimination capabilities, the results show that the proposed measures perform better than the other entropy measures used for comparison purposes.

  9. Fractal Structure and Entropy Production within the Central Nervous System

    Directory of Open Access Journals (Sweden)

    Andrew J. E. Seely

    2014-08-01

    Full Text Available Our goal is to explore the relationship between two traditionally unrelated concepts, fractal structure and entropy production, evaluating both within the central nervous system (CNS. Fractals are temporal or spatial structures with self-similarity across scales of measurement; whereas entropy production represents the necessary exportation of entropy to our environment that comes with metabolism and life. Fractals may be measured by their fractal dimension; and human entropy production may be estimated by oxygen and glucose metabolism. In this paper, we observe fractal structures ubiquitously present in the CNS, and explore a hypothetical and unexplored link between fractal structure and entropy production, as measured by oxygen and glucose metabolism. Rapid increase in both fractal structures and metabolism occur with childhood and adolescent growth, followed by slow decrease during aging. Concomitant increases and decreases in fractal structure and metabolism occur with cancer vs. Alzheimer’s and multiple sclerosis, respectively. In addition to fractals being related to entropy production, we hypothesize that the emergence of fractal structures spontaneously occurs because a fractal is more efficient at dissipating energy gradients, thus maximizing entropy production. Experimental evaluation and further understanding of limitations and necessary conditions are indicated to address broad scientific and clinical implications of this work.

  10. Refined generalized multiscale entropy analysis for physiological signals

    Science.gov (United States)

    Liu, Yunxiao; Lin, Youfang; Wang, Jing; Shang, Pengjian

    2018-01-01

    Multiscale entropy analysis has become a prevalent complexity measurement and been successfully applied in various fields. However, it only takes into account the information of mean values (first moment) in coarse-graining procedure. Then generalized multiscale entropy (MSEn) considering higher moments to coarse-grain a time series was proposed and MSEσ2 has been implemented. However, the MSEσ2 sometimes may yield an imprecise estimation of entropy or undefined entropy, and reduce statistical reliability of sample entropy estimation as scale factor increases. For this purpose, we developed the refined model, RMSEσ2, to improve MSEσ2. Simulations on both white noise and 1 / f noise show that RMSEσ2 provides higher entropy reliability and reduces the occurrence of undefined entropy, especially suitable for short time series. Besides, we discuss the effect on RMSEσ2 analysis from outliers, data loss and other concepts in signal processing. We apply the proposed model to evaluate the complexity of heartbeat interval time series derived from healthy young and elderly subjects, patients with congestive heart failure and patients with atrial fibrillation respectively, compared to several popular complexity metrics. The results demonstrate that RMSEσ2 measured complexity (a) decreases with aging and diseases, and (b) gives significant discrimination between different physiological/pathological states, which may facilitate clinical application.

  11. Holographic Entanglement Entropy

    CERN Document Server

    Rangamani, Mukund

    2016-01-01

    We review the developments in the past decade on holographic entanglement entropy, a subject that has garnered much attention owing to its potential to teach us about the emergence of spacetime in holography. We provide an introduction to the concept of entanglement entropy in quantum field theories, review the holographic proposals for computing the same, providing some justification for where these proposals arise from in the first two parts. The final part addresses recent developments linking entanglement and geometry. We provide an overview of the various arguments and technical developments that teach us how to use field theory entanglement to detect geometry. Our discussion is by design eclectic; we have chosen to focus on developments that appear to us most promising for further insights into the holographic map. This is a preliminary draft of a few chapters of a book which will appear sometime in the near future, to be published by Springer. The book in addition contains a discussion of application o...

  12. On the entanglement entropy for gauge theories

    International Nuclear Information System (INIS)

    Ghosh, Sudip; Soni, Ronak M; Trivedi, Sandip P.

    2015-01-01

    We propose a definition for the entanglement entropy of a gauge theory on a spatial lattice. Our definition applies to any subset of links in the lattice, and is valid for both Abelian and Non-Abelian gauge theories. For ℤ_N and U(1) theories, without matter, our definition agrees with a particular case of the definition given by Casini, Huerta and Rosabal. We also argue that in general, both for Abelian and Non-Abelian theories, our definition agrees with the entanglement entropy calculated using a definition of the replica trick. Our definition, however, does not agree with some standard ways to measure entanglement, like the number of Bell pairs which can be produced by entanglement distillation.

  13. Entropy region and convolution

    Czech Academy of Sciences Publication Activity Database

    Matúš, František; Csirmaz, L.

    2016-01-01

    Roč. 62, č. 11 (2016), s. 6007-6018 ISSN 0018-9448 R&D Projects: GA ČR GA13-20012S Institutional support: RVO:67985556 Keywords : entropy region * information-theoretic inequality * polymatroid Subject RIV: BD - Theory of Information Impact factor: 2.679, year: 2016 http://library.utia.cas.cz/separaty/2016/MTR/matus-0465564.pdf

  14. Equipartition of entropy production

    International Nuclear Information System (INIS)

    Tondeur, D.

    1990-01-01

    This paper deals with the optimal design or operation of heat and mass transfer processes and develops the following conjecture: for a given duty, the best configuration of the process is that in which the entropy production rate is most uniformly distributed. This principle is first analyzed in detail on the simple example of tubular heat exchangers, and within the framework of linear irreversible thermodynamics. A main result is established, which states that the total entropy production is minimal when the local production is uniformly distributed (equipartition). Corollaries then result, which relate the entropy production and the variance of its distribution to economic factors such as the duty, the exchange area, the fluid flow-rates, and the temperature changes. The equipartition principle is then extended to multiple independent variables (time and space), multicomponent transfer, and non-linear but concave flux vs force relationship. Chemical Engineering examples are discussed, where the equipartition property has been applied implicitly or explicitly: design of distillation plates, cyclic distillation, optimal state of feed, and flow-sheets in chromatographic separations. Finally, a generalization of the equipartition principle is proposed, for systems with a distributed design variable (such as the size of the various elements of a system). The optimal distribution of investment is such that the investment in each element (properly amortized) is equal to the cost of irreversible energy degradation in this element. This is equivalent to saying that the ratio of these two quantities is uniformly distributed over the system, and reduces to equipartition of entropy production when the cost factors are constant over the whole system

  15. Hyperspherical entanglement entropy

    International Nuclear Information System (INIS)

    Dowker, J S

    2010-01-01

    The coefficient of the log term in the entanglement entropy associated with hyperspherical surfaces in flat spacetime is shown to equal the conformal anomaly by conformally transforming Euclideanized spacetime to a sphere and using already existing formulae for the relevant heat-kernel coefficients after cyclic factoring. The result follows from the fact that the conformal anomaly on this lune has an extremum at the ordinary sphere limit. A proof is given. Agreement with a recent evaluation of the coefficient is found.

  16. Hyperspherical entanglement entropy

    Energy Technology Data Exchange (ETDEWEB)

    Dowker, J S, E-mail: dowker@man.ac.u [Theory Group, School of Physics and Astronomy, University of Manchester, Manchester (United Kingdom)

    2010-11-05

    The coefficient of the log term in the entanglement entropy associated with hyperspherical surfaces in flat spacetime is shown to equal the conformal anomaly by conformally transforming Euclideanized spacetime to a sphere and using already existing formulae for the relevant heat-kernel coefficients after cyclic factoring. The result follows from the fact that the conformal anomaly on this lune has an extremum at the ordinary sphere limit. A proof is given. Agreement with a recent evaluation of the coefficient is found.

  17. Entropy for Mechanically Vibrating Systems

    Science.gov (United States)

    Tufano, Dante

    The research contained within this thesis deals with the subject of entropy as defined for and applied to mechanically vibrating systems. This work begins with an overview of entropy as it is understood in the fields of classical thermodynamics, information theory, statistical mechanics, and statistical vibroacoustics. Khinchin's definition of entropy, which is the primary definition used for the work contained in this thesis, is introduced in the context of vibroacoustic systems. The main goal of this research is to to establish a mathematical framework for the application of Khinchin's entropy in the field of statistical vibroacoustics by examining the entropy context of mechanically vibrating systems. The introduction of this thesis provides an overview of statistical energy analysis (SEA), a modeling approach to vibroacoustics that motivates this work on entropy. The objective of this thesis is given, and followed by a discussion of the intellectual merit of this work as well as a literature review of relevant material. Following the introduction, an entropy analysis of systems of coupled oscillators is performed utilizing Khinchin's definition of entropy. This analysis develops upon the mathematical theory relating to mixing entropy, which is generated by the coupling of vibroacoustic systems. The mixing entropy is shown to provide insight into the qualitative behavior of such systems. Additionally, it is shown that the entropy inequality property of Khinchin's entropy can be reduced to an equality using the mixing entropy concept. This equality can be interpreted as a facet of the second law of thermodynamics for vibroacoustic systems. Following this analysis, an investigation of continuous systems is performed using Khinchin's entropy. It is shown that entropy analyses using Khinchin's entropy are valid for continuous systems that can be decomposed into a finite number of modes. The results are shown to be analogous to those obtained for simple oscillators

  18. Preimage entropy dimension of topological dynamical systems

    OpenAIRE

    Liu, Lei; Zhou, Xiaomin; Zhou, Xiaoyao

    2014-01-01

    We propose a new definition of preimage entropy dimension for continuous maps on compact metric spaces, investigate fundamental properties of the preimage entropy dimension, and compare the preimage entropy dimension with the topological entropy dimension. The defined preimage entropy dimension holds various basic properties of topological entropy dimension, for example, the preimage entropy dimension of a subsystem is bounded by that of the original system and topologically conjugated system...

  19. Information and Entropy

    Science.gov (United States)

    Caticha, Ariel

    2007-11-01

    What is information? Is it physical? We argue that in a Bayesian theory the notion of information must be defined in terms of its effects on the beliefs of rational agents. Information is whatever constrains rational beliefs and therefore it is the force that induces us to change our minds. This problem of updating from a prior to a posterior probability distribution is tackled through an eliminative induction process that singles out the logarithmic relative entropy as the unique tool for inference. The resulting method of Maximum relative Entropy (ME), which is designed for updating from arbitrary priors given information in the form of arbitrary constraints, includes as special cases both MaxEnt (which allows arbitrary constraints) and Bayes' rule (which allows arbitrary priors). Thus, ME unifies the two themes of these workshops—the Maximum Entropy and the Bayesian methods—into a single general inference scheme that allows us to handle problems that lie beyond the reach of either of the two methods separately. I conclude with a couple of simple illustrative examples.

  20. Entropy and Quantum Gravity

    Directory of Open Access Journals (Sweden)

    Bernard S. Kay

    2015-12-01

    Full Text Available We give a review, in the style of an essay, of the author’s 1998 matter-gravity entanglement hypothesis which, unlike the standard approach to entropy based on coarse-graining, offers a definition for the entropy of a closed system as a real and objective quantity. We explain how this approach offers an explanation for the Second Law of Thermodynamics in general and a non-paradoxical understanding of information loss during black hole formation and evaporation in particular. It also involves a radically different from usual description of black hole equilibrium states in which the total state of a black hole in a box together with its atmosphere is a pure state—entangled in just such a way that the reduced state of the black hole and of its atmosphere are each separately approximately thermal. We also briefly recall some recent work of the author which involves a reworking of the string-theory understanding of black hole entropy consistent with this alternative description of black hole equilibrium states and point out that this is free from some unsatisfactory features of the usual string theory understanding. We also recall the author’s recent arguments based on this alternative description which suggest that the Anti de Sitter space (AdS/conformal field theory (CFT correspondence is a bijection between the boundary CFT and just the matter degrees of freedom of the bulk theory.

  1. Entanglement entropy and differential entropy for massive flavors

    International Nuclear Information System (INIS)

    Jones, Peter A.R.; Taylor, Marika

    2015-01-01

    In this paper we compute the holographic entanglement entropy for massive flavors in the D3-D7 system, for arbitrary mass and various entangling region geometries. We show that the universal terms in the entanglement entropy exactly match those computed in the dual theory using conformal perturbation theory. We derive holographically the universal terms in the entanglement entropy for a CFT perturbed by a relevant operator, up to second order in the coupling; our results are valid for any entangling region geometry. We present a new method for computing the entanglement entropy of any top-down brane probe system using Kaluza-Klein holography and illustrate our results with massive flavors at finite density. Finally we discuss the differential entropy for brane probe systems, emphasising that the differential entropy captures only the effective lower-dimensional Einstein metric rather than the ten-dimensional geometry.

  2. Logarithmic black hole entropy corrections and holographic Renyi entropy

    Energy Technology Data Exchange (ETDEWEB)

    Mahapatra, Subhash [The Institute of Mathematical Sciences, Chennai (India); KU Leuven - KULAK, Department of Physics, Kortrijk (Belgium)

    2018-01-15

    The entanglement and Renyi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Renyi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order G{sub D}{sup 0}. The entropic c-function and the inequalities of the Renyi entropy are also satisfied even with the correction terms. (orig.)

  3. Parametric Bayesian Estimation of Differential Entropy and Relative Entropy

    Directory of Open Access Journals (Sweden)

    Maya Gupta

    2010-04-01

    Full Text Available Given iid samples drawn from a distribution with known parametric form, we propose the minimization of expected Bregman divergence to form Bayesian estimates of differential entropy and relative entropy, and derive such estimators for the uniform, Gaussian, Wishart, and inverse Wishart distributions. Additionally, formulas are given for a log gamma Bregman divergence and the differential entropy and relative entropy for the Wishart and inverse Wishart. The results, as always with Bayesian estimates, depend on the accuracy of the prior parameters, but example simulations show that the performance can be substantially improved compared to maximum likelihood or state-of-the-art nonparametric estimators.

  4. Logarithmic black hole entropy corrections and holographic Renyi entropy

    International Nuclear Information System (INIS)

    Mahapatra, Subhash

    2018-01-01

    The entanglement and Renyi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Renyi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order G D 0 . The entropic c-function and the inequalities of the Renyi entropy are also satisfied even with the correction terms. (orig.)

  5. Black Hole Entropy with and without Log Correction in Loop Quantum Gravity

    International Nuclear Information System (INIS)

    Mitra, P.

    2014-01-01

    Earlier calculations of black hole entropy in loop quantum gravity have given a term proportional to the area with a correction involving the logarithm of the area when the area eigenvalue is close to the classical area. However the calculations yield an entropy proportional to the area eigenvalue with no such correction when the area eigenvalue is large compared to the classical area

  6. Entropy: From Thermodynamics to Hydrology

    Directory of Open Access Journals (Sweden)

    Demetris Koutsoyiannis

    2014-02-01

    Full Text Available Some known results from statistical thermophysics as well as from hydrology are revisited from a different perspective trying: (a to unify the notion of entropy in thermodynamic and statistical/stochastic approaches of complex hydrological systems and (b to show the power of entropy and the principle of maximum entropy in inference, both deductive and inductive. The capability for deductive reasoning is illustrated by deriving the law of phase change transition of water (Clausius-Clapeyron from scratch by maximizing entropy in a formal probabilistic frame. However, such deductive reasoning cannot work in more complex hydrological systems with diverse elements, yet the entropy maximization framework can help in inductive inference, necessarily based on data. Several examples of this type are provided in an attempt to link statistical thermophysics with hydrology with a unifying view of entropy.

  7. Credal Networks under Maximum Entropy

    OpenAIRE

    Lukasiewicz, Thomas

    2013-01-01

    We apply the principle of maximum entropy to select a unique joint probability distribution from the set of all joint probability distributions specified by a credal network. In detail, we start by showing that the unique joint distribution of a Bayesian tree coincides with the maximum entropy model of its conditional distributions. This result, however, does not hold anymore for general Bayesian networks. We thus present a new kind of maximum entropy models, which are computed sequentially. ...

  8. Modeling multisite streamflow dependence with maximum entropy copula

    Science.gov (United States)

    Hao, Z.; Singh, V. P.

    2013-10-01

    Synthetic streamflows at different sites in a river basin are needed for planning, operation, and management of water resources projects. Modeling the temporal and spatial dependence structure of monthly streamflow at different sites is generally required. In this study, the maximum entropy copula method is proposed for multisite monthly streamflow simulation, in which the temporal and spatial dependence structure is imposed as constraints to derive the maximum entropy copula. The monthly streamflows at different sites are then generated by sampling from the conditional distribution. A case study for the generation of monthly streamflow at three sites in the Colorado River basin illustrates the application of the proposed method. Simulated streamflow from the maximum entropy copula is in satisfactory agreement with observed streamflow.

  9. Relative information entropy in cosmology: The problem of information entanglement

    Energy Technology Data Exchange (ETDEWEB)

    Czinner, Viktor G., E-mail: czinner.viktor@wigner.mta.hu [Centro de Matemática, Universidade do Minho, Campus de Gualtar, 4710-057 Braga (Portugal); HAS Wigner Research Centre for Physics, H-1525 Budapest, P.O. Box 49 (Hungary); Mena, Filipe C., E-mail: fmena@math.uminho.pt [Centro de Matemática, Universidade do Minho, Campus de Gualtar, 4710-057 Braga (Portugal)

    2016-07-10

    The necessary information to distinguish a local inhomogeneous mass density field from its spatial average on a compact domain of the universe can be measured by relative information entropy. The Kullback–Leibler (KL) formula arises very naturally in this context, however, it provides a very complicated way to compute the mutual information between spatially separated but causally connected regions of the universe in a realistic, inhomogeneous model. To circumvent this issue, by considering a parametric extension of the KL measure, we develop a simple model to describe the mutual information which is entangled via the gravitational field equations. We show that the Tsallis relative entropy can be a good approximation in the case of small inhomogeneities, and for measuring the independent relative information inside the domain, we propose the Rényi relative entropy formula.

  10. Supersymmetric Renyi entropy in CFT{sub 2} and AdS{sub 3}

    Energy Technology Data Exchange (ETDEWEB)

    Giveon, Amit [Racah Institute of Physics, The Hebrew University,Jerusalem 91904 (Israel); Kutasov, David [EFI and Department of Physics, University of Chicago,5640 S. Ellis Av., Chicago, IL 60637 (United States)

    2016-01-08

    We show that in any two dimensional conformal field theory with (2,2) supersymmetry one can define a supersymmetric analog of the usual Renyi entropy of a spatial region A. It differs from the Renyi entropy by a universal function (which we compute) of the central charge, Renyi parameter n and the geometric parameters of A. In the limit n→1 it coincides with the entanglement entropy. Thus, it contains the same information as the Renyi entropy but its computation only involves correlation functions of chiral and anti-chiral operators. We also show that this quantity appears naturally in string theory on AdS{sub 3}.

  11. Editorial: Entropy in Landscape Ecology

    Directory of Open Access Journals (Sweden)

    Samuel A. Cushman

    2018-04-01

    Full Text Available Entropy and the second law of thermodynamics are the central organizing principles of nature, but the ideas and implications of the second law are poorly developed in landscape ecology. The purpose of this Special Issue “Entropy in Landscape Ecology” in Entropy is to bring together current research on applications of thermodynamics in landscape ecology, to consolidate current knowledge and identify key areas for future research. The special issue contains six articles, which cover a broad range of topics including relationships between entropy and evolution, connections between fractal geometry and entropy, new approaches to calculate configurational entropy of landscapes, example analyses of computing entropy of landscapes, and using entropy in the context of optimal landscape planning. Collectively these papers provide a broad range of contributions to the nascent field of ecological thermodynamics. Formalizing the connections between entropy and ecology are in a very early stage, and that this special issue contains papers that address several centrally important ideas, and provides seminal work that will be a foundation for the future development of ecological and evolutionary thermodynamics.

  12. Nonextensive entropy interdisciplinary applications

    CERN Document Server

    Tsallis, Constantino

    2004-01-01

    A great variety of complex phenomena in many scientific fields exhibit power-law behavior, reflecting a hierarchical or fractal structure. Many of these phenomena seem to be susceptible to description using approaches drawn from thermodynamics or statistical mechanics, particularly approaches involving the maximization of entropy and of Boltzmann-Gibbs statistical mechanics and standard laws in a natural way. The book addresses the interdisciplinary applications of these ideas, and also on various phenomena that could possibly be quantitatively describable in terms of these ideas.

  13. Minimum Error Entropy Classification

    CERN Document Server

    Marques de Sá, Joaquim P; Santos, Jorge M F; Alexandre, Luís A

    2013-01-01

    This book explains the minimum error entropy (MEE) concept applied to data classification machines. Theoretical results on the inner workings of the MEE concept, in its application to solving a variety of classification problems, are presented in the wider realm of risk functionals. Researchers and practitioners also find in the book a detailed presentation of practical data classifiers using MEE. These include multi‐layer perceptrons, recurrent neural networks, complexvalued neural networks, modular neural networks, and decision trees. A clustering algorithm using a MEE‐like concept is also presented. Examples, tests, evaluation experiments and comparison with similar machines using classic approaches, complement the descriptions.

  14. Connecting complexity with spectral entropy using the Laplace transformed solution to the fractional diffusion equation

    Science.gov (United States)

    Liang, Yingjie; Chen, Wen; Magin, Richard L.

    2016-07-01

    Analytical solutions to the fractional diffusion equation are often obtained by using Laplace and Fourier transforms, which conveniently encode the order of the time and the space derivatives (α and β) as non-integer powers of the conjugate transform variables (s, and k) for the spectral and the spatial frequencies, respectively. This study presents a new solution to the fractional diffusion equation obtained using the Laplace transform and expressed as a Fox's H-function. This result clearly illustrates the kinetics of the underlying stochastic process in terms of the Laplace spectral frequency and entropy. The spectral entropy is numerically calculated by using the direct integration method and the adaptive Gauss-Kronrod quadrature algorithm. Here, the properties of spectral entropy are investigated for the cases of sub-diffusion and super-diffusion. We find that the overall spectral entropy decreases with the increasing α and β, and that the normal or Gaussian case with α = 1 and β = 2, has the lowest spectral entropy (i.e., less information is needed to describe the state of a Gaussian process). In addition, as the neighborhood over which the entropy is calculated increases, the spectral entropy decreases, which implies a spatial averaging or coarse graining of the material properties. Consequently, the spectral entropy is shown to provide a new way to characterize the temporal correlation of anomalous diffusion. Future studies should be designed to examine changes of spectral entropy in physical, chemical and biological systems undergoing phase changes, chemical reactions and tissue regeneration.

  15. Information Entropy Measures for Stand Structural Diversity:Joint Entropy

    Institute of Scientific and Technical Information of China (English)

    Lei Xiangdong; Lu Yuanchang

    2004-01-01

    Structural diversity is the key attribute of a stand. A set of biodiversity measures in ecology was introduced in forest management for describing stand structure, of which Shannon information entropy (Shannon index) has been the most widely used measure of species diversity. It is generally thought that tree size diversity could serve as a good proxy for height diversity. However, tree size diversity and height diversity for stand structure is not completely consistent. Stand diameter cannot reflect height information completely. Either tree size diversity or height diversity is one-dimensional information entropy measure. This paper discussed the method of multiple-dimensional information entropy measure with the concept of joint entropy. It is suggested that joint entropy is a good measure for describing overall stand structural diversity.

  16. Critical study on conventional concept of entropy

    International Nuclear Information System (INIS)

    Afridi, M.K.; Nizami, S.

    2006-01-01

    The concept of increase in entropy or disorder as a result of all natural processes has been critically reviewed on the basis of experimental facts and ongoing phenomena on our Globe. Similarly, order-disorder statements have also been judged under new and fresh look. In fact, these are not absolute but depend upon defining specific purpose and considering that whether that purpose is being served or not. The new concept has been elaborated by considering natural biological processes, spontaneous mixing of four different gases, distribution of four points in space and assembling of a packaged electronic gadget. Actually, this order-disorder dilemma is the result of not defining the specific purpose of a process which leads to so-called concept that disorder is increasing day by day in our universe. The traditional concept of entropy has been finally tested under heat exchange and probability considerations, which also yield no information to discern it as a measure of disorder. Consequently, increase of entropy translating into increase of disorder could not be applied to all natural processes especially the natural biological systems. (author)

  17. Uncertainty principle and informational entropy for partially coherent light

    NARCIS (Netherlands)

    Bastiaans, M.J.

    1986-01-01

    It is shown that, among all partially coherent wave fields having the same informational entropy, the product of the effective widths of the intensity functions in the space and the spatial-frequency domains takes its minimum value for a wave field with a Gaussian-shaped cross-spectral density

  18. Weak entropy inequalities and entropic convergence

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    A criterion for algebraic convergence of the entropy is presented and an algebraic convergence result for the entropy of an exclusion process is improved. A weak entropy inequality is considered and its relationship to entropic convergence is discussed.

  19. Entropy concentration and the empirical coding game

    NARCIS (Netherlands)

    Grünwald, P.D.

    2008-01-01

    We give a characterization of maximum entropy/minimum relative entropy inference by providing two 'strong entropy concentration' theorems. These theorems unify and generalize Jaynes''concentration phenomenon' and Van Campenhout and Cover's 'conditional limit theorem'. The theorems characterize

  20. Holographic entanglement entropy for the most general higher derivative gravity

    International Nuclear Information System (INIS)

    Miao, Rong-Xin; Guo, Wu-zhong

    2015-01-01

    The holographic entanglement entropy for the most general higher derivative gravity is investigated. We find a new type of Wald entropy, which appears on entangling surface without the rotational symmetry and reduces to usual Wald entropy on Killing horizon. Furthermore, we obtain a formal formula of HEE for the most general higher derivative gravity and work it out exactly for some squashed cones. As an important application, we derive HEE for gravitational action with one derivative of the curvature when the extrinsic curvature vanishes. We also study some toy models with non-zero extrinsic curvature. We prove that our formula yields the correct universal term of entanglement entropy for 4d CFTs. Furthermore, we solve the puzzle raised by Hung, Myers and Smolkin that the logarithmic term of entanglement entropy derived from Weyl anomaly of CFTs does not match the holographic result even if the extrinsic curvature vanishes. We find that such mismatch comes from the ‘anomaly of entropy’ of the derivative of curvature. After considering such contributions carefully, we resolve the puzzle successfully. In general, we need to fix the splitting problem for the conical metrics in order to derive the holographic entanglement entropy. We find that, at least for Einstein gravity, the splitting problem can be fixed by using equations of motion. How to derive the splittings for higher derivative gravity is a non-trivial and open question. For simplicity, we ignore the splitting problem in this paper and find that it does not affect our main results.

  1. On determining absolute entropy without quantum theory or the third law of thermodynamics

    Science.gov (United States)

    Steane, Andrew M.

    2016-04-01

    We employ classical thermodynamics to gain information about absolute entropy, without recourse to statistical methods, quantum mechanics or the third law of thermodynamics. The Gibbs-Duhem equation yields various simple methods to determine the absolute entropy of a fluid. We also study the entropy of an ideal gas and the ionization of a plasma in thermal equilibrium. A single measurement of the degree of ionization can be used to determine an unknown constant in the entropy equation, and thus determine the absolute entropy of a gas. It follows from all these examples that the value of entropy at absolute zero temperature does not need to be assigned by postulate, but can be deduced empirically.

  2. Characterization of time series via Rényi complexity-entropy curves

    Science.gov (United States)

    Jauregui, M.; Zunino, L.; Lenzi, E. K.; Mendes, R. S.; Ribeiro, H. V.

    2018-05-01

    One of the most useful tools for distinguishing between chaotic and stochastic time series is the so-called complexity-entropy causality plane. This diagram involves two complexity measures: the Shannon entropy and the statistical complexity. Recently, this idea has been generalized by considering the Tsallis monoparametric generalization of the Shannon entropy, yielding complexity-entropy curves. These curves have proven to enhance the discrimination among different time series related to stochastic and chaotic processes of numerical and experimental nature. Here we further explore these complexity-entropy curves in the context of the Rényi entropy, which is another monoparametric generalization of the Shannon entropy. By combining the Rényi entropy with the proper generalization of the statistical complexity, we associate a parametric curve (the Rényi complexity-entropy curve) with a given time series. We explore this approach in a series of numerical and experimental applications, demonstrating the usefulness of this new technique for time series analysis. We show that the Rényi complexity-entropy curves enable the differentiation among time series of chaotic, stochastic, and periodic nature. In particular, time series of stochastic nature are associated with curves displaying positive curvature in a neighborhood of their initial points, whereas curves related to chaotic phenomena have a negative curvature; finally, periodic time series are represented by vertical straight lines.

  3. Entropy and Economics

    Directory of Open Access Journals (Sweden)

    John Scales Avery

    2012-04-01

    Full Text Available In this essay, human society is regarded as a “superorganism”, analogous to colonies of social insects. The digestive system of the human superorganism is the global economy, which ingests both free energy and resources, and later excretes them in a degraded form. This process involves an increase in entropy. Early in the 20th century, both Frederick Soddy and Nicholas Georgescu-Roegen discussed the relationship between entropy and economics. Soddy called for an index system to regulate the money supply and a reform of the fractional reserve banking system, while Georgescu-Roegen pointed to the need for Ecological Economics, a steady-state economy, and population stabilization. As we reach the end of the fossil fuel era and as industrial growth falters, massive unemployment can only be avoided by responsible governmental action. The necessary steps include shifting labor to projects needed for a sustainable economy, dividing the available work fairly among those seeking employment, and reforming the practices of the financial sector.

  4. Save energy, without entropy

    International Nuclear Information System (INIS)

    Steinmeyer, D.

    1992-01-01

    When we talk about saving energy what we usually mean is not wasting work. What we try to do when we design a process, is to use work as effectively as possible. It's hard to do that if we can't see it clearly. This paper illustrates how work can be seen (or calculated) without imposing entropy as a screen in front of it. We've all heard that the second law tells us that the entropy of the universe is increasing, and we are left with the feeling that the universe is ultimately headed for chaos, but receive little other information from this statement. A slightly more useful statement of the second law is the work potential of the universe is decreasing. However, this statement carries a needlessly negative ring. A simplified definition of the second law is: It takes work to change things. With these two corollaries: We can calculate the theoretical minimum work needed for a given change; and We can express the value of all changes in terms of work

  5. Possible extended forms of thermodynamic entropy

    International Nuclear Information System (INIS)

    Sasa, Shin-ichi

    2014-01-01

    Thermodynamic entropy is determined by a heat measurement through the Clausius equality. The entropy then formalizes a fundamental limitation of operations by the second law of thermodynamics. The entropy is also expressed as the Shannon entropy of the microscopic degrees of freedom. Whenever an extension of thermodynamic entropy is attempted, we must pay special attention to how its three different aspects just mentioned are altered. In this paper, we discuss possible extensions of the thermodynamic entropy. (paper)

  6. Configurational entropy of glueball states

    Energy Technology Data Exchange (ETDEWEB)

    Bernardini, Alex E., E-mail: alexeb@ufscar.br [Departamento de Física, Universidade Federal de São Carlos, PO Box 676, 13565-905, São Carlos, SP (Brazil); Braga, Nelson R.F., E-mail: braga@if.ufrj.br [Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, RJ 21941-972 (Brazil); Rocha, Roldão da, E-mail: roldao.rocha@ufabc.edu.br [CMCC, Universidade Federal do ABC, UFABC, 09210-580, Santo André (Brazil)

    2017-02-10

    The configurational entropy of glueball states is calculated using a holographic description. Glueball states are represented by a supergravity dual picture, consisting of a 5-dimensional graviton–dilaton action of a dynamical holographic AdS/QCD model. The configurational entropy is studied as a function of the glueball spin and of the mass, providing information about the stability of the glueball states.

  7. Thermostatistical aspects of generalized entropies

    International Nuclear Information System (INIS)

    Fa, K.S.; Lenzi, E.K.

    2004-01-01

    We investigate the properties concerning a class of generalized entropies given by S q,r =k{1-[Σ i p i q ] r }/[r(q-1)] which include Tsallis' entropy (r=1), the usual Boltzmann-Gibbs entropy (q=1), Renyi's entropy (r=0) and normalized Tsallis' entropy (r=-1). In order to obtain the generalized thermodynamic relations we use the laws of thermodynamics and considering the hypothesis that the joint probability of two independent systems is given by p ij A c upB =p i A p j B . We show that the transmutation which occurs from Tsallis' entropy to Renyi's entropy also occur with S q,r . In this scenario, we also analyze the generalized variance, covariance and correlation coefficient of a non-interacting system by using extended optimal Lagrange multiplier approach. We show that the correlation coefficient tends to zero in the thermodynamic limit. However, Renyi's entropy related to this non-interacting system presents a certain degree of non-extensivity

  8. Entropy statistics and information theory

    NARCIS (Netherlands)

    Frenken, K.; Hanusch, H.; Pyka, A.

    2007-01-01

    Entropy measures provide important tools to indicate variety in distributions at particular moments in time (e.g., market shares) and to analyse evolutionary processes over time (e.g., technical change). Importantly, entropy statistics are suitable to decomposition analysis, which renders the

  9. Black brane entropy and hydrodynamics

    NARCIS (Netherlands)

    Booth, I.; Heller, M.P.; Spaliński, M.

    2010-01-01

    A generalization of entropy to near-equilibrium phenomena is provided by the notion of a hydrodynamic entropy current. Recent advances in holography have lead to the formulation of fluid-gravity duality, a remarkable connection between the hydrodynamics of certain strongly coupled media and dynamics

  10. Black brane entropy and hydrodynamics

    NARCIS (Netherlands)

    Booth, I.; Heller, M.P.; Spaliński, M.

    2011-01-01

    A generalization of entropy to near-equilibrium phenomena is provided by the notion of a hydrodynamic entropy current. Recent advances in holography have lead to the formulation of fluid-gravity duality, a remarkable connection between the hydrodynamics of certain strongly coupled media and dynamics

  11. High Entropy Random Selection Protocols

    NARCIS (Netherlands)

    H. Buhrman (Harry); M. Christandl (Matthias); M. Koucky (Michal); Z. Lotker (Zvi); B. Patt-Shamir; M. Charikar; K. Jansen; O. Reingold; J. Rolim

    2007-01-01

    textabstractIn this paper, we construct protocols for two parties that do not trust each other, to generate random variables with high Shannon entropy. We improve known bounds for the trade off between the number of rounds, length of communication and the entropy of the outcome.

  12. Absolute entropy of ions in methanol

    International Nuclear Information System (INIS)

    Abakshin, V.A.; Kobenin, V.A.; Krestov, G.A.

    1978-01-01

    By measuring the initial thermoelectromotive forces of chains with bromo-silver electrodes in tetraalkylammonium bromide solutions the absolute entropy of bromide-ion in methanol is determined in the 298.15-318.15 K range. The anti Ssub(Brsup(-))sup(0) = 9.8 entropy units value is used for calculation of the absolute partial molar entropy of alkali metal ions and halogenide ions. It has been found that, absolute entropy of Cs + =12.0 entropy units, I - =14.0 entropy units. The obtained ion absolute entropies in methanol at 298.15 K within 1-2 entropy units is in an agreement with published data

  13. Entropy and equilibrium via games of complexity

    Science.gov (United States)

    Topsøe, Flemming

    2004-09-01

    It is suggested that thermodynamical equilibrium equals game theoretical equilibrium. Aspects of this thesis are discussed. The philosophy is consistent with maximum entropy thinking of Jaynes, but goes one step deeper by deriving the maximum entropy principle from an underlying game theoretical principle. The games introduced are based on measures of complexity. Entropy is viewed as minimal complexity. It is demonstrated that Tsallis entropy ( q-entropy) and Kaniadakis entropy ( κ-entropy) can be obtained in this way, based on suitable complexity measures. A certain unifying effect is obtained by embedding these measures in a two-parameter family of entropy functions.

  14. Entropy inequalities from reflection positivity

    International Nuclear Information System (INIS)

    Casini, H

    2010-01-01

    We investigate the question of whether the entropy and the Renyi entropies of the vacuum state reduced to a region of space can be represented in terms of correlators in quantum field theory. In this case, the positivity relations for the correlators are mapped into inequalities for the entropies. We write them using a real-time version of reflection positivity, which can be generalized to general quantum systems. Using this generalization we can prove an infinite sequence of inequalities which are obeyed by the Renyi entropies of integer index. There is one independent inequality involving any number of different subsystems. In quantum field theory the inequalities acquire a simple geometrical form and are consistent with the integer index Renyi entropies being given by vacuum expectation values of twisting operators in the Euclidean formulation. Several possible generalizations and specific examples are analyzed

  15. Entropy Budget for Hawking Evaporation

    Directory of Open Access Journals (Sweden)

    Ana Alonso-Serrano

    2017-07-01

    Full Text Available Blackbody radiation, emitted from a furnace and described by a Planck spectrum, contains (on average an entropy of 3 . 9 ± 2 . 5 bits per photon. Since normal physical burning is a unitary process, this amount of entropy is compensated by the same amount of “hidden information” in correlations between the photons. The importance of this result lies in the posterior extension of this argument to the Hawking radiation from black holes, demonstrating that the assumption of unitarity leads to a perfectly reasonable entropy/information budget for the evaporation process. In order to carry out this calculation, we adopt a variant of the “average subsystem” approach, but consider a tripartite pure system that includes the influence of the rest of the universe, and which allows “young” black holes to still have a non-zero entropy; which we identify with the standard Bekenstein entropy.

  16. Equity yields

    NARCIS (Netherlands)

    Vrugt, E.; van Binsbergen, J.H.; Koijen, R.S.J.; Hueskes, W.

    2013-01-01

    We study a new data set of dividend futures with maturities up to ten years across three world regions: the US, Europe, and Japan. We use these asset prices to construct equity yields, analogous to bond yields. We decompose the equity yields to obtain a term structure of expected dividend growth

  17. Tsallis-like entropies in quantum scattering

    International Nuclear Information System (INIS)

    Ion, D.B.; Ion, M.L.

    1998-01-01

    In this work, the following entropies in quantum scattering are defined: the informational angular entropy, S θ ; Tsallis-like angular entropies, S q (θ); the angular momentum entropy, S L ; the Tsallis-like angular momentum entropies, S q (L); the angle-angular momentum entropy, S θL . These entropies are defined as natural measures of the uncertainties corresponding to the distribution probabilities. If we are interested in obtaining a measure of uncertainty of the simultaneous realization of the probability distributions, than, we have to calculate the entropy corresponding to these distributions. The expression of angle-angular momentum entropy is given. The relation between the Tsallis entropies and the angle-angular momentum entropy is derived

  18. Introduction to maximum entropy

    International Nuclear Information System (INIS)

    Sivia, D.S.

    1988-01-01

    The maximum entropy (MaxEnt) principle has been successfully used in image reconstruction in a wide variety of fields. We review the need for such methods in data analysis and show, by use of a very simple example, why MaxEnt is to be preferred over other regularizing functions. This leads to a more general interpretation of the MaxEnt method, and its use is illustrated with several different examples. Practical difficulties with non-linear problems still remain, this being highlighted by the notorious phase problem in crystallography. We conclude with an example from neutron scattering, using data from a filter difference spectrometer to contrast MaxEnt with a conventional deconvolution. 12 refs., 8 figs., 1 tab

  19. Introduction to maximum entropy

    International Nuclear Information System (INIS)

    Sivia, D.S.

    1989-01-01

    The maximum entropy (MaxEnt) principle has been successfully used in image reconstruction in a wide variety of fields. The author reviews the need for such methods in data analysis and shows, by use of a very simple example, why MaxEnt is to be preferred over other regularizing functions. This leads to a more general interpretation of the MaxEnt method, and its use is illustrated with several different examples. Practical difficulties with non-linear problems still remain, this being highlighted by the notorious phase problem in crystallography. He concludes with an example from neutron scattering, using data from a filter difference spectrometer to contrast MaxEnt with a conventional deconvolution. 12 refs., 8 figs., 1 tab

  20. Entropy and galaxy clustering

    International Nuclear Information System (INIS)

    Kandrup, H.E.

    1988-01-01

    The notion of a p-particle entropy Sp introduced by Kandrup (1987) is applied here to a Newtonian cosmology modeled as an expanding system of identical point masses studying the time dependence of S1 and S2 in the framework of the linearized theory considered by Fall and Saslaw (1976). It is found that if, at some initial time t0, the galaxy-galaxy correlation function vanished, then S1(t0) = S2(t0). At least for short times t - t0 thereafter, S1 and Delta S = S1 - S2 increase on a characteristic time scale. For all times t after t0, S1(t) = S2(t) or greater. 13 references

  1. Black hole entropy and the problem of universality

    International Nuclear Information System (INIS)

    Carlip, Steven

    2007-01-01

    A key test of any quantum theory of gravity is its ability to reproduce the known thermodynamic properties of black holes. A statistical mechanical description of the Bekenstein-Hawking entropy once seemed remote, but today we suffer an embarrassment of riches: many different approaches to quantum gravity yield the same entropy, despite counting very different states. This 'universality' suggests that some underlying feature of the classical theory may control the quantum density of states. I discuss the possibility that this feature is an approximate two-dimensional conformal symmetry near the horizon

  2. Black hole entropy and the problem of universality

    Energy Technology Data Exchange (ETDEWEB)

    Carlip, Steven [Physics Department, 1 Shields Ave., University of California at Davis, Davis, CA 95616 (United States)

    2007-05-15

    A key test of any quantum theory of gravity is its ability to reproduce the known thermodynamic properties of black holes. A statistical mechanical description of the Bekenstein-Hawking entropy once seemed remote, but today we suffer an embarrassment of riches: many different approaches to quantum gravity yield the same entropy, despite counting very different states. This 'universality' suggests that some underlying feature of the classical theory may control the quantum density of states. I discuss the possibility that this feature is an approximate two-dimensional conformal symmetry near the horizon.

  3. Renormalized thermodynamic entropy of black holes in higher dimensions

    International Nuclear Information System (INIS)

    Kim, S.P.; Kim, S.K.; Soh, K.; Yee, J.H.

    1997-01-01

    We study the ultraviolet divergent structures of the matter (scalar) field in a higher D-dimensional Reissner-Nordstroem black hole and compute the matter field contribution to the Bekenstein-Hawking entropy by using the Pauli-Villars regularization method. We find that the matter field contribution to the black hole entropy does not, in general, yield the correct renormalization of the gravitational coupling constants. In particular, we show that the matter field contribution in odd dimensions does not give the term proportional to the area of the black hole event horizon. copyright 1997 The American Physical Society

  4. Bubble Entropy: An Entropy Almost Free of Parameters.

    Science.gov (United States)

    Manis, George; Aktaruzzaman, Md; Sassi, Roberto

    2017-11-01

    Objective : A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new definition of entropy aiming to reduce the significance of this selection. Methods: We call the new definition Bubble Entropy . Bubble Entropy is based on permutation entropy, where the vectors in the embedding space are ranked. We use the bubble sort algorithm for the ordering procedure and count instead the number of swaps performed for each vector. Doing so, we create a more coarse-grained distribution and then compute the entropy of this distribution. Results: Experimental results with both real and synthetic HRV signals showed that bubble entropy presents remarkable stability and exhibits increased descriptive and discriminating power compared to all other definitions, including the most popular ones. Conclusion: The definition proposed is almost free of parameters. The most common ones are the scale factor r and the embedding dimension m . In our definition, the scale factor is totally eliminated and the importance of m is significantly reduced. The proposed method presents increased stability and discriminating power. Significance: After the extensive use of some entropy measures in physiological signals, typical values for their parameters have been suggested, or at least, widely used. However, the parameters are still there, application and dataset dependent, influencing the computed value and affecting the descriptive power. Reducing their significance or eliminating them alleviates the problem, decoupling the method from the data and the application, and eliminating subjective factors. Objective : A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new definition of entropy aiming to reduce the significance of this selection. Methods: We call the new definition Bubble Entropy . Bubble Entropy is based on permutation

  5. The concept of entropy. Relation between action and entropy

    Directory of Open Access Journals (Sweden)

    J.-P.Badiali

    2005-01-01

    Full Text Available The Boltzmann expression for entropy represents the traditional link between thermodynamics and statistical mechanics. New theoretical developments like the Unruh effect or the black hole theory suggest a new definition of entropy. In this paper we consider the thermodynamics of black holes as seriously founded and we try to see what we can learn from it in the case of ordinary systems for which a pre-relativistic description is sufficient. We introduce a space-time model and a new definition of entropy considering the thermal equilibrium from a dynamic point of view. Then we show that for black hole and ordinary systems we have the same relation relating a change of entropy to a change of action.

  6. Zero modes and entanglement entropy

    Energy Technology Data Exchange (ETDEWEB)

    Yazdi, Yasaman K. [Perimeter Institute for Theoretical Physics,31 Caroline St. N., Waterloo, ON, N2L 2Y5 (Canada); Department of Physics and Astronomy, University of Waterloo,200 University Avenue West, Waterloo, ON, N2L 3G1 (Canada)

    2017-04-26

    Ultraviolet divergences are widely discussed in studies of entanglement entropy. Also present, but much less understood, are infrared divergences due to zero modes in the field theory. In this note, we discuss the importance of carefully handling zero modes in entanglement entropy. We give an explicit example for a chain of harmonic oscillators in 1D, where a mass regulator is necessary to avoid an infrared divergence due to a zero mode. We also comment on a surprising contribution of the zero mode to the UV-scaling of the entanglement entropy.

  7. Shannon's information is not entropy

    International Nuclear Information System (INIS)

    Schiffer, M.

    1990-01-01

    In this letter we clear up the long-standing misidentification of Shannon's Information with Entropy. We show that Information, in contrast to Entropy, is not invariant under unitary transformations and that these quantities are only equivalent for representations consisting of Hamiltonian eigenstates. We illustrate this fact through a toy system consisting of a harmonic oscillator in a coherent state. It is further proved that the representations which maximize the information are those which are energy-eigenstates. This fact sets the entropy as an upper bound for Shannon's Information. (author)

  8. Entropy Learning in Neural Network

    Directory of Open Access Journals (Sweden)

    Geok See Ng

    2017-12-01

    Full Text Available In this paper, entropy term is used in the learning phase of a neural network.  As learning progresses, more hidden nodes get into saturation.  The early creation of such hidden nodes may impair generalisation.  Hence entropy approach is proposed to dampen the early creation of such nodes.  The entropy learning also helps to increase the importance of relevant nodes while dampening the less important nodes.  At the end of learning, the less important nodes can then be eliminated to reduce the memory requirements of the neural network.

  9. On quantum Rényi entropies

    DEFF Research Database (Denmark)

    Müller-Lennert, Martin; Dupont-Dupuis, Fréderic; Szehr, Oleg

    2013-01-01

    The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies, or mutual information, and have found many applications in in...

  10. Dynamical entropy for infinite quantum systems

    International Nuclear Information System (INIS)

    Hudetz, T.

    1990-01-01

    We review the recent physical application of the so-called Connes-Narnhofer-Thirring entropy, which is the successful quantum mechanical generalization of the classical Kolmogorov-Sinai entropy and, by its very conception, is a dynamical entropy for infinite quantum systems. We thus comparingly review also the physical applications of the classical dynamical entropy for infinite classical systems. 41 refs. (Author)

  11. Short interval expansion of Rényi entropy on torus

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Bin [Department of Physics and State Key Laboratory of Nuclear Physics and Technology,Peking University,5 Yiheyuan Rd, Beijing 100871 (China); Collaborative Innovation Center of Quantum Matter,5 Yiheyuan Rd, Beijing 100871 (China); Center for High Energy Physics, Peking University,5 Yiheyuan Rd, Beijing 100871 (China); Wu, Jun-Bao [Theoretical Physics Division, Institute of High Energy Physics, Chinese Academy of Sciences,19B Yuquan Rd, Beijing 100049 (China); Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences,19B Yuquan Rd, Beijing 100049 (China); Center for High Energy Physics, Peking University,5 Yiheyuan Rd, Beijing 100871 (China); Zhang, Jia-ju [Theoretical Physics Division, Institute of High Energy Physics, Chinese Academy of Sciences,19B Yuquan Rd, Beijing 100049 (China); Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences,19B Yuquan Rd, Beijing 100049 (China)

    2016-08-23

    We investigate the short interval expansion of the Rényi entropy for two-dimensional conformal field theory (CFT) on a torus. We require the length of the interval ℓ to be small with respect to the spatial and temporal sizes of the torus. The operator product expansion of the twist operators allows us to compute the short interval expansion of the Rényi entropy at any temperature. In particular, we pay special attention to the large c CFTs dual to the AdS{sub 3} gravity and its cousins. At both low and high temperature limits, we read the Rényi entropies to order ℓ{sup 6}, and find good agreements with holographic results. Moreover, the expansion allows us to read 1/c contribution, which is hard to get by expanding the thermal density matrix. We generalize the study to the case with the chemical potential as well.

  12. A Note on Burg’s Modified Entropy in Statistical Mechanics

    Directory of Open Access Journals (Sweden)

    Amritansu Ray

    2016-02-01

    Full Text Available Burg’s entropy plays an important role in this age of information euphoria, particularly in understanding the emergent behavior of a complex system such as statistical mechanics. For discrete or continuous variable, maximization of Burg’s Entropy subject to its only natural and mean constraint always provide us a positive density function though the Entropy is always negative. On the other hand, Burg’s modified entropy is a better measure than the standard Burg’s entropy measure since this is always positive and there is no computational problem for small probabilistic values. Moreover, the maximum value of Burg’s modified entropy increases with the number of possible outcomes. In this paper, a premium has been put on the fact that if Burg’s modified entropy is used instead of conventional Burg’s entropy in a maximum entropy probability density (MEPD function, the result yields a better approximation of the probability distribution. An important lemma in basic algebra and a suitable example with tables and graphs in statistical mechanics have been given to illustrate the whole idea appropriately.

  13. Analysis of thermal systems using the entropy balance method

    Energy Technology Data Exchange (ETDEWEB)

    Huang, C L.D.; Fartaj, S A; Fenton, D L [Kansas State Univ., Manhattan, KS (United States). Dept. of Mechanical Engineering

    1992-04-01

    This study investigates the applicability of the second law of thermodynamics using an entropy balance method to analyse and design thermal systems. As examples, the entropy balance method is used to analyse a single stage chiller system and a single stage heat transformer, both with lithium-bromide/water as the working fluid. The entropy method yields not only the same information as is conveyed by the methods of energy and exergy analysis, but it also predicts clearly the influence of irreversibilities of individual components on the coefficient of performance and its effectiveness, based on the process properties, rather than on ambient conditions. Furthermore, this method is capable of presenting the overall distribution of the heat input by displaying the additional heat required to overcome irreversibility of each component without ambiguity. (Author).

  14. Classification of epileptic seizures using wavelet packet log energy and norm entropies with recurrent Elman neural network classifier.

    Science.gov (United States)

    Raghu, S; Sriraam, N; Kumar, G Pradeep

    2017-02-01

    Electroencephalogram shortly termed as EEG is considered as the fundamental segment for the assessment of the neural activities in the brain. In cognitive neuroscience domain, EEG-based assessment method is found to be superior due to its non-invasive ability to detect deep brain structure while exhibiting superior spatial resolutions. Especially for studying the neurodynamic behavior of epileptic seizures, EEG recordings reflect the neuronal activity of the brain and thus provide required clinical diagnostic information for the neurologist. This specific proposed study makes use of wavelet packet based log and norm entropies with a recurrent Elman neural network (REN) for the automated detection of epileptic seizures. Three conditions, normal, pre-ictal and epileptic EEG recordings were considered for the proposed study. An adaptive Weiner filter was initially applied to remove the power line noise of 50 Hz from raw EEG recordings. Raw EEGs were segmented into 1 s patterns to ensure stationarity of the signal. Then wavelet packet using Haar wavelet with a five level decomposition was introduced and two entropies, log and norm were estimated and were applied to REN classifier to perform binary classification. The non-linear Wilcoxon statistical test was applied to observe the variation in the features under these conditions. The effect of log energy entropy (without wavelets) was also studied. It was found from the simulation results that the wavelet packet log entropy with REN classifier yielded a classification accuracy of 99.70 % for normal-pre-ictal, 99.70 % for normal-epileptic and 99.85 % for pre-ictal-epileptic.

  15. Information loss in effective field theory: Entanglement and thermal entropies

    Science.gov (United States)

    Boyanovsky, Daniel

    2018-03-01

    Integrating out high energy degrees of freedom to yield a low energy effective field theory leads to a loss of information with a concomitant increase in entropy. We obtain the effective field theory of a light scalar field interacting with heavy fields after tracing out the heavy degrees of freedom from the time evolved density matrix. The initial density matrix describes the light field in its ground state and the heavy fields in equilibrium at a common temperature T . For T =0 , we obtain the reduced density matrix in a perturbative expansion; it reveals an emergent mixed state as a consequence of the entanglement between light and heavy fields. We obtain the effective action that determines the time evolution of the reduced density matrix for the light field in a nonperturbative Dyson resummation of one-loop correlations of the heavy fields. The Von-Neumann entanglement entropy associated with the reduced density matrix is obtained for the nonresonant and resonant cases in the asymptotic long time limit. In the nonresonant case the reduced density matrix displays an incipient thermalization albeit with a wave-vector, time and coupling dependent effective temperature as a consequence of memory of initial conditions. The entanglement entropy is time independent and is the thermal entropy for this effective, nonequilibrium temperature. In the resonant case the light field fully thermalizes with the heavy fields, the reduced density matrix loses memory of the initial conditions and the entanglement entropy becomes the thermal entropy of the light field. We discuss the relation between the entanglement entropy ultraviolet divergences and renormalization.

  16. Non-Equilibrium Heavy Flavored Hadron Yields from Chemical Equilibrium Strangeness-Rich QGP

    OpenAIRE

    Kuznetsova, Inga; Rafelski, Johann

    2008-01-01

    The yields of heavy flavored hadrons emitted from strangeness-rich QGP are evaluated within chemical non-equilibrium statistical hadronization model, conserving strangeness, charm, and entropy yields at hadronization.

  17. Phase transitions and quantum entropy

    International Nuclear Information System (INIS)

    Arrachea, L.; Canosa, N.; Plastino, A.; Portesi, M.; Rossignoli, R.

    1990-01-01

    An examination is made of the possibility to predict phase transitions of the fundamental state of finite quantum system, knowing the quantum entropy of these states, defined on the basis of the information theory. (Author). 7 refs., 3 figs

  18. Renyi entropy and conformal defects

    Energy Technology Data Exchange (ETDEWEB)

    Bianchi, Lorenzo [Humboldt-Univ. Berlin (Germany). Inst. fuer Physik; Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; Meineri, Marco [Scuola Normale Superiore, Pisa (Italy); Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); Istituto Nazionale di Fisica Nucleare, Pisa (Italy); Myers, Robert C. [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); Smolkin, Michael [California Univ., Berkely, CA (United States). Center for Theoretical Physics and Department of Physics

    2016-04-18

    We propose a field theoretic framework for calculating the dependence of Renyi entropies on the shape of the entangling surface in a conformal field theory. Our approach rests on regarding the corresponding twist operator as a conformal defect and in particular, we define the displacement operator which implements small local deformations of the entangling surface. We identify a simple constraint between the coefficient defining the two-point function of the displacement operator and the conformal weight of the twist operator, which consolidates a number of distinct conjectures on the shape dependence of the Renyi entropy. As an example, using this approach, we examine a conjecture regarding the universal coefficient associated with a conical singularity in the entangling surface for CFTs in any number of spacetime dimensions. We also provide a general formula for the second order variation of the Renyi entropy arising from small deformations of a spherical entangling surface, extending Mezei's results for the entanglement entropy.

  19. Quantum entropy and special relativity.

    Science.gov (United States)

    Peres, Asher; Scudo, Petra F; Terno, Daniel R

    2002-06-10

    We consider a single free spin- 1 / 2 particle. The reduced density matrix for its spin is not covariant under Lorentz transformations. The spin entropy is not a relativistic scalar and has no invariant meaning.

  20. Renyi entropy and conformal defects

    International Nuclear Information System (INIS)

    Bianchi, Lorenzo; Myers, Robert C.; Smolkin, Michael

    2016-01-01

    We propose a field theoretic framework for calculating the dependence of Renyi entropies on the shape of the entangling surface in a conformal field theory. Our approach rests on regarding the corresponding twist operator as a conformal defect and in particular, we define the displacement operator which implements small local deformations of the entangling surface. We identify a simple constraint between the coefficient defining the two-point function of the displacement operator and the conformal weight of the twist operator, which consolidates a number of distinct conjectures on the shape dependence of the Renyi entropy. As an example, using this approach, we examine a conjecture regarding the universal coefficient associated with a conical singularity in the entangling surface for CFTs in any number of spacetime dimensions. We also provide a general formula for the second order variation of the Renyi entropy arising from small deformations of a spherical entangling surface, extending Mezei's results for the entanglement entropy.

  1. Algorithmic randomness and physical entropy

    International Nuclear Information System (INIS)

    Zurek, W.H.

    1989-01-01

    Algorithmic randomness provides a rigorous, entropylike measure of disorder of an individual, microscopic, definite state of a physical system. It is defined by the size (in binary digits) of the shortest message specifying the microstate uniquely up to the assumed resolution. Equivalently, algorithmic randomness can be expressed as the number of bits in the smallest program for a universal computer that can reproduce the state in question (for instance, by plotting it with the assumed accuracy). In contrast to the traditional definitions of entropy, algorithmic randomness can be used to measure disorder without any recourse to probabilities. Algorithmic randomness is typically very difficult to calculate exactly but relatively easy to estimate. In large systems, probabilistic ensemble definitions of entropy (e.g., coarse-grained entropy of Gibbs and Boltzmann's entropy H=lnW, as well as Shannon's information-theoretic entropy) provide accurate estimates of the algorithmic entropy of an individual system or its average value for an ensemble. One is thus able to rederive much of thermodynamics and statistical mechanics in a setting very different from the usual. Physical entropy, I suggest, is a sum of (i) the missing information measured by Shannon's formula and (ii) of the algorithmic information content---algorithmic randomness---present in the available data about the system. This definition of entropy is essential in describing the operation of thermodynamic engines from the viewpoint of information gathering and using systems. These Maxwell demon-type entities are capable of acquiring and processing information and therefore can ''decide'' on the basis of the results of their measurements and computations the best strategy for extracting energy from their surroundings. From their internal point of view the outcome of each measurement is definite

  2. Proof of the holographic formula for entanglement entropy

    International Nuclear Information System (INIS)

    Fursaev, Dmitri V.

    2006-01-01

    Entanglement entropy for a spatial partition of a quantum system is studied in theories which admit a dual description in terms of the anti-de Sitter (AdS) gravity one dimension higher. A general proof of the holographic formula which relates the entropy to the area of a codimension 2 minimal hypersurface embedded in the bulk AdS space is given. The entanglement entropy is determined by a partition function which is defined as a path integral over Riemannian AdS geometries with non-trivial boundary conditions. The topology of the Riemannian spaces puts restrictions on the choice of the minimal hypersurface for a given boundary conditions. The entanglement entropy is also considered in Randall-Sundrum braneworld models where its asymptotic expansion is derived when the curvature radius of the brane is much larger than the AdS radius. Special attention is paid to the geometrical structure of anomalous terms in the entropy in four dimensions. Modification of the holographic formula by the higher curvature terms in the bulk is briefly discussed

  3. Applications of Entropy in Finance: A Review

    Directory of Open Access Journals (Sweden)

    Guanqun Tong

    2013-11-01

    Full Text Available Although the concept of entropy is originated from thermodynamics, its concepts and relevant principles, especially the principles of maximum entropy and minimum cross-entropy, have been extensively applied in finance. In this paper, we review the concepts and principles of entropy, as well as their applications in the field of finance, especially in portfolio selection and asset pricing. Furthermore, we review the effects of the applications of entropy and compare them with other traditional and new methods.

  4. Spontaneous entropy decrease and its statistical formula

    OpenAIRE

    Xing, Xiu-San

    2007-01-01

    Why can the world resist the law of entropy increase and produce self-organizing structure? Does the entropy of an isolated system always only increase and never decrease? Can be thermodymamic degradation and self-organizing evolution united? How to unite? In this paper starting out from nonequilibrium entropy evolution equation we proved that a new entropy decrease could spontaneously emerge in nonequilibrium system with internal attractive interaction. This new entropy decrease coexists wit...

  5. Arithmetic of quantum entropy function

    International Nuclear Information System (INIS)

    Sen, Ashoke

    2009-01-01

    Quantum entropy function is a proposal for computing the entropy associated with the horizon of a black hole in the extremal limit, and is related via AdS/CFT correspondence to the dimension of the Hilbert space in a dual quantum mechanics. We show that in N = 4 supersymmetric string theories, quantum entropy function formalism naturally explains the origin of the subtle differences between the microscopic degeneracies of quarter BPS dyons carrying different torsion, i.e. different arithmetical properties. These arise from additional saddle points in the path integral - whose existence depends on the arithmetical properties of the black hole charges - constructed as freely acting orbifolds of the original AdS 2 x S 2 near horizon geometry. During this analysis we demonstrate that the quantum entropy function is insensitive to the details of the infrared cutoff used in the computation, and the details of the boundary terms added to the action. We also discuss the role of the asymptotic symmetries of AdS 2 in carrying out the path integral in the definition of quantum entropy function. Finally we show that even though quantum entropy function is expected to compute the absolute degeneracy in a given charge and angular momentum sector, it can also be used to compute the index. This can then be compared with the microscopic computation of the index.

  6. Mixing, entropy and competition

    International Nuclear Information System (INIS)

    Klimenko, A Y

    2012-01-01

    Non-traditional thermodynamics, applied to random behaviour associated with turbulence, mixing and competition, is reviewed and analysed. Competitive mixing represents a general framework for the study of generic properties of competitive systems and can be used to model a wide class of non-equilibrium phenomena ranging from turbulent premixed flames and invasion waves to complex competitive systems. We demonstrate consistency of the general principles of competition with thermodynamic description, review and analyse the related entropy concepts and introduce the corresponding competitive H-theorem. A competitive system can be characterized by a thermodynamic quantity—competitive potential—which determines the likely direction of evolution of the system. Contested resources tend to move between systems from lower to higher values of the competitive potential. There is, however, an important difference between conventional thermodynamics and competitive thermodynamics. While conventional thermodynamics is constrained by its zeroth law and is fundamentally transitive, the transitivity of competitive thermodynamics depends on the transitivity of the competition rules. Intransitivities are common in the real world and are responsible for complex behaviour in competitive systems. This work follows ideas and methods that have originated from the analysis of turbulent combustion, but reviews a much broader scope of issues linked to mixing and competition, including thermodynamic characterization of complex competitive systems with self-organization. The approach presented here is interdisciplinary and is addressed to the general educated readers, whereas the mathematical details can be found in the appendices. (comment)

  7. Parameterized entropy analysis of EEG following hypoxic-ischemic brain injury

    International Nuclear Information System (INIS)

    Tong Shanbao; Bezerianos, Anastasios; Malhotra, Amit; Zhu Yisheng; Thakor, Nitish

    2003-01-01

    In the present study Tsallis and Renyi entropy methods were used to study the electric activity of brain following hypoxic-ischemic (HI) injury. We investigated the performances of these parameterized information measures in describing the electroencephalogram (EEG) signal of controlled experimental animal HI injury. The results show that (a): compared with Shannon and Renyi entropy, the parameterized Tsallis entropy acts like a spatial filter and the information rate can either tune to long range rhythms or to short abrupt changes, such as bursts or spikes during the beginning of recovery, by the entropic index q; (b): Renyi entropy is a compact and predictive indicator for monitoring the physiological changes during the recovery of brain injury. There is a reduction in the Renyi entropy after brain injury followed by a gradual recovery upon resuscitation

  8. Information entropy of earthquake populations in northeastern Italy and western Slovenia

    Science.gov (United States)

    Bressan, G.; Barnaba, C.; Gentili, S.; Rossi, G.

    2017-10-01

    The spatio-temporal evolution of eight seismicity populations, preceding and following moderate earthquake sequences occurred in NE-Italy and W-Slovenia, are investigated by means of the normalized Shannon entropy and the fractal dimension. Three phases are recognized in the temporal seismic series. The period preceding the mainshock is characterized by oscillations of the Shannon entropy around a nearly constant level and by fluctuations of the fractal dimension. The phase of mainshock and aftershock sequences is characterized by a significant decrease of the Shannon entropy. A simultaneous marked decrease of the fractal dimension is observed in five cases. After the sequence, the entropy recovers the nearly constant trend before the mainshock and the fractal dimension is characterized by fluctuations. We interpreted the fluctuations of the normalized Shannon entropy and the fractal dimension caused by the coupling between the stress field and the mechanical heterogeneities of the crust that results in spatial and temporal fluctuations of the strain energy.

  9. Entropy Stable Wall Boundary Conditions for the Three-Dimensional Compressible Navier-Stokes Equations

    Science.gov (United States)

    Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

    2015-01-01

    Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

  10. Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations

    Science.gov (United States)

    Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

    2014-01-01

    Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

  11. Energy conservation and maximal entropy production in enzyme reactions.

    Science.gov (United States)

    Dobovišek, Andrej; Vitas, Marko; Brumen, Milan; Fajmut, Aleš

    2017-08-01

    A procedure for maximization of the density of entropy production in a single stationary two-step enzyme reaction is developed. Under the constraints of mass conservation, fixed equilibrium constant of a reaction and fixed products of forward and backward enzyme rate constants the existence of maximum in the density of entropy production is demonstrated. In the state with maximal density of entropy production the optimal enzyme rate constants, the stationary concentrations of the substrate and the product, the stationary product yield as well as the stationary reaction flux are calculated. The test, whether these calculated values of the reaction parameters are consistent with their corresponding measured values, is performed for the enzyme Glucose Isomerase. It is found that calculated and measured rate constants agree within an order of magnitude, whereas the calculated reaction flux and the product yield differ from their corresponding measured values for less than 20 % and 5 %, respectively. This indicates that the enzyme Glucose Isomerase, considered in a non-equilibrium stationary state, as found in experiments using the continuous stirred tank reactors, possibly operates close to the state with the maximum in the density of entropy production. Copyright © 2017 Elsevier B.V. All rights reserved.

  12. Quantum key distribution with finite resources: Smooth Min entropy vs. Smooth Renyi entropy

    Energy Technology Data Exchange (ETDEWEB)

    Mertz, Markus; Abruzzo, Silvestre; Bratzik, Sylvia; Kampermann, Hermann; Bruss, Dagmar [Institut fuer Theoretische Physik III, Duesseldorf (Germany)

    2010-07-01

    We consider different entropy measures that play an important role in the analysis of the security of QKD with finite resources. The smooth min entropy leads to an optimal bound for the length of a secure key. Another bound on the secure key length was derived by using Renyi entropies. Unfortunately, it is very hard or even impossible to calculate these entropies for realistic QKD scenarios. To estimate the security rate it becomes important to find computable bounds on these entropies. Here, we compare a lower bound for the smooth min entropy with a bound using Renyi entropies. We compare these entropies for the six-state protocol with symmetric attacks.

  13. Adaptable recursive binary entropy coding technique

    Science.gov (United States)

    Kiely, Aaron B.; Klimesh, Matthew A.

    2002-07-01

    We present a novel data compression technique, called recursive interleaved entropy coding, that is based on recursive interleaving of variable-to variable length binary source codes. A compression module implementing this technique has the same functionality as arithmetic coding and can be used as the engine in various data compression algorithms. The encoder compresses a bit sequence by recursively encoding groups of bits that have similar estimated statistics, ordering the output in a way that is suited to the decoder. As a result, the decoder has low complexity. The encoding process for our technique is adaptable in that each bit to be encoded has an associated probability-of-zero estimate that may depend on previously encoded bits; this adaptability allows more effective compression. Recursive interleaved entropy coding may have advantages over arithmetic coding, including most notably the admission of a simple and fast decoder. Much variation is possible in the choice of component codes and in the interleaving structure, yielding coder designs of varying complexity and compression efficiency; coder designs that achieve arbitrarily small redundancy can be produced. We discuss coder design and performance estimation methods. We present practical encoding and decoding algorithms, as well as measured performance results.

  14. DNA entropy reveals a significant difference in complexity between housekeeping and tissue specific gene promoters.

    Science.gov (United States)

    Thomas, David; Finan, Chris; Newport, Melanie J; Jones, Susan

    2015-10-01

    The complexity of DNA can be quantified using estimates of entropy. Variation in DNA complexity is expected between the promoters of genes with different transcriptional mechanisms; namely housekeeping (HK) and tissue specific (TS). The former are transcribed constitutively to maintain general cellular functions, and the latter are transcribed in restricted tissue and cells types for specific molecular events. It is known that promoter features in the human genome are related to tissue specificity, but this has been difficult to quantify on a genomic scale. If entropy effectively quantifies DNA complexity, calculating the entropies of HK and TS gene promoters as profiles may reveal significant differences. Entropy profiles were calculated for a total dataset of 12,003 human gene promoters and for 501 housekeeping (HK) and 587 tissue specific (TS) human gene promoters. The mean profiles show the TS promoters have a significantly lower entropy (pentropy distributions for the 3 datasets show that promoter entropies could be used to identify novel HK genes. Functional features comprise DNA sequence patterns that are non-random and hence they have lower entropies. The lower entropy of TS gene promoters can be explained by a higher density of positive and negative regulatory elements, required for genes with complex spatial and temporary expression. Copyright © 2015 Elsevier Ltd. All rights reserved.

  15. Análise de dados de produção em um pomar jovem de laranjeiras Hamlin: II. classificação de dados espaço-temporais Yield data analysis in a commercial orchard of young Hamlin trees: classification of spatial-temporal yield data

    Directory of Open Access Journals (Sweden)

    Francisco José de Oliveira Parise

    2005-04-01

    Full Text Available Em um pomar jovem de laranjeiras Hamlin, não-irrigado, foi realizado um estudo que procurou investigar a potencialidade da utilização de dados espaço-temporais de produção por árvore para o gerenciamento localizado. A produção de 1.471 árvores georreferenciadas foi levantada em dois ciclos sucessivos, 2000-2001 e 2001-2002, e classificada por meio de uma análise de agrupamentos via lógica fuzzy. Ainda, foi realizada uma análise de correlação intraclasse com dados de resposta espectral de 52 árvores, extraída de imagens aéreas multiespectrais de alta resolução espacial. Os resultados mostraram que foi possível a formação de classes distintas de comportamento produtivo, em função dos padrões de variabilidade espacial e temporal da produção. No entanto, as classes apresentaram baixa coerência espacial, o que dificulta o gerenciamento localizado da produção em nível de árvores individuais. A despeito disso, a resposta espectral esteve significativamente relacionada às classes formadas.Yield data of 1471 young Hamlin trees in a commercial orchard were collected in two seasons, 2000/2001 and 2001/2002, to identify the patterns of spatial and temporal yield variability. Fuzzy cluster analysis was used for interpreting the temporal and spatial variation. 52 trees were also selected for calculating the intra-class correlation of the spectral response extracted from high resolution multispectral digital aerial images. The results showed that some general patterns of season-to-season variation could be identified and related to spectral response of the trees. But, these patterns correspond to regions poorly spatially coherent.

  16. Covariant entropy bound and loop quantum cosmology

    International Nuclear Information System (INIS)

    Ashtekar, Abhay; Wilson-Ewing, Edward

    2008-01-01

    We examine Bousso's covariant entropy bound conjecture in the context of radiation filled, spatially flat, Friedmann-Robertson-Walker models. The bound is violated near the big bang. However, the hope has been that quantum gravity effects would intervene and protect it. Loop quantum cosmology provides a near ideal setting for investigating this issue. For, on the one hand, quantum geometry effects resolve the singularity and, on the other hand, the wave function is sharply peaked at a quantum corrected but smooth geometry, which can supply the structure needed to test the bound. We find that the bound is respected. We suggest that the bound need not be an essential ingredient for a quantum gravity theory but may emerge from it under suitable circumstances.

  17. A student's guide to entropy

    CERN Document Server

    Lemons, Don S

    2013-01-01

    Striving to explore the subject in as simple a manner as possible, this book helps readers understand the elusive concept of entropy. Innovative aspects of the book include the construction of statistical entropy, the derivation of the entropy of classical systems from purely classical assumptions, and a statistical thermodynamics approach to the ideal Fermi and ideal Bose gases. Derivations are worked through step-by-step and important applications are highlighted in over 20 worked examples. Nearly 50 end-of-chapter exercises test readers' understanding. The book also features a glossary giving definitions for all essential terms, a time line showing important developments, and list of books for further study. It is an ideal supplement to undergraduate courses in physics, engineering, chemistry and mathematics.

  18. Statistical Entropy of Schwarzschild Black Holes

    CERN Document Server

    Englert, F

    1998-01-01

    The entropy of a seven dimensional Schwarzschild black hole of arbitrary large radius is obtained by a mapping onto a near extremal self-dual three-brane whose partition function can be evaluated. The three-brane arises from duality after submitting a neutral blackbrane, from which the Schwarzschild black hole can be obtained by compactification, to an infinite boost in non compact eleven dimensional space-time and then to a Kaluza-Klein compactification. This limit can be defined in precise terms and yields the Beckenstein-Hawking value up to a factor of order one which can be set to be exactly one with the extra assumption of keeping only transverse brane excitations. The method can be generalized to five and four dimensional black holes.

  19. Shannon entropy and particle decays

    Science.gov (United States)

    Carrasco Millán, Pedro; García-Ferrero, M. Ángeles; Llanes-Estrada, Felipe J.; Porras Riojano, Ana; Sánchez García, Esteban M.

    2018-05-01

    We deploy Shannon's information entropy to the distribution of branching fractions in a particle decay. This serves to quantify how important a given new reported decay channel is, from the point of view of the information that it adds to the already known ones. Because the entropy is additive, one can subdivide the set of channels and discuss, for example, how much information the discovery of a new decay branching would add; or subdivide the decay distribution down to the level of individual quantum states (which can be quickly counted by the phase space). We illustrate the concept with some examples of experimentally known particle decay distributions.

  20. Methods for calculating nonconcave entropies

    International Nuclear Information System (INIS)

    Touchette, Hugo

    2010-01-01

    Five different methods which can be used to analytically calculate entropies that are nonconcave as functions of the energy in the thermodynamic limit are discussed and compared. The five methods are based on the following ideas and techniques: (i) microcanonical contraction, (ii) metastable branches of the free energy, (iii) generalized canonical ensembles with specific illustrations involving the so-called Gaussian and Betrag ensembles, (iv) the restricted canonical ensemble, and (v) the inverse Laplace transform. A simple long-range spin model having a nonconcave entropy is used to illustrate each method

  1. Examples of Entropy-driven Ordering

    Indian Academy of Sciences (India)

    driven Ordering. Orientational ordering of long objects. Entropy of sliding increases. Freezing in hard-sphere systems. Vibrational entropy increases. Phase separation in hard-sphere binary mixtures with disparate sizes. More room for smaller ...

  2. Using entropy measures to characterize human locomotion.

    Science.gov (United States)

    Leverick, Graham; Szturm, Tony; Wu, Christine Q

    2014-12-01

    Entropy measures have been widely used to quantify the complexity of theoretical and experimental dynamical systems. In this paper, the value of using entropy measures to characterize human locomotion is demonstrated based on their construct validity, predictive validity in a simple model of human walking and convergent validity in an experimental study. Results show that four of the five considered entropy measures increase meaningfully with the increased probability of falling in a simple passive bipedal walker model. The same four entropy measures also experienced statistically significant increases in response to increasing age and gait impairment caused by cognitive interference in an experimental study. Of the considered entropy measures, the proposed quantized dynamical entropy (QDE) and quantization-based approximation of sample entropy (QASE) offered the best combination of sensitivity to changes in gait dynamics and computational efficiency. Based on these results, entropy appears to be a viable candidate for assessing the stability of human locomotion.

  3. On thermodynamic limits of entropy densities

    NARCIS (Netherlands)

    Moriya, H; Van Enter, A

    We give some sufficient conditions which guarantee that the entropy density in the thermodynamic limit is equal to the thermodynamic limit of the entropy densities of finite-volume (local) Gibbs states.

  4. The entropy principle thermodynamics for the unsatisfied

    CERN Document Server

    Thess, André

    2011-01-01

    Entropy is the most important and the most difficult to understand term of thermodynamics. This book helps make this key concept understandable. It includes seven illustrative examples of applications of entropy, which are presented step by step.

  5. A brief introduction to sofic entropy theory

    OpenAIRE

    Bowen, Lewis

    2017-01-01

    Sofic entropy theory is a generalization of the classical Kolmogorov-Sinai entropy theory to actions of large class of non-amenable groups called sofic groups. This is a short introduction with a guide to the literature.

  6. Notes on entanglement entropy in string theory

    International Nuclear Information System (INIS)

    He, Song; Numasawa, Tokiro; Takayanagi, Tadashi; Watanabe, Kento

    2015-01-01

    In this paper, we study the conical entropy in string theory in the simplest setup of dividing the nine dimensional space into two halves. This corresponds to the leading quantum correction to the horizon entropy in string theory on the Rindler space. This entropy is also called the conical entropy and includes surface term contributions. We first derive a new simple formula of the conical entropy for any free higher spin fields. Then we apply this formula to computations of conical entropy in open and closed superstring. In our analysis of closed string, we study the twisted conical entropy defined by making use of string theory on Melvin backgrounds. This quantity is easier to calculate owing to the folding trick. Our analysis shows that the conical entropy in closed superstring is UV finite owing to the string scale cutoff.

  7. Temporal and Spatial Variations in Precipitation, Streamflow, Suspended-Sediment Loads and Yields, and Land-Condition Trend Analysis at the U.S. Army Pinon Canyon Maneuver Site, Las Animas County, Colorado, 1983 through 2007

    Science.gov (United States)

    Stevens, M.R.; Dupree, J.; Kuzmiak, J.M.

    2008-01-01

    In 2007, the U.S. Geological Survey, in cooperation with the U.S. Department of the Army, began an assessment of the spatial and temporal variations in precipitation, streamflow, suspended-sediment loads and yields, changes in land condition, effects of the tributaries on the Purgatoire River and the possible relation of effects from military training to hydrology and land conditions that have occurred at Pinon Canyon Maneuver Site (PCMS) from 1983 through 2007. Data were collected for precipitation (19 stations) and streamflow and sediment load (5 tributary and 2 main-stem Purgatoire River stations) during 1983 through 2007 for various time periods. The five tributary stations were Van Bremer Arroyo near Model, Taylor Arroyo below Rock Crossing, Lockwood Canyon Creek near Thatcher, Red Rock Canyon Creek at the mouth, and Bent Canyon Creek at the mouth. In addition, data were collected at two Purgatoire River stations: Purgatoire River near Thatcher and Purgatoire River at Rock Crossing.

  8. Definition of Nonequilibrium Entropy of General Systems

    OpenAIRE

    Mei, Xiaochun

    1999-01-01

    The definition of nonequilibrium entropy is provided for the general nonequilibrium processes by connecting thermodynamics with statistical physics, and the principle of entropy increment in the nonequilibrium processes is also proved in the paper. The result shows that the definition of nonequilibrium entropy is not unique.

  9. Logical entropy of quantum dynamical systems

    Directory of Open Access Journals (Sweden)

    Ebrahimzadeh Abolfazl

    2016-01-01

    Full Text Available This paper introduces the concepts of logical entropy and conditional logical entropy of hnite partitions on a quantum logic. Some of their ergodic properties are presented. Also logical entropy of a quantum dynamical system is dehned and ergodic properties of dynamical systems on a quantum logic are investigated. Finally, the version of Kolmogorov-Sinai theorem is proved.

  10. The Wehrl entropy has Gaussian optimizers

    DEFF Research Database (Denmark)

    De Palma, Giacomo

    2018-01-01

    We determine the minimum Wehrl entropy among the quantum states with a given von Neumann entropy and prove that it is achieved by thermal Gaussian states. This result determines the relation between the von Neumann and the Wehrl entropies. The key idea is proving that the quantum-classical channel...

  11. Algebraic entropy for differential-delay equations

    OpenAIRE

    Viallet, Claude M.

    2014-01-01

    We extend the definition of algebraic entropy to a class of differential-delay equations. The vanishing of the entropy, as a structural property of an equation, signals its integrability. We suggest a simple way to produce differential-delay equations with vanishing entropy from known integrable differential-difference equations.

  12. Universal canonical entropy for gravitating systems

    Indian Academy of Sciences (India)

    Similar to this is the case of ref. [12] which also uses the saddle point approximation to express the microcanonical entropy in terms of the canonical entropy [12a]. Recalling that there is at least 'circumstantial' evidence that the microcanonical entropy has a 'universal' form [13–15], identical to that obtained in ref. [6] quoted.

  13. Regularities of changes of metal melting entropy

    International Nuclear Information System (INIS)

    Kats, S.A.; Chekhovskoj, V.Ya.

    1980-01-01

    Most trustworthy data on temperatures, heats and entropies of fusion of metals have been used as a basis to throw light on the laws governing variations of the entropy of metals fusion. The elaborated procedure is used to predict the entropies of the metals fusion whose thermodynamic properties under high temperatures have not yet been investigated

  14. Single Particle Entropy in Heated Nuclei

    International Nuclear Information System (INIS)

    Guttormsen, M.; Chankova, R.; Hjorth-Jensen, M.; Rekstad, J.; Siem, S.; Sunde, A. C.; Syed, N. U. H.; Agvaanluvsan, U.; Schiller, A.; Voinov, A.

    2006-01-01

    The thermal motion of single particles represents the largest contribution to level density (or entropy) in atomic nuclei. The concept of single particle entropy is presented and shown to be an approximate extensive (additive) quantity for mid-shell nuclei. A few applications of single particle entropy are demonstrated

  15. The dynamical entropy of quantum systems

    International Nuclear Information System (INIS)

    Connes, A.; Narnhofer, H.; Thirring, W.

    1987-01-01

    The definition of the dynamical entropy for automorphisms of C * - algebras is represented. Several properties are discussed; especially it is argued that the entropy of the shift can be shown in special cases to be equal with the entropy density. (Author)

  16. Epoch-based Entropy for Early Screening of Alzheimer's Disease.

    Science.gov (United States)

    Houmani, N; Dreyfus, G; Vialatte, F B

    2015-12-01

    In this paper, we introduce a novel entropy measure, termed epoch-based entropy. This measure quantifies disorder of EEG signals both at the time level and spatial level, using local density estimation by a Hidden Markov Model on inter-channel stationary epochs. The investigation is led on a multi-centric EEG database recorded from patients at an early stage of Alzheimer's disease (AD) and age-matched healthy subjects. We investigate the classification performances of this method, its robustness to noise, and its sensitivity to sampling frequency and to variations of hyperparameters. The measure is compared to two alternative complexity measures, Shannon's entropy and correlation dimension. The classification accuracies for the discrimination of AD patients from healthy subjects were estimated using a linear classifier designed on a development dataset, and subsequently tested on an independent test set. Epoch-based entropy reached a classification accuracy of 83% on the test dataset (specificity = 83.3%, sensitivity = 82.3%), outperforming the two other complexity measures. Furthermore, it was shown to be more stable to hyperparameter variations, and less sensitive to noise and sampling frequency disturbances than the other two complexity measures.

  17. Entropy-driven phase transitions

    NARCIS (Netherlands)

    Frenkel, D.

    1999-01-01

    Increase in visible order can be associated with an increase in microscopic disorder. This phenomenon leads to many counter-intuitive phenomena such as entropy driven crystallization and phase separation. I devote special attention to the entropic depletion interaction as a means to tune the range

  18. Properties of von Neumann entropy

    Indian Academy of Sciences (India)

    disentangled) as seen by moving observers, is used to investigate the properties of von Neumann entropy, as a measure of spin–momentum entanglement. To do so, we partition the total Hilbert space into momentum and spin subspaces so that the ...

  19. Entropy, Coding and Data Compression

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 9. Entropy, Coding and Data Compression. S Natarajan. General Article Volume 6 Issue 9 September 2001 pp 35-45. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/006/09/0035-0045 ...

  20. Entropy of dynamical social networks

    Science.gov (United States)

    Zhao, Kun; Karsai, Marton; Bianconi, Ginestra

    2012-02-01

    Dynamical social networks are evolving rapidly and are highly adaptive. Characterizing the information encoded in social networks is essential to gain insight into the structure, evolution, adaptability and dynamics. Recently entropy measures have been used to quantify the information in email correspondence, static networks and mobility patterns. Nevertheless, we still lack methods to quantify the information encoded in time-varying dynamical social networks. In this talk we present a model to quantify the entropy of dynamical social networks and use this model to analyze the data of phone-call communication. We show evidence that the entropy of the phone-call interaction network changes according to circadian rhythms. Moreover we show that social networks are extremely adaptive and are modified by the use of technologies such as mobile phone communication. Indeed the statistics of duration of phone-call is described by a Weibull distribution and is significantly different from the distribution of duration of face-to-face interactions in a conference. Finally we investigate how much the entropy of dynamical social networks changes in realistic models of phone-call or face-to face interactions characterizing in this way different type human social behavior.

  1. Maximum entropy beam diagnostic tomography

    International Nuclear Information System (INIS)

    Mottershead, C.T.

    1985-01-01

    This paper reviews the formalism of maximum entropy beam diagnostic tomography as applied to the Fusion Materials Irradiation Test (FMIT) prototype accelerator. The same formalism has also been used with streak camera data to produce an ultrahigh speed movie of the beam profile of the Experimental Test Accelerator (ETA) at Livermore. 11 refs., 4 figs

  2. Maximum entropy beam diagnostic tomography

    International Nuclear Information System (INIS)

    Mottershead, C.T.

    1985-01-01

    This paper reviews the formalism of maximum entropy beam diagnostic tomography as applied to the Fusion Materials Irradiation Test (FMIT) prototype accelerator. The same formalism has also been used with streak camera data to produce an ultrahigh speed movie of the beam profile of the Experimental Test Accelerator (ETA) at Livermore

  3. Hidden states and hidden entropy

    International Nuclear Information System (INIS)

    Betak, E.

    1993-06-01

    We study the properties of master equations of the pre-equilibrium exciton model. For the case when the emission is included, we have proved the entropy to be a nondecreasing function of time. The opposite statement in the recent paper of Pan et al. has been caused mainly by neglecting a part of the exciton states. (author). 17 refs

  4. Vibrational entropies in metallic alloys

    Science.gov (United States)

    Ozolins, Vidvuds; Asta, Mark; Wolverton, Christopher

    2000-03-01

    Recently, it has been recognized that vibrational entropy can have significant effects on the phase stability of metallic alloys. Using density functional linear response calculations and molecular dynamics simulations we study three representative cases: (i) phase diagram of Al-rich Al-Sc alloys, (ii) stability of precipitate phases in CuAl_2, and (iii) phonon dynamics in bcc Zr. We find large vibrational entropy effects in all cases. In the Al-Sc system, vibrations increase the solid solubility of Sc in Al by decreasing the stability of the L12 (Al_3Sc) phase. This leads to a nearly ten-fold increase in the solid solubility of Sc in Al at T=800 K. In the Cu-Al system, our calculations predict that the tetragonal Laves phase of CuAl2 has 0.35 kB/atom higher vibrational entropy than the cubic CaF_2-type phase (the latter is predicted to be the T=0 K ground state of CuAl_2). This entropy difference causes a structural transformation in CuAl2 precipitates from the fluorite to the tetragonal Laves phase around T=500 K. Finally, we analyze the highly unusual dynamics of anharmonically stabilized bcc Zr, finding large diffuse-scattering intensity streaks between the bcc Bragg peaks.

  5. Entanglement entropy of non-unitary integrable quantum field theory

    Directory of Open Access Journals (Sweden)

    Davide Bianchini

    2015-07-01

    Full Text Available In this paper we study the simplest massive 1+1 dimensional integrable quantum field theory which can be described as a perturbation of a non-unitary minimal conformal field theory: the Lee–Yang model. We are particularly interested in the features of the bi-partite entanglement entropy for this model and on building blocks thereof, namely twist field form factors. Non-unitarity selects out a new type of twist field as the operator whose two-point function (appropriately normalized yields the entanglement entropy. We compute this two-point function both from a form factor expansion and by means of perturbed conformal field theory. We find good agreement with CFT predictions put forward in a recent work involving the present authors. In particular, our results are consistent with a scaling of the entanglement entropy given by ceff3log⁡ℓ where ceff is the effective central charge of the theory (a positive number related to the central charge and ℓ is the size of the region. Furthermore the form factor expansion of twist fields allows us to explore the large region limit of the entanglement entropy and find the next-to-leading order correction to saturation. We find that this correction is very different from its counterpart in unitary models. Whereas in the latter case, it had a form depending only on few parameters of the model (the particle spectrum, it appears to be much more model-dependent for non-unitary models.

  6. Computing algebraic transfer entropy and coupling directions via transcripts

    Science.gov (United States)

    Amigó, José M.; Monetti, Roberto; Graff, Beata; Graff, Grzegorz

    2016-11-01

    Most random processes studied in nonlinear time series analysis take values on sets endowed with a group structure, e.g., the real and rational numbers, and the integers. This fact allows to associate with each pair of group elements a third element, called their transcript, which is defined as the product of the second element in the pair times the first one. The transfer entropy of two such processes is called algebraic transfer entropy. It measures the information transferred between two coupled processes whose values belong to a group. In this paper, we show that, subject to one constraint, the algebraic transfer entropy matches the (in general, conditional) mutual information of certain transcripts with one variable less. This property has interesting practical applications, especially to the analysis of short time series. We also derive weak conditions for the 3-dimensional algebraic transfer entropy to yield the same coupling direction as the corresponding mutual information of transcripts. A related issue concerns the use of mutual information of transcripts to determine coupling directions in cases where the conditions just mentioned are not fulfilled. We checked the latter possibility in the lowest dimensional case with numerical simulations and cardiovascular data, and obtained positive results.

  7. Relation Entropy and Transferable Entropy Think of Aggregation on Group Decision Making

    Institute of Scientific and Technical Information of China (English)

    CHENG Qi-yue; QIU Wan-hua; LIU Xiao-feng

    2002-01-01

    In this paper, aggregation question based on group decision making and a single decision making is studied. The theory of entropy is applied to the sets pair analysis. The system of relation entropy and the transferable entropy notion are put. The character is studied. An potential by the relation entropy and transferable entropy are defined. It is the consistency measure on the group between a single decision making. We gained a new aggregation effective definition on the group misjudge.

  8. Misuse of thermodynamic entropy in economics

    International Nuclear Information System (INIS)

    Kovalev, Andrey V.

    2016-01-01

    The direct relationship between thermodynamic entropy and economic scarcity is only valid for a thermodynamically isolated economy. References to the second law of thermodynamics in economics within the context of scarcity ignore the fact that the earth is not an isolated system. The earth interacts with external sources and sinks of entropy and the resulting total entropy fluctuates around a constant. Even if the mankind finally proves unable to recycle industrial waste and close the technological cycle, the economic disruption caused by the depletion of natural resources may happen while the total thermodynamic entropy of the ecosystem remains essentially at the present level, because the transfer of chemically refined products may not increase significantly the total entropy, but it may decrease their recyclability. The inutility of industrial waste is not connected with its entropy, which may be exemplified with the case of alumina production. The case also demonstrates that industrially generated entropy is discharged into surroundings without being accumulated in ‘thermodynamically unavailable matter’. Material entropy, as a measure of complexity and economic dispersal of resources, can be a recyclability metric, but it is not a thermodynamic parameter, and its growth is not equivalent to the growth of thermodynamic entropy. - Highlights: • Entropy cannot be used as a measure of economic scarcity. • There is no anthropogenic entropy separate from the entropy produced naturally. • Inutility of industrial waste is not connected with its thermodynamic entropy. • Industrially generated entropy may or may not be accumulated in industrial waste. • Recyclability is more important than thermodynamic entropy of a product.

  9. Enthalpy-entropy compensation in protein unfolding

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    Enthalpy-entropy compensation was found to be a universal law in protein unfolding based on over 3 000 experimental data. Water molecular reorganization accompanying the protein unfolding was suggested as the origin of the enthalpy-entropy compensation in protein unfolding. It is indicated that the enthalpy-entropy compensation constitutes the physical foundation that satisfies the biological need of the small free energy changes in protein unfolding, without the sacrifice of the bio-diversity of proteins. The enthalpy-entropy compensation theory proposed herein also provides valuable insights into the Privalov's puzzle of enthalpy and entropy convergence in protein unfolding.

  10. Receiver function estimated by maximum entropy deconvolution

    Institute of Scientific and Technical Information of China (English)

    吴庆举; 田小波; 张乃铃; 李卫平; 曾融生

    2003-01-01

    Maximum entropy deconvolution is presented to estimate receiver function, with the maximum entropy as the rule to determine auto-correlation and cross-correlation functions. The Toeplitz equation and Levinson algorithm are used to calculate the iterative formula of error-predicting filter, and receiver function is then estimated. During extrapolation, reflective coefficient is always less than 1, which keeps maximum entropy deconvolution stable. The maximum entropy of the data outside window increases the resolution of receiver function. Both synthetic and real seismograms show that maximum entropy deconvolution is an effective method to measure receiver function in time-domain.

  11. Controlling the Shannon Entropy of Quantum Systems

    Science.gov (United States)

    Xing, Yifan; Wu, Jun

    2013-01-01

    This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking. PMID:23818819

  12. Entropy evaporated by a black hole

    International Nuclear Information System (INIS)

    Zurek, W.H.

    1982-01-01

    It is shown that the entropy of the radiation evaporated by an uncharged, nonrotating black hole into vacuum in the course of its lifetime is approximately (4/3) times the initial entropy of this black hole. Also considered is a thermodynamically reversible process in which an increase of black-hole entropy is equal to the decrease of the entropy of its surroundings. Implications of these results for the generalized second law of thermodynamics and for the interpretation of black-hole entropy are pointed out

  13. q-entropy for symbolic dynamical systems

    International Nuclear Information System (INIS)

    Zhao, Yun; Pesin, Yakov

    2015-01-01

    For symbolic dynamical systems we use the Carathéodory construction as described in (Pesin 1997 Dimension Theory in Dynamical Systems, ConTemporary Views and Applications (Chicago: University of Chicago Press)) to introduce the notions of q-topological and q-metric entropies. We describe some basic properties of these entropies and in particular, discuss relations between q-metric entropy and local metric entropy. Both q-topological and q-metric entropies are new invariants respectively under homeomorphisms and metric isomorphisms of dynamical systems. (paper)

  14. Holographic charged Rényi entropies

    Science.gov (United States)

    Belin, Alexandre; Hung, Ling-Yan; Maloney, Alexander; Matsuura, Shunji; Myers, Robert C.; Sierens, Todd

    2013-12-01

    We construct a new class of entanglement measures by extending the usual definition of Rényi entropy to include a chemical potential. These charged Rényi entropies measure the degree of entanglement in different charge sectors of the theory and are given by Euclidean path integrals with the insertion of a Wilson line encircling the entangling surface. We compute these entropies for a spherical entangling surface in CFT's with holographic duals, where they are related to entropies of charged black holes with hyperbolic horizons. We also compute charged Rényi entropies in free field theories.

  15. Controlling the Shannon Entropy of Quantum Systems

    Directory of Open Access Journals (Sweden)

    Yifan Xing

    2013-01-01

    Full Text Available This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking.

  16. Entropy-Corrected Holographic Dark Energy

    International Nuclear Information System (INIS)

    Wei Hao

    2009-01-01

    The holographic dark energy (HDE) is now an interesting candidate of dark energy, which has been studied extensively in the literature. In the derivation of HDE, the black hole entropy plays an important role. In fact, the entropy-area relation can be modified due to loop quantum gravity or other reasons. With the modified entropy-area relation, we propose the so-called 'entropy-corrected holographic dark energy' (ECHDE) in the present work. We consider many aspects of ECHDE and find some interesting results. In addition, we briefly consider the so-called 'entropy-corrected agegraphic dark energy' (ECADE). (geophysics, astronomy, and astrophysics)

  17. Entropy-based financial asset pricing.

    Directory of Open Access Journals (Sweden)

    Mihály Ormos

    Full Text Available We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing model. For asset pricing we define the continuous entropy as an alternative measure of risk. Our results show that entropy decreases in the function of the number of securities involved in a portfolio in a similar way to the standard deviation, and that efficient portfolios are situated on a hyperbola in the expected return-entropy system. For empirical investigation we use daily returns of 150 randomly selected securities for a period of 27 years. Our regression results show that entropy has a higher explanatory power for the expected return than the capital asset pricing model beta. Furthermore we show the time varying behavior of the beta along with entropy.

  18. Entropy Generation Across Earth's Bow Shock

    Science.gov (United States)

    Parks, George K.; McCarthy, Michael; Fu, Suiyan; Lee E. s; Cao, Jinbin; Goldstein, Melvyn L.; Canu, Patrick; Dandouras, Iannis S.; Reme, Henri; Fazakerley, Andrew; hide

    2011-01-01

    Earth's bow shock is a transition layer that causes an irreversible change in the state of plasma that is stationary in time. Theories predict entropy increases across the bow shock but entropy has never been directly measured. Cluster and Double Star plasma experiments measure 3D plasma distributions upstream and downstream of the bow shock that allow calculation of Boltzmann's entropy function H and his famous H-theorem, dH/dt O. We present the first direct measurements of entropy density changes across Earth's bow shock. We will show that this entropy generation may be part of the processes that produce the non-thermal plasma distributions is consistent with a kinetic entropy flux model derived from the collisionless Boltzmann equation, giving strong support that solar wind's total entropy across the bow shock remains unchanged. As far as we know, our results are not explained by any existing shock models and should be of interests to theorists.

  19. Wavelet entropy characterization of elevated intracranial pressure.

    Science.gov (United States)

    Xu, Peng; Scalzo, Fabien; Bergsneider, Marvin; Vespa, Paul; Chad, Miller; Hu, Xiao

    2008-01-01

    Intracranial Hypertension (ICH) often occurs for those patients with traumatic brain injury (TBI), stroke, tumor, etc. Pathology of ICH is still controversial. In this work, we used wavelet entropy and relative wavelet entropy to study the difference existed between normal and hypertension states of ICP for the first time. The wavelet entropy revealed the similar findings as the approximation entropy that entropy during ICH state is smaller than that in normal state. Moreover, with wavelet entropy, we can see that ICH state has the more focused energy in the low wavelet frequency band (0-3.1 Hz) than the normal state. The relative wavelet entropy shows that the energy distribution in the wavelet bands between these two states is actually different. Based on these results, we suggest that ICH may be formed by the re-allocation of oscillation energy within brain.

  20. Entropy-based financial asset pricing.

    Science.gov (United States)

    Ormos, Mihály; Zibriczky, Dávid

    2014-01-01

    We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing model. For asset pricing we define the continuous entropy as an alternative measure of risk. Our results show that entropy decreases in the function of the number of securities involved in a portfolio in a similar way to the standard deviation, and that efficient portfolios are situated on a hyperbola in the expected return-entropy system. For empirical investigation we use daily returns of 150 randomly selected securities for a period of 27 years. Our regression results show that entropy has a higher explanatory power for the expected return than the capital asset pricing model beta. Furthermore we show the time varying behavior of the beta along with entropy.

  1. Entropy of space-time outcome in a movement speed-accuracy task.

    Science.gov (United States)

    Hsieh, Tsung-Yu; Pacheco, Matheus Maia; Newell, Karl M

    2015-12-01

    The experiment reported was set-up to investigate the space-time entropy of movement outcome as a function of a range of spatial (10, 20 and 30 cm) and temporal (250-2500 ms) criteria in a discrete aiming task. The variability and information entropy of the movement spatial and temporal errors considered separately increased and decreased on the respective dimension as a function of an increment of movement velocity. However, the joint space-time entropy was lowest when the relative contribution of spatial and temporal task criteria was comparable (i.e., mid-range of space-time constraints), and it increased with a greater trade-off between spatial or temporal task demands, revealing a U-shaped function across space-time task criteria. The traditional speed-accuracy functions of spatial error and temporal error considered independently mapped to this joint space-time U-shaped entropy function. The trade-off in movement tasks with joint space-time criteria is between spatial error and timing error, rather than movement speed and accuracy. Copyright © 2015 Elsevier B.V. All rights reserved.

  2. The inverse Fourier problem in the case of poor resolution in one given direction: the maximum-entropy solution

    International Nuclear Information System (INIS)

    Papoular, R.J.; Zheludev, A.; Ressouche, E.; Schweizer, J.

    1995-01-01

    When density distributions in crystals are reconstructed from 3D diffraction data, a problem sometimes occurs when the spatial resolution in one given direction is very small compared to that in perpendicular directions. In this case, a 2D projected density is usually reconstructed. For this task, the conventional Fourier inversion method only makes use of those structure factors measured in the projection plane. All the other structure factors contribute zero to the reconstruction of a projected density. On the contrary, the maximum-entropy method uses all the 3D data, to yield 3D-enhanced 2D projected density maps. It is even possible to reconstruct a projection in the extreme case when not one structure factor in the plane of projection is known. In the case of poor resolution along one given direction, a Fourier inversion reconstruction gives very low quality 3D densities 'smeared' in the third dimension. The application of the maximum-entropy procedure reduces the smearing significantly and reasonably well resolved projections along most directions can now be obtained from the MaxEnt 3D density. To illustrate these two ideas, particular examples based on real polarized neutron diffraction data sets are presented. (orig.)

  3. Entropy and Entropy Production: Old Misconceptions and New Breakthroughs

    Directory of Open Access Journals (Sweden)

    Leonid M. Martyushev

    2013-03-01

    Full Text Available Persistent misconceptions existing for dozens of years and influencing progress in various fields of science are sometimes encountered in the scientific and especially, the popular-science literature. The present brief review deals with two such interrelated misconceptions (misunderstandings. The first misunderstanding: entropy is a measure of disorder. This is an old and very common opinion. The second misconception is that the entropy production minimizes in the evolution of nonequilibrium systems. However, as it has recently become clear, evolution (progress in Nature demonstrates the opposite, i.e., maximization of the entropy production. The principal questions connected with this maximization are considered herein. The two misconceptions mentioned above can lead to the apparent contradiction between the conclusions of modern thermodynamics and the basic conceptions of evolution existing in biology. In this regard, the analysis of these issues seems extremely important and timely as it contributes to the deeper understanding of the laws of development of the surrounding World and the place of humans in it.

  4. Driver Fatigue Detection System Using Electroencephalography Signals Based on Combined Entropy Features

    Directory of Open Access Journals (Sweden)

    Zhendong Mu

    2017-02-01

    Full Text Available Driver fatigue has become one of the major causes of traffic accidents, and is a complicated physiological process. However, there is no effective method to detect driving fatigue. Electroencephalography (EEG signals are complex, unstable, and non-linear; non-linear analysis methods, such as entropy, maybe more appropriate. This study evaluates a combined entropy-based processing method of EEG data to detect driver fatigue. In this paper, 12 subjects were selected to take part in an experiment, obeying driving training in a virtual environment under the instruction of the operator. Four types of enthrones (spectrum entropy, approximate entropy, sample entropy and fuzzy entropy were used to extract features for the purpose of driver fatigue detection. Electrode selection process and a support vector machine (SVM classification algorithm were also proposed. The average recognition accuracy was 98.75%. Retrospective analysis of the EEG showed that the extracted features from electrodes T5, TP7, TP8 and FP1 may yield better performance. SVM classification algorithm using radial basis function as kernel function obtained better results. A combined entropy-based method demonstrates good classification performance for studying driver fatigue detection.

  5. Manufacturing of High Entropy Alloys

    Science.gov (United States)

    Jablonski, Paul D.; Licavoli, Joseph J.; Gao, Michael C.; Hawk, Jeffrey A.

    2015-07-01

    High entropy alloys (HEAs) have generated interest in recent years due to their unique positioning within the alloy world. By incorporating a number of elements in high proportion they have high configurational entropy, and thus they hold the promise of interesting and useful properties such as enhanced strength and phase stability. The present study investigates the microstructure of two single-phase face-centered cubic (FCC) HEAs, CoCrFeNi and CoCrFeNiMn, with special attention given to melting, homogenization and thermo-mechanical processing. Large-scale ingots were made by vacuum induction melting to avoid the extrinsic factors inherent in small-scale laboratory button samples. A computationally based homogenization heat treatment was applied to both alloys in order to eliminate segregation due to normal ingot solidification. The alloys fabricated well, with typical thermo-mechanical processing parameters being employed.

  6. On Maximum Entropy and Inference

    Directory of Open Access Journals (Sweden)

    Luigi Gresele

    2017-11-01

    Full Text Available Maximum entropy is a powerful concept that entails a sharp separation between relevant and irrelevant variables. It is typically invoked in inference, once an assumption is made on what the relevant variables are, in order to estimate a model from data, that affords predictions on all other (dependent variables. Conversely, maximum entropy can be invoked to retrieve the relevant variables (sufficient statistics directly from the data, once a model is identified by Bayesian model selection. We explore this approach in the case of spin models with interactions of arbitrary order, and we discuss how relevant interactions can be inferred. In this perspective, the dimensionality of the inference problem is not set by the number of parameters in the model, but by the frequency distribution of the data. We illustrate the method showing its ability to recover the correct model in a few prototype cases and discuss its application on a real dataset.

  7. Entropy favours open colloidal lattices

    Science.gov (United States)

    Mao, Xiaoming; Chen, Qian; Granick, Steve

    2013-03-01

    Burgeoning experimental and simulation activity seeks to understand the existence of self-assembled colloidal structures that are not close-packed. Here we describe an analytical theory based on lattice dynamics and supported by experiments that reveals the fundamental role entropy can play in stabilizing open lattices. The entropy we consider is associated with the rotational and vibrational modes unique to colloids interacting through extended attractive patches. The theory makes predictions of the implied temperature, pressure and patch-size dependence of the phase diagram of open and close-packed structures. More generally, it provides guidance for the conditions at which targeted patchy colloidal assemblies in two and three dimensions are stable, thus overcoming the difficulty in exploring by experiment or simulation the full range of conceivable parameters.

  8. Maximizing Entropy over Markov Processes

    DEFF Research Database (Denmark)

    Biondi, Fabrizio; Legay, Axel; Nielsen, Bo Friis

    2013-01-01

    The channel capacity of a deterministic system with confidential data is an upper bound on the amount of bits of data an attacker can learn from the system. We encode all possible attacks to a system using a probabilistic specification, an Interval Markov Chain. Then the channel capacity...... as a reward function, a polynomial algorithm to verify the existence of an system maximizing entropy among those respecting a specification, a procedure for the maximization of reward functions over Interval Markov Chains and its application to synthesize an implementation maximizing entropy. We show how...... to use Interval Markov Chains to model abstractions of deterministic systems with confidential data, and use the above results to compute their channel capacity. These results are a foundation for ongoing work on computing channel capacity for abstractions of programs derived from code....

  9. Maximizing entropy over Markov processes

    DEFF Research Database (Denmark)

    Biondi, Fabrizio; Legay, Axel; Nielsen, Bo Friis

    2014-01-01

    The channel capacity of a deterministic system with confidential data is an upper bound on the amount of bits of data an attacker can learn from the system. We encode all possible attacks to a system using a probabilistic specification, an Interval Markov Chain. Then the channel capacity...... as a reward function, a polynomial algorithm to verify the existence of a system maximizing entropy among those respecting a specification, a procedure for the maximization of reward functions over Interval Markov Chains and its application to synthesize an implementation maximizing entropy. We show how...... to use Interval Markov Chains to model abstractions of deterministic systems with confidential data, and use the above results to compute their channel capacity. These results are a foundation for ongoing work on computing channel capacity for abstractions of programs derived from code. © 2014 Elsevier...

  10. Preserved entropy and fragile magnetism.

    Science.gov (United States)

    Canfield, Paul C; Bud'ko, Sergey L

    2016-08-01

    A large swath of quantum critical and strongly correlated electron systems can be associated with the phenomena of preserved entropy and fragile magnetism. In this overview we present our thoughts and plans for the discovery and development of lanthanide and transition metal based, strongly correlated systems that are revealed by suppressed, fragile magnetism, quantum criticality, or grow out of preserved entropy. We will present and discuss current examples such as YbBiPt, YbAgGe, YbFe2Zn20, PrAg2In, BaFe2As2, CaFe2As2, LaCrSb3 and LaCrGe3 as part of our motivation and to provide illustrative examples.

  11. ASSESSMENT OF MOTIVATION BY ENTROPY

    OpenAIRE

    Tadeusz G³owacki

    2014-01-01

    Motivation is inseparable from human work. It is also one of the five most important elements of the management process. The ability to determine the level of motivation would therefore be very useful in the work of every manager. This paper is an attempt to quantify motivation and evaluate its size, using the concept of entropy. The main reason to try defining a method of measuring the amount of motivation is to improve the management techniques of companies.

  12. Multivariate Generalized Multiscale Entropy Analysis

    Directory of Open Access Journals (Sweden)

    Anne Humeau-Heurtier

    2016-11-01

    Full Text Available Multiscale entropy (MSE was introduced in the 2000s to quantify systems’ complexity. MSE relies on (i a coarse-graining procedure to derive a set of time series representing the system dynamics on different time scales; (ii the computation of the sample entropy for each coarse-grained time series. A refined composite MSE (rcMSE—based on the same steps as MSE—also exists. Compared to MSE, rcMSE increases the accuracy of entropy estimation and reduces the probability of inducing undefined entropy for short time series. The multivariate versions of MSE (MMSE and rcMSE (MrcMSE have also been introduced. In the coarse-graining step used in MSE, rcMSE, MMSE, and MrcMSE, the mean value is used to derive representations of the original data at different resolutions. A generalization of MSE was recently published, using the computation of different moments in the coarse-graining procedure. However, so far, this generalization only exists for univariate signals. We therefore herein propose an extension of this generalized MSE to multivariate data. The multivariate generalized algorithms of MMSE and MrcMSE presented herein (MGMSE and MGrcMSE, respectively are first analyzed through the processing of synthetic signals. We reveal that MGrcMSE shows better performance than MGMSE for short multivariate data. We then study the performance of MGrcMSE on two sets of short multivariate electroencephalograms (EEG available in the public domain. We report that MGrcMSE may show better performance than MrcMSE in distinguishing different types of multivariate EEG data. MGrcMSE could therefore supplement MMSE or MrcMSE in the processing of multivariate datasets.

  13. Normalized Minimum Error Entropy Algorithm with Recursive Power Estimation

    Directory of Open Access Journals (Sweden)

    Namyong Kim

    2016-06-01

    Full Text Available The minimum error entropy (MEE algorithm is known to be superior in signal processing applications under impulsive noise. In this paper, based on the analysis of behavior of the optimum weight and the properties of robustness against impulsive noise, a normalized version of the MEE algorithm is proposed. The step size of the MEE algorithm is normalized with the power of input entropy that is estimated recursively for reducing its computational complexity. The proposed algorithm yields lower minimum MSE (mean squared error and faster convergence speed simultaneously than the original MEE algorithm does in the equalization simulation. On the condition of the same convergence speed, its performance enhancement in steady state MSE is above 3 dB.

  14. Entropy in an expanding universe

    International Nuclear Information System (INIS)

    Frautschi, S.

    1982-01-01

    The question of how the observed evolution of organized structures from initial chaos in the expanding universe can be reconciled with the laws of statistical mechanics is studied, with emphasis on effects of the expansion and gravity. Some major sources of entropy increase are listed. An expanding causal region is defined in which the entropy, though increasing, tends to fall further and further behind its maximum possible value, thus allowing for the development of order. The related questions of whether entropy will continue increasing without limit in the future, and whether such increase in the form of Hawking radiation or radiation from positronium might enable life to maintain itself permanently, are considered. Attempts to find a scheme for preserving life based on solid structures fail because events such as quantum tunneling recurrently disorganize matter on a very long but fixed time scale, whereas all energy sources slow down progressively in an expanding universe. However, there remains hope that other modes of life capable of maintaining themselves permanently can be found

  15. Resonance transport and kinetic entropy

    International Nuclear Information System (INIS)

    Ivanov, Yu.B.; Knoll, J.; Voskresensky, D.N.

    2000-01-01

    We continue the description of the dynamics of unstable particles within the real-time formulation of nonequilibrium field theory initiated in a previous paper . There we suggest to use Baym's PHI-functional method in order to achieve approximation schemes with 'built in' consistency with respect to conservation laws and thermodynamics even in the case of particles with finite damping width. Starting from Kadanoff-Baym equations we discuss a consistent first order gradient approach to transport which preserves the PHI-derivable properties. The validity conditions for the resulting quantum four-phase-space kinetic theory are discussed under the perspective to treat particles with broad damping widths. This non-equilibrium dynamics naturally includes all those quantum features already inherent in the corresponding equilibrium limit (e.g. Matsubara formalism) at the same level of PHI-derivable approximation. Various collision-term diagrams are discussed including those of higher order which lead to memory effects. As an important novel part we derive a generalized nonequilibrium expression for the kinetic entropy flow, which includes contributions from fluctuations and mass-width effects. In special cases an H-theorem is derived implying that the entropy can only increase with time. Memory effects in the kinetic terms provide contributions to the kinetic entropy flow that in the equilibrium limit recover the famous bosonic type T 3 lnT correction to the specific heat in the case of Fermi liquids like Helium-3

  16. Linearity of holographic entanglement entropy

    Energy Technology Data Exchange (ETDEWEB)

    Almheiri, Ahmed [Stanford Institute for Theoretical Physics, Department of Physics,Stanford University, Stanford, CA 94305 (United States); Dong, Xi [School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States); Swingle, Brian [Stanford Institute for Theoretical Physics, Department of Physics,Stanford University, Stanford, CA 94305 (United States)

    2017-02-14

    We consider the question of whether the leading contribution to the entanglement entropy in holographic CFTs is truly given by the expectation value of a linear operator as is suggested by the Ryu-Takayanagi formula. We investigate this property by computing the entanglement entropy, via the replica trick, in states dual to superpositions of macroscopically distinct geometries and find it consistent with evaluating the expectation value of the area operator within such states. However, we find that this fails once the number of semi-classical states in the superposition grows exponentially in the central charge of the CFT. Moreover, in certain such scenarios we find that the choice of surface on which to evaluate the area operator depends on the density matrix of the entire CFT. This nonlinearity is enforced in the bulk via the homology prescription of Ryu-Takayanagi. We thus conclude that the homology constraint is not a linear property in the CFT. We also discuss the existence of ‘entropy operators’ in general systems with a large number of degrees of freedom.

  17. Statistical mechanical theory of liquid entropy

    International Nuclear Information System (INIS)

    Wallace, D.C.

    1993-01-01

    The multiparticle correlation expansion for the entropy of a classical monatomic liquid is presented. This entropy expresses the physical picture in which there is no free particle motion, but rather, each atom moves within a cage formed by its neighbors. The liquid expansion, including only pair correlations, gives an excellent account of the experimental entropy of most liquid metals, of liquid argon, and the hard sphere liquid. The pair correlation entropy is well approximated by a universal function of temperature. Higher order correlation entropy, due to n-particle irreducible correlations for n≥3, is significant in only a few liquid metals, and its occurrence suggests the presence of n-body forces. When the liquid theory is applied to the study of melting, the author discovers the important classification of normal and anomalous melting, according to whether there is not or is a significant change in the electronic structure upon melting, and he discovers the universal disordering entropy for melting of a monatomic crystal. Interesting directions for future research are: extension to include orientational correlations of molecules, theoretical calculation of the entropy of water, application to the entropy of the amorphous state, and correlational entropy of compressed argon. The author clarifies the relation among different entropy expansions in the recent literature

  18. Entropy in molecular recognition by proteins.

    Science.gov (United States)

    Caro, José A; Harpole, Kyle W; Kasinath, Vignesh; Lim, Jackwee; Granja, Jeffrey; Valentine, Kathleen G; Sharp, Kim A; Wand, A Joshua

    2017-06-20

    Molecular recognition by proteins is fundamental to molecular biology. Dissection of the thermodynamic energy terms governing protein-ligand interactions has proven difficult, with determination of entropic contributions being particularly elusive. NMR relaxation measurements have suggested that changes in protein conformational entropy can be quantitatively obtained through a dynamical proxy, but the generality of this relationship has not been shown. Twenty-eight protein-ligand complexes are used to show a quantitative relationship between measures of fast side-chain motion and the underlying conformational entropy. We find that the contribution of conformational entropy can range from favorable to unfavorable, which demonstrates the potential of this thermodynamic variable to modulate protein-ligand interactions. For about one-quarter of these complexes, the absence of conformational entropy would render the resulting affinity biologically meaningless. The dynamical proxy for conformational entropy or "entropy meter" also allows for refinement of the contributions of solvent entropy and the loss in rotational-translational entropy accompanying formation of high-affinity complexes. Furthermore, structure-based application of the approach can also provide insight into long-lived specific water-protein interactions that escape the generic treatments of solvent entropy based simply on changes in accessible surface area. These results provide a comprehensive and unified view of the general role of entropy in high-affinity molecular recognition by proteins.

  19. Thermodynamic Model of Spatial Memory

    Science.gov (United States)

    Kaufman, Miron; Allen, P.

    1998-03-01

    We develop and test a thermodynamic model of spatial memory. Our model is an application of statistical thermodynamics to cognitive science. It is related to applications of the statistical mechanics framework in parallel distributed processes research. Our macroscopic model allows us to evaluate an entropy associated with spatial memory tasks. We find that older adults exhibit higher levels of entropy than younger adults. Thurstone's Law of Categorical Judgment, according to which the discriminal processes along the psychological continuum produced by presentations of a single stimulus are normally distributed, is explained by using a Hooke spring model of spatial memory. We have also analyzed a nonlinear modification of the ideal spring model of spatial memory. This work is supported by NIH/NIA grant AG09282-06.

  20. Judging The Effectiveness Of Wool Combing By The Entropy Of The Images Of Wool Slivers

    Science.gov (United States)

    Rodrigues, F. Carvalho; Carvalho, Fernando D.; Peixoto, J. Pinto; Silva, M. Santos

    1989-04-01

    In general it can be said that the textile industry endeavours to render a bunch of fibers chaotically distributed in space into an ordered spatial distribution. This fact is independent of the nature the fibers, i.e., the aim of getting into higher order states in the spatial distribution of the fibers dictates different industrial processes depending on whether the fibers are wool, cotton or man made but the all effect is centred on obtaining at every step of any of the processes a more ordered state regarding the spatial distribution of the fibers. Thinking about the textile processes as a method of getting order out of chaos, the concept of entropy appears as the most appropriate judging parameter on the effectiveness of a step in the chain of an industrial process to produce a regular textile. In fact, entropy is the hidden parameter not only for the textile industry but also for the non woven and paper industrial processes. It happens that in these industries the state of order is linked with the spatial distribution of fibers and to obtain an image of a spatial distribution is an easy matter. To compute the image entropy from the grey level distribution requires only the use of the Shannon formula. In this paper to illustrate the usefulness of employing the entropy of an image concept to textiles the evolution of the entropy of wool slivers along the combing process is matched against the state of parallelization of the fibbers along the seven steps as measured by the existing method. The advantages of the entropy method over the previous method based on diffraction is also demonstrated.

  1. On Thermodynamic Interpretation of Transfer Entropy

    Directory of Open Access Journals (Sweden)

    Don C. Price

    2013-02-01

    Full Text Available We propose a thermodynamic interpretation of transfer entropy near equilibrium, using a specialised Boltzmann’s principle. The approach relates conditional probabilities to the probabilities of the corresponding state transitions. This in turn characterises transfer entropy as a difference of two entropy rates: the rate for a resultant transition and another rate for a possibly irreversible transition within the system affected by an additional source. We then show that this difference, the local transfer entropy, is proportional to the external entropy production, possibly due to irreversibility. Near equilibrium, transfer entropy is also interpreted as the difference in equilibrium stabilities with respect to two scenarios: a default case and the case with an additional source. Finally, we demonstrated that such a thermodynamic treatment is not applicable to information flow, a measure of causal effect.

  2. Black hole entropy functions and attractor equations

    International Nuclear Information System (INIS)

    Lopes Cardoso, Gabriel; Wit, Bernard de; Mahapatra, Swapna

    2007-01-01

    The entropy and the attractor equations for static extremal black hole solutions follow from a variational principle based on an entropy function. In the general case such an entropy function can be derived from the reduced action evaluated in a near-horizon geometry. BPS black holes constitute special solutions of this variational principle, but they can also be derived directly from a different entropy function based on supersymmetry enhancement at the horizon. Both functions are consistent with electric/magnetic duality and for BPS black holes their corresponding OSV-type integrals give identical results at the semi-classical level. We clarify the relation between the two entropy functions and the corresponding attractor equations for N = 2 supergravity theories with higher-derivative couplings in four space-time dimensions. We discuss how non-holomorphic corrections will modify these entropy functions

  3. Large Field Inflation and Gravitational Entropy

    DEFF Research Database (Denmark)

    Kaloper, Nemanja; Kleban, Matthew; Lawrence, Albion

    2016-01-01

    species will lead to a violation of the covariant entropy bound at large $N$. If so, requiring the validity of the covariant entropy bound could limit the number of light species and their couplings, which in turn could severely constrain axion-driven inflation. Here we show that there is no such problem...... entropy of de Sitter or near-de Sitter backgrounds at leading order. Working in detail with $N$ scalar fields in de Sitter space, renormalized to one loop order, we show that the gravitational entropy automatically obeys the covariant entropy bound. Furthermore, while the axion decay constant is a strong...... in this light, and show that they are perfectly consistent with the covariant entropy bound. Thus, while quantum gravity might yet spoil large field inflation, holographic considerations in the semiclassical theory do not obstruct it....

  4. Entropy type complexity of quantum processes

    International Nuclear Information System (INIS)

    Watanabe, Noboru

    2014-01-01

    von Neumann entropy represents the amount of information in the quantum state, and this was extended by Ohya for general quantum systems [10]. Umegaki first defined the quantum relative entropy for σ-finite von Neumann algebras, which was extended by Araki, and Uhlmann, for general von Neumann algebras and *-algebras, respectively. In 1983 Ohya introduced the quantum mutual entropy by using compound states; this describes the amount of information correctly transmitted through the quantum channel, which was also extended by Ohya for general quantum systems. In this paper, we briefly explain Ohya's S-mixing entropy and the quantum mutual entropy for general quantum systems. By using structure equivalent class, we will introduce entropy type functionals based on quantum information theory to improve treatment for the Gaussian communication process. (paper)

  5. Relative entropy and the RG flow

    Energy Technology Data Exchange (ETDEWEB)

    Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo [Centro Atómico Bariloche and CONICET,S.C. de Bariloche, Río Negro, R8402AGP (Argentina)

    2017-03-16

    We consider the relative entropy between vacuum states of two different theories: a conformal field theory (CFT), and the CFT perturbed by a relevant operator. By restricting both states to the null Cauchy surface in the causal domain of a sphere, we make the relative entropy equal to the difference of entanglement entropies. As a result, this difference has the positivity and monotonicity properties of relative entropy. From this it follows a simple alternative proof of the c-theorem in d=2 space-time dimensions and, for d>2, the proof that the coefficient of the area term in the entanglement entropy decreases along the renormalization group (RG) flow between fixed points. We comment on the regimes of convergence of relative entropy, depending on the space-time dimensions and the conformal dimension Δ of the perturbation that triggers the RG flow.

  6. Curvature Entropy for Curved Profile Generation

    Directory of Open Access Journals (Sweden)

    Koichiro Sato

    2012-03-01

    Full Text Available In a curved surface design, the overall shape features that emerge from combinations of shape elements are important. However, controlling the features of the overall shape in curved profiles is difficult using conventional microscopic shape information such as dimension. Herein two types of macroscopic shape information, curvature entropy and quadrature curvature entropy, quantitatively represent the features of the overall shape. The curvature entropy is calculated by the curvature distribution, and represents the complexity of a shape (one of the overall shape features. The quadrature curvature entropy is an improvement of the curvature entropy by introducing a Markov process to evaluate the continuity of a curvature and to approximate human cognition of the shape. Additionally, a shape generation method using a genetic algorithm as a calculator and the entropy as a shape generation index is presented. Finally, the applicability of the proposed method is demonstrated using the side view of an automobile as a design example.

  7. Black hole versus cosmological horizon entropy

    International Nuclear Information System (INIS)

    Davis, Tamara M; Davies, P C W; Lineweaver, Charles H

    2003-01-01

    The generalized second law of thermodynamics states that entropy always increases when all event horizons are attributed with an entropy proportional to their area. We test the generalized second law by investigating the change in entropy when dust, radiation and black holes cross a cosmological event horizon. We generalize for flat, open and closed Friedmann-Robertson-Walker universes by using numerical calculations to determine the cosmological horizon evolution. In most cases, the loss of entropy from within the cosmological horizon is more than balanced by an increase in cosmological event horizon entropy, maintaining the validity of the generalized second law of thermodynamics. However, an intriguing set of open universe models shows an apparent entropy decrease when black holes disappear over the cosmological event horizon. We anticipate that this apparent violation of the generalized second law will disappear when solutions are available for black holes embedded in arbitrary backgrounds

  8. Entropy jump across an inviscid shock wave

    Science.gov (United States)

    Salas, Manuel D.; Iollo, Angelo

    1995-01-01

    The shock jump conditions for the Euler equations in their primitive form are derived by using generalized functions. The shock profiles for specific volume, speed, and pressure are shown to be the same, however density has a different shock profile. Careful study of the equations that govern the entropy shows that the inviscid entropy profile has a local maximum within the shock layer. We demonstrate that because of this phenomenon, the entropy, propagation equation cannot be used as a conservation law.

  9. New Definition and Properties of Fuzzy Entropy

    Institute of Scientific and Technical Information of China (English)

    Qing Ming; Qin Yingbing

    2006-01-01

    Let X = (x1,x2 ,…,xn ) and F(X) be a fuzzy set on a universal set X. A new definition of fuzzy entropy about a fuzzy set A on F(X), e*, is defined based on the order relation "≤" on [0,1/2] n. It is proved that e* is a σ-entropy under an additional requirement. Besides, some entropy formulas are presented and related properties are discussed.

  10. Permutation Entropy: New Ideas and Challenges

    Directory of Open Access Journals (Sweden)

    Karsten Keller

    2017-03-01

    Full Text Available Over recent years, some new variants of Permutation entropy have been introduced and applied to EEG analysis, including a conditional variant and variants using some additional metric information or being based on entropies that are different from the Shannon entropy. In some situations, it is not completely clear what kind of information the new measures and their algorithmic implementations provide. We discuss the new developments and illustrate them for EEG data.

  11. Entropy In the Universe: A New Approach

    Directory of Open Access Journals (Sweden)

    Antonio Alfonso-Faus

    2000-09-01

    Full Text Available Abstract: We propose a new definition of entropy for any mass m, based on gravitation and through the concept of a gravitational cross section. It turns out to be proportional to mass, and therefore extensive, and to the age of the Universe. It is a Machian approach. It is also the number of gravity quanta the mass has emitted through its age. The entropy of the Uni-verse is so determined and the cosmological entropy problem solved.

  12. Curvature Entropy for Curved Profile Generation

    OpenAIRE

    Ujiie, Yoshiki; Kato, Takeo; Sato, Koichiro; Matsuoka, Yoshiyuki

    2012-01-01

    In a curved surface design, the overall shape features that emerge from combinations of shape elements are important. However, controlling the features of the overall shape in curved profiles is difficult using conventional microscopic shape information such as dimension. Herein two types of macroscopic shape information, curvature entropy and quadrature curvature entropy, quantitatively represent the features of the overall shape. The curvature entropy is calculated by the curvature distribu...

  13. Nonextensive entropies derived from Gauss' principle

    International Nuclear Information System (INIS)

    Wada, Tatsuaki

    2011-01-01

    Gauss' principle in statistical mechanics is generalized for a q-exponential distribution in nonextensive statistical mechanics. It determines the associated stochastic and statistical nonextensive entropies which satisfy Greene-Callen principle concerning on the equivalence between microcanonical and canonical ensembles. - Highlights: → Nonextensive entropies are derived from Gauss' principle and ensemble equivalence. → Gauss' principle is generalized for a q-exponential distribution. → I have found the condition for satisfying Greene-Callen principle. → The associated statistical q-entropy is found to be normalized Tsallis entropy.

  14. Entropy as a measure of diffusion

    International Nuclear Information System (INIS)

    Aghamohammadi, Amir; Fatollahi, Amir H.; Khorrami, Mohammad; Shariati, Ahmad

    2013-01-01

    The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large times the entropy tends exponentially to a constant. For systems with no stationary density, at large times the entropy is logarithmic with a coefficient specifying the speed of the diffusion. As an example, the large-time behaviors of the entropy and the variance are compared for various types of fractional-derivative diffusions.

  15. Entropy as a measure of diffusion

    Energy Technology Data Exchange (ETDEWEB)

    Aghamohammadi, Amir, E-mail: mohamadi@alzahra.ac.ir; Fatollahi, Amir H., E-mail: fath@alzahra.ac.ir; Khorrami, Mohammad, E-mail: mamwad@mailaps.org; Shariati, Ahmad, E-mail: shariati@mailaps.org

    2013-10-15

    The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large times the entropy tends exponentially to a constant. For systems with no stationary density, at large times the entropy is logarithmic with a coefficient specifying the speed of the diffusion. As an example, the large-time behaviors of the entropy and the variance are compared for various types of fractional-derivative diffusions.

  16. Holographic entanglement entropy and cyclic cosmology

    Science.gov (United States)

    Frampton, Paul H.

    2018-06-01

    We discuss a cyclic cosmology in which the visible universe, or introverse, is all that is accessible to an observer while the extroverse represents the total spacetime originating from the time when the dark energy began to dominate. It is argued that entanglement entropy of the introverse is the more appropriate quantity to render infinitely cyclic, rather than the entropy of the total universe. Since vanishing entanglement entropy implies disconnected spacetimes, at the turnaround when the introverse entropy is zero the disconnected extroverse can be jettisoned with impunity.

  17. All Inequalities for the Relative Entropy

    Science.gov (United States)

    Ibinson, Ben; Linden, Noah; Winter, Andreas

    2007-01-01

    The relative entropy of two n-party quantum states is an important quantity exhibiting, for example, the extent to which the two states are different. The relative entropy of the states formed by reducing two n-party states to a smaller number m of parties is always less than or equal to the relative entropy of the two original n-party states. This is the monotonicity of relative entropy. Using techniques from convex geometry, we prove that monotonicity under restrictions is the only general inequality satisfied by quantum relative entropies. In doing so we make a connection to secret sharing schemes with general access structures: indeed, it turns out that the extremal rays of the cone defined by monotonicity are populated by classical secret sharing schemes. A surprising outcome is that the structure of allowed relative entropy values of subsets of multiparty states is much simpler than the structure of allowed entropy values. And the structure of allowed relative entropy values (unlike that of entropies) is the same for classical probability distributions and quantum states.

  18. Entanglement entropy for a particle coupled with its surrounding

    International Nuclear Information System (INIS)

    Puttarprom, C.; Yoo-Kong, S.; Tanasittikosol, M.; Liewrian, W.

    2014-01-01

    We investigate the entanglement for a model of a particle moving in the lattice (many-body system). The interaction between the particle and the lattice is modelled using Hooke's law. The Feynman path integral approach is applied to compute the density matrix of the system. The complexity of the problem is reduced by considering two-body system (bipartite system). The spatial entanglement of ground state is studied using the linear entropy. We find that increasing the confining potential implies a large spatial separation between the two particles. Thus the interaction between the particles increases according to Hooke's law. This results in the increase in the spatial entanglement

  19. Entropy of the electroencephalogram as applied in the M-Entropy S ...

    African Journals Online (AJOL)

    Background: It has been suggested that spectral entropy of the electroencephalogram as applied in the M-Entropy S/5TM Module (GE Healthcare) does not detect the effects of nitrous oxide (N2O). The aim of this study was to investigate the effect on entropy by graded increases in N2O concentrations in the presence of a ...

  20. The Dynameomics Entropy Dictionary: A Large-Scale Assessment of Conformational Entropy across Protein Fold Space.

    Science.gov (United States)

    Towse, Clare-Louise; Akke, Mikael; Daggett, Valerie

    2017-04-27

    Molecular dynamics (MD) simulations contain considerable information with regard to the motions and fluctuations of a protein, the magnitude of which can be used to estimate conformational entropy. Here we survey conformational entropy across protein fold space using the Dynameomics database, which represents the largest existing data set of protein MD simulations for representatives of essentially all known protein folds. We provide an overview of MD-derived entropies accounting for all possible degrees of dihedral freedom on an unprecedented scale. Although different side chains might be expected to impose varying restrictions on the conformational space that the backbone can sample, we found that the backbone entropy and side chain size are not strictly coupled. An outcome of these analyses is the Dynameomics Entropy Dictionary, the contents of which have been compared with entropies derived by other theoretical approaches and experiment. As might be expected, the conformational entropies scale linearly with the number of residues, demonstrating that conformational entropy is an extensive property of proteins. The calculated conformational entropies of folding agree well with previous estimates. Detailed analysis of specific cases identifies deviations in conformational entropy from the average values that highlight how conformational entropy varies with sequence, secondary structure, and tertiary fold. Notably, α-helices have lower entropy on average than do β-sheets, and both are lower than coil regions.

  1. Three faces of entropy for complex systems: Information, thermodynamics, and the maximum entropy principle

    Science.gov (United States)

    Thurner, Stefan; Corominas-Murtra, Bernat; Hanel, Rudolf

    2017-09-01

    There are at least three distinct ways to conceptualize entropy: entropy as an extensive thermodynamic quantity of physical systems (Clausius, Boltzmann, Gibbs), entropy as a measure for information production of ergodic sources (Shannon), and entropy as a means for statistical inference on multinomial processes (Jaynes maximum entropy principle). Even though these notions represent fundamentally different concepts, the functional form of the entropy for thermodynamic systems in equilibrium, for ergodic sources in information theory, and for independent sampling processes in statistical systems, is degenerate, H (p ) =-∑ipilogpi . For many complex systems, which are typically history-dependent, nonergodic, and nonmultinomial, this is no longer the case. Here we show that for such processes, the three entropy concepts lead to different functional forms of entropy, which we will refer to as SEXT for extensive entropy, SIT for the source information rate in information theory, and SMEP for the entropy functional that appears in the so-called maximum entropy principle, which characterizes the most likely observable distribution functions of a system. We explicitly compute these three entropy functionals for three concrete examples: for Pólya urn processes, which are simple self-reinforcing processes, for sample-space-reducing (SSR) processes, which are simple history dependent processes that are associated with power-law statistics, and finally for multinomial mixture processes.

  2. Monotonicity of the von Neumann entropy expressed as a function of R\\'enyi entropies

    OpenAIRE

    Fannes, Mark

    2013-01-01

    The von Neumann entropy of a density matrix of dimension d, expressed in terms of the first d-1 integer order R\\'enyi entropies, is monotonically increasing in R\\'enyi entropies of even order and decreasing in those of odd order.

  3. Entanglement entropy of excited states

    International Nuclear Information System (INIS)

    Alba, Vincenzo; Fagotti, Maurizio; Calabrese, Pasquale

    2009-01-01

    We study the entanglement entropy of a block of contiguous spins in excited states of spin chains. We consider the XY model in a transverse field and the XXZ Heisenberg spin chain. For the latter, we developed a numerical application of the algebraic Bethe ansatz. We find two main classes of states with logarithmic and extensive behavior in the dimension of the block, characterized by the properties of excitations of the state. This behavior can be related to the locality properties of the Hamiltonian having a given state as the ground state. We also provide several details of the finite size scaling

  4. Entropy analysis in yeast DNA

    International Nuclear Information System (INIS)

    Kim, Jongkwang; Kim, Sowun; Lee, Kunsang; Kwon, Younghun

    2009-01-01

    In this article, we investigate the language structure in yeast 16 chromosomes. In order to find it, we use the entropy analysis for codons (or amino acids) of yeast 16 chromosomes, developed in analysis of natural language by Montemurro et al. From the analysis, we can see that there exists a language structure in codons (or amino acids) of yeast 16 chromosomes. Also we find that the grammar structure of amino acids of yeast 16 chromosomes has a deep relationship with secondary structure of protein.

  5. Gravitational entropy and the cosmological no-hair conjecture

    Science.gov (United States)

    Bolejko, Krzysztof

    2018-04-01

    The gravitational entropy and no-hair conjectures seem to predict contradictory future states of our Universe. The growth of the gravitational entropy is associated with the growth of inhomogeneity, while the no-hair conjecture argues that a universe dominated by dark energy should asymptotically approach a homogeneous and isotropic de Sitter state. The aim of this paper is to study these two conjectures. The investigation is based on the Simsilun simulation, which simulates the universe using the approximation of the Silent Universe. The Silent Universe is a solution to the Einstein equations that assumes irrotational, nonviscous, and insulated dust, with vanishing magnetic part of the Weyl curvature. The initial conditions for the Simsilun simulation are sourced from the Millennium simulation, which results with a realistically appearing but relativistic at origin simulation of a universe. The Simsilun simulation is evolved from the early universe (t =25 Myr ) until far future (t =1000 Gyr ). The results of this investigation show that both conjectures are correct. On global scales, a universe with a positive cosmological constant and nonpositive spatial curvature does indeed approach the de Sitter state. At the same time it keeps generating the gravitational entropy.

  6. Clausius entropy for arbitrary bifurcate null surfaces

    International Nuclear Information System (INIS)

    Baccetti, Valentina; Visser, Matt

    2014-01-01

    Jacobson’s thermodynamic derivation of the Einstein equations was originally applied only to local Rindler horizons. But at least some parts of that construction can usefully be extended to give meaningful results for arbitrary bifurcate null surfaces. As presaged in Jacobson’s original article, this more general construction sharply brings into focus the questions: is entropy objectively ‘real’? Or is entropy in some sense subjective and observer-dependent? These innocent questions open a Pandora’s box of often inconclusive debate. A consensus opinion, though certainly not universally held, seems to be that Clausius entropy (thermodynamic entropy, defined via a Clausius relation dS=đQ/T) should be objectively real, but that the ontological status of statistical entropy (Shannon or von Neumann entropy) is much more ambiguous, and much more likely to be observer-dependent. This question is particularly pressing when it comes to understanding Bekenstein entropy (black hole entropy). To perhaps further add to the confusion, we shall argue that even the Clausius entropy can often be observer-dependent. In the current article we shall conclusively demonstrate that one can meaningfully assign a notion of Clausius entropy to arbitrary bifurcate null surfaces—effectively defining a ‘virtual Clausius entropy’ for arbitrary ‘virtual (local) causal horizons’. As an application, we see that we can implement a version of the generalized second law (GSL) for this virtual Clausius entropy. This version of GSL can be related to certain (nonstandard) integral variants of the null energy condition. Because the concepts involved are rather subtle, we take some effort in being careful and explicit in developing our framework. In future work we will apply this construction to generalize Jacobson’s derivation of the Einstein equations. (paper)

  7. The effect of turbulence-radiation interaction on radiative entropy generation and heat transfer

    International Nuclear Information System (INIS)

    Caldas, Miguel; Semiao, Viriato

    2007-01-01

    The analysis under the second law of thermodynamics is the gateway for optimisation in thermal equipments and systems. Through entropy minimisation techniques it is possible to increase the efficiency and overall performance of all kinds of thermal systems. Radiation, being the dominant mechanism of heat transfer in high-temperature systems, plays a determinant role in entropy generation within such equipments. Turbulence is also known to be a major player in the phenomenon of entropy generation. Therefore, turbulence-radiation interaction is expected to have a determinant effect on entropy generation. However, this is a subject that has not been dealt with so far, at least to the extent of the authors' knowledge. The present work attempts to fill that void, by studying the effect of turbulence-radiation interaction on entropy generation. All calculations are approached in such a way as to make them totally compatible with standard engineering methods for radiative heat transfer, namely the discrete ordinates method. It was found that turbulence-radiation interaction does not significantly change the spatial pattern of entropy generation, or heat transfer, but does change significantly their magnitude, in a way approximately proportional to the square of the intensity of turbulence

  8. Entropy production in a box: Analysis of instabilities in confined hydrothermal systems

    Science.gov (United States)

    Börsing, N.; Wellmann, J. F.; Niederau, J.; Regenauer-Lieb, K.

    2017-09-01

    We evaluate if the concept of thermal entropy production can be used as a measure to characterize hydrothermal convection in a confined porous medium as a valuable, thermodynamically motivated addition to the standard Rayleigh number analysis. Entropy production has been used widely in the field of mechanical and chemical engineering as a way to characterize the thermodynamic state and irreversibility of an investigated system. Pioneering studies have since adapted these concepts to natural systems, and we apply this measure here to investigate the specific case of hydrothermal convection in a "box-shaped" confined porous medium, as a simplified analog for, e.g., hydrothermal convection in deep geothermal aquifers. We perform various detailed numerical experiments to assess the response of the convective system to changing boundary conditions or domain aspect ratios, and then determine the resulting entropy production for each experiment. In systems close to the critical Rayleigh number, we derive results that are in accordance to the analytically derived predictions. At higher Rayleigh numbers, however, we observe multiple possible convection modes, and the analysis of the integrated entropy production reveals distinct curves of entropy production that provide an insight into the hydrothermal behavior in the system, both for cases of homogeneous materials, as well as for heterogeneous spatial material distributions. We conclude that the average thermal entropy production characterizes the internal behavior of hydrothermal systems with a meaningful thermodynamic measure, and we expect that it can be useful for the investigation of convection systems in many similar hydrogeological and geophysical settings.

  9. A two-phase copula entropy-based multiobjective optimization approach to hydrometeorological gauge network design

    Science.gov (United States)

    Xu, Pengcheng; Wang, Dong; Singh, Vijay P.; Wang, Yuankun; Wu, Jichun; Wang, Lachun; Zou, Xinqing; Chen, Yuanfang; Chen, Xi; Liu, Jiufu; Zou, Ying; He, Ruimin

    2017-12-01

    Hydrometeorological data are needed for obtaining point and areal mean, quantifying the spatial variability of hydrometeorological variables, and calibration and verification of hydrometeorological models. Hydrometeorological networks are utilized to collect such data. Since data collection is expensive, it is essential to design an optimal network based on the minimal number of hydrometeorological stations in order to reduce costs. This study proposes a two-phase copula entropy- based multiobjective optimization approach that includes: (1) copula entropy-based directional information transfer (CDIT) for clustering the potential hydrometeorological gauges into several groups, and (2) multiobjective method for selecting the optimal combination of gauges for regionalized groups. Although entropy theory has been employed for network design before, the joint histogram method used for mutual information estimation has several limitations. The copula entropy-based mutual information (MI) estimation method is shown to be more effective for quantifying the uncertainty of redundant information than the joint histogram (JH) method. The effectiveness of this approach is verified by applying to one type of hydrometeorological gauge network, with the use of three model evaluation measures, including Nash-Sutcliffe Coefficient (NSC), arithmetic mean of the negative copula entropy (MNCE), and MNCE/NSC. Results indicate that the two-phase copula entropy-based multiobjective technique is capable of evaluating the performance of regional hydrometeorological networks and can enable decision makers to develop strategies for water resources management.

  10. Entanglement of heavy quark impurities and generalized gravitational entropy

    Science.gov (United States)

    Kumar, S. Prem; Silvani, Dorian

    2018-01-01

    We calculate the contribution from non-conformal heavy quark sources to the entanglement entropy (EE) of a spherical region in N=4 SUSY Yang-Mills theory. We apply the generalized gravitational entropy method to non-conformal probe D-brane embeddings in AdS5×S5, dual to pointlike impurities exhibiting flows between quarks in large-rank tensor representations and the fundamental representation. For the D5-brane embedding which describes the screening of fundamental quarks in the UV to the antisymmetric tensor representation in the IR, the EE excess decreases non-monotonically towards its IR asymptotic value, tracking the qualitative behaviour of the one-point function of static fields sourced by the impurity. We also examine two classes of D3-brane embeddings, one which connects a symmetric representation source in the UV to fundamental quarks in the IR, and a second category which yields the symmetric representation source on the Coulomb branch. The EE excess for the former increases from the UV to the IR, whilst decreasing and becoming negative for the latter. In all cases, the probe free energy on hyperbolic space with β = 2 π increases monotonically towards the IR, supporting its interpretation as a relative entropy. We identify universal corrections, depending logarithmically on the VEV, for the symmetric representation on the Coulomb branch.

  11. Entropy coders of the H.264/AVC standard

    CERN Document Server

    Tian, Xiaohua; Lian, Yong

    2010-01-01

    This book presents a collection of algorithms and VLSI architectures of entropy (or statistical) codecs of recent video compression standards, with focus on the H.264/AVC standard. For any visual data compression scheme, there exists a combination of two, or all of the following three stages: spatial, temporal, and statistical compression. General readers are first introduced with the various algorithms of the statistical coders. The VLSI implementations are also reviewed and discussed. Readers with limited hardware design background are also introduced with a design methodology starting from

  12. Mammographic image restoration using maximum entropy deconvolution

    International Nuclear Information System (INIS)

    Jannetta, A; Jackson, J C; Kotre, C J; Birch, I P; Robson, K J; Padgett, R

    2004-01-01

    An image restoration approach based on a Bayesian maximum entropy method (MEM) has been applied to a radiological image deconvolution problem, that of reduction of geometric blurring in magnification mammography. The aim of the work is to demonstrate an improvement in image spatial resolution in realistic noisy radiological images with no associated penalty in terms of reduction in the signal-to-noise ratio perceived by the observer. Images of the TORMAM mammographic image quality phantom were recorded using the standard magnification settings of 1.8 magnification/fine focus and also at 1.8 magnification/broad focus and 3.0 magnification/fine focus; the latter two arrangements would normally give rise to unacceptable geometric blurring. Measured point-spread functions were used in conjunction with the MEM image processing to de-blur these images. The results are presented as comparative images of phantom test features and as observer scores for the raw and processed images. Visualization of high resolution features and the total image scores for the test phantom were improved by the application of the MEM processing. It is argued that this successful demonstration of image de-blurring in noisy radiological images offers the possibility of weakening the link between focal spot size and geometric blurring in radiology, thus opening up new approaches to system optimization

  13. BAYESIAN ENTROPY FOR SPATIAL SAMPLING DESIGN OF ENVIRONMENTAL DATA

    Science.gov (United States)

    Particulate Matter (PM) has been linked to widespread public health effects, including a range of serious respiratory and cardiovascular problems, and to reduced visibility in may parts of the United States, see the Environmental Protection Agency (EPA) report (2004) and relevant...

  14. Maximum entropy principle and hydrodynamic models in statistical mechanics

    International Nuclear Information System (INIS)

    Trovato, M.; Reggiani, L.

    2012-01-01

    This review presents the state of the art of the maximum entropy principle (MEP) in its classical and quantum (QMEP) formulation. Within the classical MEP we overview a general theory able to provide, in a dynamical context, the macroscopic relevant variables for carrier transport in the presence of electric fields of arbitrary strength. For the macroscopic variables the linearized maximum entropy approach is developed including full-band effects within a total energy scheme. Under spatially homogeneous conditions, we construct a closed set of hydrodynamic equations for the small-signal (dynamic) response of the macroscopic variables. The coupling between the driving field and the energy dissipation is analyzed quantitatively by using an arbitrary number of moments of the distribution function. Analogously, the theoretical approach is applied to many one-dimensional n + nn + submicron Si structures by using different band structure models, different doping profiles, different applied biases and is validated by comparing numerical calculations with ensemble Monte Carlo simulations and with available experimental data. Within the quantum MEP we introduce a quantum entropy functional of the reduced density matrix, the principle of quantum maximum entropy is then asserted as fundamental principle of quantum statistical mechanics. Accordingly, we have developed a comprehensive theoretical formalism to construct rigorously a closed quantum hydrodynamic transport within a Wigner function approach. The theory is formulated both in thermodynamic equilibrium and nonequilibrium conditions, and the quantum contributions are obtained by only assuming that the Lagrange multipliers can be expanded in powers of ħ 2 , being ħ the reduced Planck constant. In particular, by using an arbitrary number of moments, we prove that: i) on a macroscopic scale all nonlocal effects, compatible with the uncertainty principle, are imputable to high-order spatial derivatives both of the

  15. Some relations between entropy and approximation numbers

    Institute of Scientific and Technical Information of China (English)

    郑志明

    1999-01-01

    A general result is obtained which relates the entropy numbers of compact maps on Hilbert space to its approximation numbers. Compared with previous works in this area, it is particularly convenient for dealing with the cases where the approximation numbers decay rapidly. A nice estimation between entropy and approximation numbers for noncompact maps is given.

  16. Length scale for configurational entropy in microemulsions

    NARCIS (Netherlands)

    Reiss, H.; Kegel, W.K.; Groenewold, J.

    1996-01-01

    In this paper we study the length scale that must be used in evaluating the mixing entropy in a microemulsion. The central idea involves the choice of a length scale in configuration space that is consistent with the physical definition of entropy in phase space. We show that this scale may be

  17. Chemical Engineering Students' Ideas of Entropy

    Science.gov (United States)

    Haglund, Jesper; Andersson, Staffan; Elmgren, Maja

    2015-01-01

    Thermodynamics, and in particular entropy, has been found to be challenging for students, not least due to its abstract character. Comparisons with more familiar and concrete domains, by means of analogy and metaphor, are commonly used in thermodynamics teaching, in particular the metaphor "entropy is disorder." However, this particular…

  18. Invariant of dynamical systems: A generalized entropy

    International Nuclear Information System (INIS)

    Meson, A.M.; Vericat, F.

    1996-01-01

    In this work the concept of entropy of a dynamical system, as given by Kolmogorov, is generalized in the sense of Tsallis. It is shown that this entropy is an isomorphism invariant, being complete for Bernoulli schemes. copyright 1996 American Institute of Physics

  19. Entropy and Certainty in Lossless Data Compression

    Science.gov (United States)

    Jacobs, James Jay

    2009-01-01

    Data compression is the art of using encoding techniques to represent data symbols using less storage space compared to the original data representation. The encoding process builds a relationship between the entropy of the data and the certainty of the system. The theoretical limits of this relationship are defined by the theory of entropy in…

  20. Problems in black-hole entropy interpretation

    International Nuclear Information System (INIS)

    Liberati, S.

    1997-01-01

    In this work some proposals for black-hole entropy interpretation are exposed and investigated. In particular, the author will firstly consider the so-called 'entanglement entropy' interpretation, in the framework of the brick wall model and the divergence problem arising in the one-loop calculations of various thermodynamical quantities, like entropy, internal energy and heat capacity. It is shown that the assumption of equality of entanglement entropy and Bekenstein-Hawking one appears to give inconsistent results. These will be a starting point for a different interpretation of black.hole entropy based on peculiar topological structures of manifolds with 'intrinsic' thermodynamical features. It is possible to show an exact relation between black-hole gravitational entropy and topology of these Euclidean space-times. the expression for the Euler characteristic, through the Gauss-Bonnet integral, and the one for entropy for gravitational instantons are proposed in a form which makes the relation between these self-evident. Using this relation he propose a generalization of the Bekenstein-Hawking entropy in which the former and Euler characteristic are related in the equation S = χA / 8. Finally, he try to expose some conclusions and hypotheses about possible further development of this research

  1. Ehrenfest's Lottery--Time and Entropy Maximization

    Science.gov (United States)

    Ashbaugh, Henry S.

    2010-01-01

    Successful teaching of the Second Law of Thermodynamics suffers from limited simple examples linking equilibrium to entropy maximization. I describe a thought experiment connecting entropy to a lottery that mixes marbles amongst a collection of urns. This mixing obeys diffusion-like dynamics. Equilibrium is achieved when the marble distribution is…

  2. Does black-hole entropy make sense

    International Nuclear Information System (INIS)

    Wilkins, D.

    1979-01-01

    Bekenstein and Hawking saved the second law of thermodynamics near a black hole by assigning to the hole an entropy Ssub(h) proportional to the area of its event horizon. It is tempting to assume that Ssub(h) possesses all the features commonly associated with the physical entropy. Kundt has shown, however, that Ssub(h) violates several reasonable physical expectations. This criticism is reviewed, augmenting it as follows: (a) Ssub(h) is a badly behaved state function requiring knowledge of the hole's future history; and (b) close analogs of event horizons in other space-times do not possess an 'entropy'. These questions are also discussed: (c) Is Ssub(h) suitable for all regions of a black-hole space-time. And (b) should Ssub(h) be attributed to the exterior of a white hole. One can retain Ssub(h) for the interior (respectively, exterior) of a black (respectively, white) hole, but is rejected as contrary to the information-theoretic derivation of horizon entropy given by Berkenstein. The total entropy defined by Kundt (all ordinary entropy on space-section cutting through the hole, no horizon term) and that of Bekenstein-Hawking (ordinary entropy outside horizon plus horizon term) appear to be complementary concepts with separate domains of validity. In the most natural choice, an observer inside a black hole will use Kundt's entropy, and one remaining outside that of Bekenstein-Hawking. (author)

  3. Towards operational interpretations of generalized entropies

    DEFF Research Database (Denmark)

    Topsøe, Flemming

    Operationelle fortolkninger af nye entropimål, f.eks. af Tsallis entropi, angives med udgangspunkt i erkendelsesteoretiske betragtninger.......Operationelle fortolkninger af nye entropimål, f.eks. af Tsallis entropi, angives med udgangspunkt i erkendelsesteoretiske betragtninger....

  4. Quantum aspects of black hole entropy

    Indian Academy of Sciences (India)

    Quantum corrections to the semiclassical Bekenstein–Hawking area law for black hole entropy, obtained within the quantum geometry framework, are treated in some detail. Their ramification for the holographic entropy bound for bounded stationary spacetimes is discussed. Four dimensional supersymmetric extremal black ...

  5. Entropy Generation in a Chemical Reaction

    Science.gov (United States)

    Miranda, E. N.

    2010-01-01

    Entropy generation in a chemical reaction is analysed without using the general formalism of non-equilibrium thermodynamics at a level adequate for advanced undergraduates. In a first approach to the problem, the phenomenological kinetic equation of an elementary first-order reaction is used to show that entropy production is always positive. A…

  6. The Thermal Entropy Density of Spacetime

    Directory of Open Access Journals (Sweden)

    Rongjia Yang

    2013-01-01

    Full Text Available Introducing the notion of thermal entropy density via the first law of thermodynamics and assuming the Einstein equation as an equation of thermal state, we obtain the thermal entropy density of any arbitrary spacetime without assuming a temperature or a horizon. The results confirm that there is a profound connection between gravity and thermodynamics.

  7. Holographic entanglement entropy in Lovelock gravities

    NARCIS (Netherlands)

    de Boer, J.; Kulaxizi, M.; Parnachev, A.

    2011-01-01

    We study entanglement entropies of simply connected surfaces in field theories dual to Lovelock gravities. We consider Gauss-Bonnet and cubic Lovelock gravities in detail. In the conformal case the logarithmic terms in the entanglement entropy are governed by the conformal anomalies of the CFT; we

  8. Entropies, Partitionings and Heart Rate Variability

    Czech Academy of Sciences Publication Activity Database

    Paluš, Milan; Zebrowski, J.

    2009-01-01

    Roč. 51, č. 2 (2009), s. 65-72 ISSN 0001-7604 Institutional research plan: CEZ:AV0Z10300504 Keywords : coarse-grained entropy rate * HR variability * entropy Subject RIV: BB - Applied Statistics, Operational Research http://www.activitas.org/index.php/nervosa/article/view/25

  9. Evaluation of the entropy consistent euler flux on 1D and 2D test problems

    Science.gov (United States)

    Roslan, Nur Khairunnisa Hanisah; Ismail, Farzad

    2012-06-01

    Perhaps most CFD simulations may yield good predictions of pressure and velocity when compared to experimental data. Unfortunately, these results will most likely not adhere to the second law of thermodynamics hence comprising the authenticity of predicted data. Currently, the test of a good CFD code is to check how much entropy is generated in a smooth flow and hope that the numerical entropy produced is of the correct sign when a shock is encountered. Herein, a shock capturing code written in C++ based on a recent entropy consistent Euler flux is developed to simulate 1D and 2D flows. Unlike other finite volume schemes in commercial CFD code, this entropy consistent flux (EC) function precisely satisfies the discrete second law of thermodynamics. This EC flux has an entropy-conserved part, preserving entropy for smooth flows and a numerical diffusion part that will accurately produce the proper amount of entropy, consistent with the second law. Several numerical simulations of the entropy consistent flux have been tested on two dimensional test cases. The first case is a Mach 3 flow over a forward facing step. The second case is a flow over a NACA 0012 airfoil while the third case is a hypersonic flow passing over a 2D cylinder. Local flow quantities such as velocity and pressure are analyzed and then compared with mainly the Roe flux. The results herein show that the EC flux does not capture the unphysical rarefaction shock unlike the Roe-flux and does not easily succumb to the carbuncle phenomenon. In addition, the EC flux maintains good performance in cases where the Roe flux is known to be superior.

  10. The improvement of Clausius entropy and its application in entropy analysis

    Institute of Scientific and Technical Information of China (English)

    WU Jing; GUO ZengYuan

    2008-01-01

    The defects of Cleusius entropy which Include s premise of reversible process and a process quantlty of heat in Its definition are discussed in this paper. Moreover, the heat temperature quotient under reversible conditions, i.e. (δQ/T)rev, is essentially a process quantity although it is numerically equal to the entropy change. The sum of internal energy temperature quotient and work temperature quotient is defined as the improved form of Clausius entropy and it can be further proved to be a state funcllon. Unlike Clausius entropy, the improved deflnltion consists of system properties wlthout premise just like other state functions, for example, pressure p and enthalpy h, etc. it is unnecessary to invent reversible paths when calculating entropy change for irreversible processes based on the improved form of entropy since it is independent of process. Furthermore, entropy balance equations for internally and externally irreversible processes are deduced respectively based on the concepts of thermal reservoir entropy transfer and system entropy transfer. Finally, some examples are presented to show that the improved deflnitlon of Clausius entropy provides a clear concept as well as a convenient method for en-tropy change calculation.

  11. Estimation of yield and water requirements of maize crops combining high spatial and temporal resolution images with a simple crop model, in the perspective of the Sentinel-2 mission

    Science.gov (United States)

    Battude, Marjorie; Bitar, Ahmad Al; Brut, Aurore; Cros, Jérôme; Dejoux, Jean-François; Huc, Mireille; Marais Sicre, Claire; Tallec, Tiphaine; Demarez, Valérie

    2016-04-01

    Water resources are under increasing pressure as a result of global change and of a raising competition among the different users (agriculture, industry, urban). It is therefore important to develop tools able to estimate accurately crop water requirements in order to optimize irrigation while maintaining acceptable production. In this context, remote sensing is a valuable tool to monitor vegetation development and water demand. This work aims at developing a robust and generic methodology mainly based on high resolution remote sensing data to provide accurate estimates of maize yield and water needs at the watershed scale. Evapotranspiration (ETR) and dry aboveground biomass (DAM) of maize crops were modeled using time series of GAI images used to drive a simple agro-meteorological crop model (SAFYE, Duchemin et al., 2005). This model is based on a leaf partitioning function (Maas, 1993) for the simulation of crop biomass and on the FAO-56 methodology for the ETR simulation. The model also contains a module to simulate irrigation. This study takes advantage of the SPOT4 and SPOT5 Take5 experiments initiated by CNES (http://www.cesbio.ups-tlse.fr/multitemp/). They provide optical images over the watershed from February to May 2013 and from April to August 2015 respectively, with a temporal and spatial resolution similar to future images from the Sentinel-2 and VENμS missions. This dataset was completed with LandSat8 and Deimos1 images in order to cover the whole growing season while reducing the gaps in remote sensing time series. Radiometric, geometric and atmospheric corrections were achieved by the THEIA land data center, and the KALIDEOS processing chain. The temporal dynamics of the green area index (GAI) plays a key role in soil-plant-atmosphere interactions and in biomass accumulation process. Consistent seasonal dynamics of the remotely sensed GAI was estimated by applying a radiative transfer model based on artificial neural networks (BVNET, Baret

  12. On S-mixing entropy of quantum channels

    Science.gov (United States)

    Mukhamedov, Farrukh; Watanabe, Noboru

    2018-06-01

    In this paper, an S-mixing entropy of quantum channels is introduced as a generalization of Ohya's S-mixing entropy. We investigate several properties of the introduced entropy. Moreover, certain relations between the S-mixing entropy and the existing map and output entropies of quantum channels are investigated as well. These relations allowed us to find certain connections between separable states and the introduced entropy. Hence, there is a sufficient condition to detect entangled states. Moreover, several properties of the introduced entropy are investigated. Besides, entropies of qubit and phase-damping channels are calculated.

  13. Shannon versus Kullback-Leibler entropies in nonequilibrium random motion

    International Nuclear Information System (INIS)

    Garbaczewski, Piotr

    2005-01-01

    We analyze dynamical properties of the Shannon information entropy of a continuous probability distribution, which is driven by a standard diffusion process. This entropy choice is confronted with another option, employing the conditional Kullback-Leibler entropy. Both entropies discriminate among various probability distributions, either statically or in the time domain. An asymptotic approach towards equilibrium is typically monotonic in terms of the Kullback entropy. The Shannon entropy time rate needs not to be positive and is a sensitive indicator of the power transfer processes (removal/supply) due to an active environment. In the case of Smoluchowski diffusions, the Kullback entropy time rate coincides with the Shannon entropy 'production' rate

  14. On the way towards a generalized entropy maximization procedure

    International Nuclear Information System (INIS)

    Bagci, G. Baris; Tirnakli, Ugur

    2009-01-01

    We propose a generalized entropy maximization procedure, which takes into account the generalized averaging procedures and information gain definitions underlying the generalized entropies. This novel generalized procedure is then applied to Renyi and Tsallis entropies. The generalized entropy maximization procedure for Renyi entropies results in the exponential stationary distribution asymptotically for q element of (0,1] in contrast to the stationary distribution of the inverse power law obtained through the ordinary entropy maximization procedure. Another result of the generalized entropy maximization procedure is that one can naturally obtain all the possible stationary distributions associated with the Tsallis entropies by employing either ordinary or q-generalized Fourier transforms in the averaging procedure.

  15. What is the entropy of the universe?

    International Nuclear Information System (INIS)

    Frampton, Paul H; Hsu, Stephen D H; Reeb, David; Kephart, Thomas W

    2009-01-01

    Standard calculations suggest that the entropy of our universe is dominated by black holes, whose entropy is of order their area in Planck units, although they comprise only a tiny fraction of its total energy. Statistical entropy is the logarithm of the number of microstates consistent with the observed macroscopic properties of a system, hence a measure of uncertainty about its precise state. Therefore, assuming unitarity in black hole evaporation, the standard results suggest that the largest uncertainty in the future quantum state of the universe is due to the Hawking radiation from evaporating black holes. However, the entropy of the matter precursors to astrophysical black holes is enormously less than that given by area entropy. If unitarity relates the future radiation states to the black hole precursor states, then the standard results are highly misleading, at least for an observer that can differentiate the individual states of the Hawking radiation.

  16. What is the entropy of the universe?

    Energy Technology Data Exchange (ETDEWEB)

    Frampton, Paul H [Department of Physics and Astronomy, UNC-Chapel Hill, NC 27599 (United States); Hsu, Stephen D H; Reeb, David [Institute of Theoretical Science, University of Oregon, Eugene, OR 97403 (United States); Kephart, Thomas W, E-mail: frampton@physics.unc.ed, E-mail: hsu@uoregon.ed, E-mail: tom.kephart@gmail.co, E-mail: dreeb@uoregon.ed [Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235 (United States)

    2009-07-21

    Standard calculations suggest that the entropy of our universe is dominated by black holes, whose entropy is of order their area in Planck units, although they comprise only a tiny fraction of its total energy. Statistical entropy is the logarithm of the number of microstates consistent with the observed macroscopic properties of a system, hence a measure of uncertainty about its precise state. Therefore, assuming unitarity in black hole evaporation, the standard results suggest that the largest uncertainty in the future quantum state of the universe is due to the Hawking radiation from evaporating black holes. However, the entropy of the matter precursors to astrophysical black holes is enormously less than that given by area entropy. If unitarity relates the future radiation states to the black hole precursor states, then the standard results are highly misleading, at least for an observer that can differentiate the individual states of the Hawking radiation.

  17. Entropy of black holes with multiple horizons

    Directory of Open Access Journals (Sweden)

    Yun He

    2018-05-01

    Full Text Available We examine the entropy of black holes in de Sitter space and black holes surrounded by quintessence. These black holes have multiple horizons, including at least the black hole event horizon and a horizon outside it (cosmological horizon for de Sitter black holes and “quintessence horizon” for the black holes surrounded by quintessence. Based on the consideration that the two horizons are not independent each other, we conjecture that the total entropy of these black holes should not be simply the sum of entropies of the two horizons, but should have an extra term coming from the correlations between the two horizons. Different from our previous works, in this paper we consider the cosmological constant as the variable and employ an effective method to derive the explicit form of the entropy. We also try to discuss the thermodynamic stabilities of these black holes according to the entropy and the effective temperature.

  18. Black hole entropy, curved space and monsters

    International Nuclear Information System (INIS)

    Hsu, Stephen D.H.; Reeb, David

    2008-01-01

    We investigate the microscopic origin of black hole entropy, in particular the gap between the maximum entropy of ordinary matter and that of black holes. Using curved space, we construct configurations with entropy greater than the area A of a black hole of equal mass. These configurations have pathological properties and we refer to them as monsters. When monsters are excluded we recover the entropy bound on ordinary matter S 3/4 . This bound implies that essentially all of the microstates of a semiclassical black hole are associated with the growth of a slightly smaller black hole which absorbs some additional energy. Our results suggest that the area entropy of black holes is the logarithm of the number of distinct ways in which one can form the black hole from ordinary matter and smaller black holes, but only after the exclusion of monster states

  19. Constant conditional entropy and related hypotheses

    International Nuclear Information System (INIS)

    Ferrer-i-Cancho, Ramon; Dębowski, Łukasz; Moscoso del Prado Martín, Fermín

    2013-01-01

    Constant entropy rate (conditional entropies must remain constant as the sequence length increases) and uniform information density (conditional probabilities must remain constant as the sequence length increases) are two information theoretic principles that are argued to underlie a wide range of linguistic phenomena. Here we revise the predictions of these principles in the light of Hilberg’s law on the scaling of conditional entropy in language and related laws. We show that constant entropy rate (CER) and two interpretations for uniform information density (UID), full UID and strong UID, are inconsistent with these laws. Strong UID implies CER but the reverse is not true. Full UID, a particular case of UID, leads to costly uncorrelated sequences that are totally unrealistic. We conclude that CER and its particular cases are incomplete hypotheses about the scaling of conditional entropies. (letter)

  20. Entropy of black holes with multiple horizons

    Science.gov (United States)

    He, Yun; Ma, Meng-Sen; Zhao, Ren

    2018-05-01

    We examine the entropy of black holes in de Sitter space and black holes surrounded by quintessence. These black holes have multiple horizons, including at least the black hole event horizon and a horizon outside it (cosmological horizon for de Sitter black holes and "quintessence horizon" for the black holes surrounded by quintessence). Based on the consideration that the two horizons are not independent each other, we conjecture that the total entropy of these black holes should not be simply the sum of entropies of the two horizons, but should have an extra term coming from the correlations between the two horizons. Different from our previous works, in this paper we consider the cosmological constant as the variable and employ an effective method to derive the explicit form of the entropy. We also try to discuss the thermodynamic stabilities of these black holes according to the entropy and the effective temperature.

  1. Entanglement entropy in top-down models

    Energy Technology Data Exchange (ETDEWEB)

    Jones, Peter A.R.; Taylor, Marika [Mathematical Sciences and STAG Research Centre, University of Southampton,Highfield, Southampton, SO17 1BJ (United Kingdom)

    2016-08-26

    We explore holographic entanglement entropy in ten-dimensional supergravity solutions. It has been proposed that entanglement entropy can be computed in such top-down models using minimal surfaces which asymptotically wrap the compact part of the geometry. We show explicitly in a wide range of examples that the holographic entanglement entropy thus computed agrees with the entanglement entropy computed using the Ryu-Takayanagi formula from the lower-dimensional Einstein metric obtained from reduction over the compact space. Our examples include not only consistent truncations but also cases in which no consistent truncation exists and Kaluza-Klein holography is used to identify the lower-dimensional Einstein metric. We then give a general proof, based on the Lewkowycz-Maldacena approach, of the top-down entanglement entropy formula.

  2. Entanglement entropy in top-down models

    International Nuclear Information System (INIS)

    Jones, Peter A.R.; Taylor, Marika

    2016-01-01

    We explore holographic entanglement entropy in ten-dimensional supergravity solutions. It has been proposed that entanglement entropy can be computed in such top-down models using minimal surfaces which asymptotically wrap the compact part of the geometry. We show explicitly in a wide range of examples that the holographic entanglement entropy thus computed agrees with the entanglement entropy computed using the Ryu-Takayanagi formula from the lower-dimensional Einstein metric obtained from reduction over the compact space. Our examples include not only consistent truncations but also cases in which no consistent truncation exists and Kaluza-Klein holography is used to identify the lower-dimensional Einstein metric. We then give a general proof, based on the Lewkowycz-Maldacena approach, of the top-down entanglement entropy formula.

  3. Low Streamflow Forcasting using Minimum Relative Entropy

    Science.gov (United States)

    Cui, H.; Singh, V. P.

    2013-12-01

    Minimum relative entropy spectral analysis is derived in this study, and applied to forecast streamflow time series. Proposed method extends the autocorrelation in the manner that the relative entropy of underlying process is minimized so that time series data can be forecasted. Different prior estimation, such as uniform, exponential and Gaussian assumption, is taken to estimate the spectral density depending on the autocorrelation structure. Seasonal and nonseasonal low streamflow series obtained from Colorado River (Texas) under draught condition is successfully forecasted using proposed method. Minimum relative entropy determines spectral of low streamflow series with higher resolution than conventional method. Forecasted streamflow is compared to the prediction using Burg's maximum entropy spectral analysis (MESA) and Configurational entropy. The advantage and disadvantage of each method in forecasting low streamflow is discussed.

  4. Applying Improved Multiscale Fuzzy Entropy for Feature Extraction of MI-EEG

    Directory of Open Access Journals (Sweden)

    Ming-ai Li

    2017-01-01

    Full Text Available Electroencephalography (EEG is considered the output of a brain and it is a bioelectrical signal with multiscale and nonlinear properties. Motor Imagery EEG (MI-EEG not only has a close correlation with the human imagination and movement intention but also contains a large amount of physiological or disease information. As a result, it has been fully studied in the field of rehabilitation. To correctly interpret and accurately extract the features of MI-EEG signals, many nonlinear dynamic methods based on entropy, such as Approximate Entropy (ApEn, Sample Entropy (SampEn, Fuzzy Entropy (FE, and Permutation Entropy (PE, have been proposed and exploited continuously in recent years. However, these entropy-based methods can only measure the complexity of MI-EEG based on a single scale and therefore fail to account for the multiscale property inherent in MI-EEG. To solve this problem, Multiscale Sample Entropy (MSE, Multiscale Permutation Entropy (MPE, and Multiscale Fuzzy Entropy (MFE are developed by introducing scale factor. However, MFE has not been widely used in analysis of MI-EEG, and the same parameter values are employed when the MFE method is used to calculate the fuzzy entropy values on multiple scales. Actually, each coarse-grained MI-EEG carries the characteristic information of the original signal on different scale factors. It is necessary to optimize MFE parameters to discover more feature information. In this paper, the parameters of MFE are optimized independently for each scale factor, and the improved MFE (IMFE is applied to the feature extraction of MI-EEG. Based on the event-related desynchronization (ERD/event-related synchronization (ERS phenomenon, IMFE features from multi channels are fused organically to construct the feature vector. Experiments are conducted on a public dataset by using Support Vector Machine (SVM as a classifier. The experiment results of 10-fold cross-validation show that the proposed method yields

  5. On unified-entropy characterization of quantum channels

    International Nuclear Information System (INIS)

    Rastegin, A E

    2012-01-01

    We consider properties of quantum channels with the use of unified entropies. Extremal unravelings of quantum channel with respect to these entropies are examined. The concept of map entropy is extended in terms of the unified entropies. The map (q, s)-entropy is naturally defined as the unified (q, s)-entropy of a rescaled dynamical matrix of given quantum channel. Inequalities of Fannes type are obtained for introduced entropies in terms of both the trace and Frobenius norms of difference between corresponding dynamical matrices. Additivity properties of introduced map entropies are discussed. The known inequality of Lindblad with the entropy exchange is generalized to many of the unified entropies. For the tensor product of a pair of quantum channels, we derive a two-sided estimate on the output entropy of a maximally entangled input state. (paper)

  6. Maximum Entropy: Clearing up Mysteries

    Directory of Open Access Journals (Sweden)

    Marian Grendár

    2001-04-01

    Full Text Available Abstract: There are several mystifications and a couple of mysteries pertinent to MaxEnt. The mystifications, pitfalls and traps are set up mainly by an unfortunate formulation of Jaynes' die problem, the cause célèbre of MaxEnt. After discussing the mystifications a new formulation of the problem is proposed. Then we turn to the mysteries. An answer to the recurring question 'Just what are we accomplishing when we maximize entropy?' [8], based on MaxProb rationale of MaxEnt [6], is recalled. A brief view on the other mystery: 'What is the relation between MaxEnt and the Bayesian method?' [9], in light of the MaxProb rationale of MaxEnt suggests that there is not and cannot be a conflict between MaxEnt and Bayes Theorem.

  7. Sphere Rényi entropies

    International Nuclear Information System (INIS)

    Dowker, J S

    2013-01-01

    I give some scalar field theory calculations on a d-dimensional lune of arbitrary angle, evaluating, numerically, the effective action which is expressed as a simple quadrature, for conformal coupling. Using this, the entanglement and Rényi entropies are computed. Massive fields are also considered and a renormalization to make the (one-loop) effective action vanish for infinite mass is suggested and used, not entirely successfully. However a universal coefficient is derived from the large mass expansion. From the deformation of the corresponding lune result, I conjecture that the effective action on all odd manifolds with a simple conical singularity has an extremum when the singularity disappears. For the round sphere, I show how to convert the quadrature form of the conformal Laplacian determinant into the more usual sum of Riemann ζ-functions (and log 2). (paper)

  8. Quantum Entanglement and Shannon Information Entropy for the Doubly Excited Resonance State in Positronium Negative Ion

    Directory of Open Access Journals (Sweden)

    Chien-Hao Lin

    2015-09-01

    Full Text Available In the present work, we report an investigation on quantum entanglement in the doubly excited 2s2 1Se resonance state of the positronium negative ion by using highly correlated Hylleraas type wave functions, determined by calculation of the density of resonance states with the stabilization method. Once the resonance wave function is obtained, the spatial (electron-electron orbital entanglement entropies (von Neumann and linear can be quantified using the Schmidt decomposition method. Furthermore, Shannon entropy in position space, a measure for localization (or delocalization for such a doubly excited state, is also calculated.

  9. The improvement of Clausius entropy and its application in entropy analysis

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    The defects of Clausius entropy which include a premise of reversible process and a process quantity of heat in its definition are discussed in this paper. Moreover, the heat temperature quotient under reversible conditions, i.e. (δQ/T)rev, is essentially a process quantity although it is numerically equal to the entropy change. The sum of internal energy temperature quotient and work temperature quotient is defined as the improved form of Clausius entropy and it can be further proved to be a state function. Unlike Clausius entropy, the improved definition consists of system properties without premise just like other state functions, for example, pressure p and enthalpy h, etc. It is unnecessary to invent reversible paths when calculating entropy change for irreversible processes based on the improved form of entropy since it is independent of process. Furthermore, entropy balance equations for internally and externally irreversible processes are deduced respectively based on the concepts of thermal reservoir entropy transfer and system entropy transfer. Finally, some examples are presented to show that the improved definition of Clausius entropy provides a clear concept as well as a convenient method for en- tropy change calculation.

  10. How multiplicity determines entropy and the derivation of the maximum entropy principle for complex systems.

    Science.gov (United States)

    Hanel, Rudolf; Thurner, Stefan; Gell-Mann, Murray

    2014-05-13

    The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and Markovian systems in statistical mechanics, information theory, and statistics. For several decades there has been an ongoing controversy over whether the notion of the maximum entropy principle can be extended in a meaningful way to nonextensive, nonergodic, and complex statistical systems and processes. In this paper we start by reviewing how Boltzmann-Gibbs-Shannon entropy is related to multiplicities of independent random processes. We then show how the relaxation of independence naturally leads to the most general entropies that are compatible with the first three Shannon-Khinchin axioms, the (c,d)-entropies. We demonstrate that the MEP is a perfectly consistent concept for nonergodic and complex statistical systems if their relative entropy can be factored into a generalized multiplicity and a constraint term. The problem of finding such a factorization reduces to finding an appropriate representation of relative entropy in a linear basis. In a particular example we show that path-dependent random processes with memory naturally require specific generalized entropies. The example is to our knowledge the first exact derivation of a generalized entropy from the microscopic properties of a path-dependent random process.

  11. Conditional maximum-entropy method for selecting prior distributions in Bayesian statistics

    Science.gov (United States)

    Abe, Sumiyoshi

    2014-11-01

    The conditional maximum-entropy method (abbreviated here as C-MaxEnt) is formulated for selecting prior probability distributions in Bayesian statistics for parameter estimation. This method is inspired by a statistical-mechanical approach to systems governed by dynamics with largely separated time scales and is based on three key concepts: conjugate pairs of variables, dimensionless integration measures with coarse-graining factors and partial maximization of the joint entropy. The method enables one to calculate a prior purely from a likelihood in a simple way. It is shown, in particular, how it not only yields Jeffreys's rules but also reveals new structures hidden behind them.

  12. Relative entropy for hyperbolic-parabolic systems and application to the constitutive theory of thermoviscoelasticity

    KAUST Repository

    Christoforou, Cleopatra

    2017-12-10

    We extend the relative entropy identity to the class of hyperbolic-parabolic systems whose hyperbolic part is symmetrizable. The resulting identity is useful to provide measure valued weak versus strong uniqueness theorems for the hyperbolic problem. Also, it yields a convergence result in the zero-viscosity limit to smooth solutions in an Lp framework. The relative entropy identity is also developed for the system of gas dynamics for viscous and heat conducting gases, and for the system of thermoviscoelasticity with viscosity and heat-conduction. Existing differences between the example and the general hyperbolic theory are underlined.

  13. Relative entropy for hyperbolic-parabolic systems and application to the constitutive theory of thermoviscoelasticity

    KAUST Repository

    Christoforou, Cleopatra; Tzavaras, Athanasios

    2017-01-01

    We extend the relative entropy identity to the class of hyperbolic-parabolic systems whose hyperbolic part is symmetrizable. The resulting identity is useful to provide measure valued weak versus strong uniqueness theorems for the hyperbolic problem. Also, it yields a convergence result in the zero-viscosity limit to smooth solutions in an Lp framework. The relative entropy identity is also developed for the system of gas dynamics for viscous and heat conducting gases, and for the system of thermoviscoelasticity with viscosity and heat-conduction. Existing differences between the example and the general hyperbolic theory are underlined.

  14. Decomposing global crop yield variability

    Science.gov (United States)

    Ben-Ari, Tamara; Makowski, David

    2014-11-01

    Recent food crises have highlighted the need to better understand the between-year variability of agricultural production. Although increasing future production seems necessary, the globalization of commodity markets suggests that the food system would also benefit from enhanced supplies stability through a reduction in the year-to-year variability. Here, we develop an analytical expression decomposing global crop yield interannual variability into three informative components that quantify how evenly are croplands distributed in the world, the proportion of cultivated areas allocated to regions of above or below average variability and the covariation between yields in distinct world regions. This decomposition is used to identify drivers of interannual yield variations for four major crops (i.e., maize, rice, soybean and wheat) over the period 1961-2012. We show that maize production is fairly spread but marked by one prominent region with high levels of crop yield interannual variability (which encompasses the North American corn belt in the USA, and Canada). In contrast, global rice yields have a small variability because, although spatially concentrated, much of the production is located in regions of below-average variability (i.e., South, Eastern and South Eastern Asia). Because of these contrasted land use allocations, an even cultivated land distribution across regions would reduce global maize yield variance, but increase the variance of global yield rice. Intermediate results are obtained for soybean and wheat for which croplands are mainly located in regions with close-to-average variability. At the scale of large world regions, we find that covariances of regional yields have a negligible contribution to global yield variance. The proposed decomposition could be applied at any spatial and time scales, including the yearly time step. By addressing global crop production stability (or lack thereof) our results contribute to the understanding of a key

  15. Entropy of self-gravitating radiation

    International Nuclear Information System (INIS)

    Sorkin, R.D.; Wald, R.M.; Jiu, Z.Z.

    1981-01-01

    The entropy of self-gravitating radiation confined to a spherical box of radius R is examined in the context of general relativity. It is expected that configurations (i.e., initial data) which extremize total entropy will be spherically symmetric, time symmetric distributions of radiation in local thermodynamic equilibrium. Assuming this is the case, it is proved that extrema of S coincide precisely with static equilibrium configurations of the radiation fluid. Furthermore, dynamically stable equilibrium configurations are shown to coincide with local maxima of S. The equilibrium configurations and their entropies are calculated and their properties are discussed. However, it is shown that entropies higher than these local extrema can be achieved and, indeed, arbitrarily high entropies can be attained by configurations inside of or outside but arbitrarily near their own Schwarzschild radius. However, consideration is limited to configurations which are outside their own Schwarzschild radius by at least one radiation wavelength, then the entropy is bounded and it is found Ssub(max) < is approximately equal to MR, where M is the total mass. This supports the validity for self-gravitating systems of the Bekenstein upper limit on the entropy to energy ratio of material bodies. (author)

  16. Towards operational interpretations of generalized entropies

    Science.gov (United States)

    Topsøe, Flemming

    2010-12-01

    The driving force behind our study has been to overcome the difficulties you encounter when you try to extend the clear and convincing operational interpretations of classical Boltzmann-Gibbs-Shannon entropy to other notions, especially to generalized entropies as proposed by Tsallis. Our approach is philosophical, based on speculations regarding the interplay between truth, belief and knowledge. The main result demonstrates that, accepting philosophically motivated assumptions, the only possible measures of entropy are those suggested by Tsallis - which, as we know, include classical entropy. This result constitutes, so it seems, a more transparent interpretation of entropy than previously available. However, further research to clarify the assumptions is still needed. Our study points to the thesis that one should never consider the notion of entropy in isolation - in order to enable a rich and technically smooth study, further concepts, such as divergence, score functions and descriptors or controls should be included in the discussion. This will clarify the distinction between Nature and Observer and facilitate a game theoretical discussion. The usefulness of this distinction and the subsequent exploitation of game theoretical results - such as those connected with the notion of Nash equilibrium - is demonstrated by a discussion of the Maximum Entropy Principle.

  17. Towards operational interpretations of generalized entropies

    International Nuclear Information System (INIS)

    Topsoee, Flemming

    2010-01-01

    The driving force behind our study has been to overcome the difficulties you encounter when you try to extend the clear and convincing operational interpretations of classical Boltzmann-Gibbs-Shannon entropy to other notions, especially to generalized entropies as proposed by Tsallis. Our approach is philosophical, based on speculations regarding the interplay between truth, belief and knowledge. The main result demonstrates that, accepting philosophically motivated assumptions, the only possible measures of entropy are those suggested by Tsallis - which, as we know, include classical entropy. This result constitutes, so it seems, a more transparent interpretation of entropy than previously available. However, further research to clarify the assumptions is still needed. Our study points to the thesis that one should never consider the notion of entropy in isolation - in order to enable a rich and technically smooth study, further concepts, such as divergence, score functions and descriptors or controls should be included in the discussion. This will clarify the distinction between Nature and Observer and facilitate a game theoretical discussion. The usefulness of this distinction and the subsequent exploitation of game theoretical results - such as those connected with the notion of Nash equilibrium - is demonstrated by a discussion of the Maximum Entropy Principle.

  18. Entropy Generation Analysis of Desalination Technologies

    Directory of Open Access Journals (Sweden)

    John H. Lienhard V

    2011-09-01

    Full Text Available Increasing global demand for fresh water is driving the development and implementation of a wide variety of seawater desalination technologies. Entropy generation analysis, and specifically, Second Law efficiency, is an important tool for illustrating the influence of irreversibilities within a system on the required energy input. When defining Second Law efficiency, the useful exergy output of the system must be properly defined. For desalination systems, this is the minimum least work of separation required to extract a unit of water from a feed stream of a given salinity. In order to evaluate the Second Law efficiency, entropy generation mechanisms present in a wide range of desalination processes are analyzed. In particular, entropy generated in the run down to equilibrium of discharge streams must be considered. Physical models are applied to estimate the magnitude of entropy generation by component and individual processes. These formulations are applied to calculate the total entropy generation in several desalination systems including multiple effect distillation, multistage flash, membrane distillation, mechanical vapor compression, reverse osmosis, and humidification-dehumidification. Within each technology, the relative importance of each source of entropy generation is discussed in order to determine which should be the target of entropy generation minimization. As given here, the correct application of Second Law efficiency shows which systems operate closest to the reversible limit and helps to indicate which systems have the greatest potential for improvement.

  19. Chemical library subset selection algorithms: a unified derivation using spatial statistics.

    Science.gov (United States)

    Hamprecht, Fred A; Thiel, Walter; van Gunsteren, Wilfred F

    2002-01-01

    If similar compounds have similar activity, rational subset selection becomes superior to random selection in screening for pharmacological lead discovery programs. Traditional approaches to this experimental design problem fall into two classes: (i) a linear or quadratic response function is assumed (ii) some space filling criterion is optimized. The assumptions underlying the first approach are clear but not always defendable; the second approach yields more intuitive designs but lacks a clear theoretical foundation. We model activity in a bioassay as realization of a stochastic process and use the best linear unbiased estimator to construct spatial sampling designs that optimize the integrated mean square prediction error, the maximum mean square prediction error, or the entropy. We argue that our approach constitutes a unifying framework encompassing most proposed techniques as limiting cases and sheds light on their underlying assumptions. In particular, vector quantization is obtained, in dimensions up to eight, in the limiting case of very smooth response surfaces for the integrated mean square error criterion. Closest packing is obtained for very rough surfaces under the integrated mean square error and entropy criteria. We suggest to use either the integrated mean square prediction error or the entropy as optimization criteria rather than approximations thereof and propose a scheme for direct iterative minimization of the integrated mean square prediction error. Finally, we discuss how the quality of chemical descriptors manifests itself and clarify the assumptions underlying the selection of diverse or representative subsets.

  20. Applications of the maximum entropy principle in nuclear physics

    International Nuclear Information System (INIS)

    Froehner, F.H.

    1990-01-01

    Soon after the advent of information theory the principle of maximum entropy was recognized as furnishing the missing rationale for the familiar rules of classical thermodynamics. More recently it has also been applied successfully in nuclear physics. As an elementary example we derive a physically meaningful macroscopic description of the spectrum of neutrons emitted in nuclear fission, and compare the well known result with accurate data on 252 Cf. A second example, derivation of an expression for resonance-averaged cross sections for nuclear reactions like scattering or fission, is less trivial. Entropy maximization, constrained by given transmission coefficients, yields probability distributions for the R- and S-matrix elements, from which average cross sections can be calculated. If constrained only by the range of the spectrum of compound-nuclear levels it produces the Gaussian Orthogonal Ensemble (GOE) of Hamiltonian matrices that again yields expressions for average cross sections. Both avenues give practically the same numbers in spite of the quite different cross section formulae. These results were employed in a new model-aided evaluation of the 238 U neutron cross sections in the unresolved resonance region. (orig.) [de

  1. Option price calibration from Renyi entropy

    International Nuclear Information System (INIS)

    Brody, Dorje C.; Buckley, Ian R.C.; Constantinou, Irene C.

    2007-01-01

    The calibration of the risk-neutral density function for the future asset price, based on the maximisation of the entropy measure of Renyi, is proposed. Whilst the conventional approach based on the use of logarithmic entropy measure fails to produce the observed power-law distribution when calibrated against option prices, the approach outlined here is shown to produce the desired form of the distribution. Procedures for the maximisation of the Renyi entropy under constraints are outlined in detail, and a number of interesting properties of the resulting power-law distributions are also derived. The result is applied to efficiently evaluate prices of path-independent derivatives

  2. The covariant entropy bound in gravitational collapse

    International Nuclear Information System (INIS)

    Gao, Sijie; Lemos, Jose P. S.

    2004-01-01

    We study the covariant entropy bound in the context of gravitational collapse. First, we discuss critically the heuristic arguments advanced by Bousso. Then we solve the problem through an exact model: a Tolman-Bondi dust shell collapsing into a Schwarzschild black hole. After the collapse, a new black hole with a larger mass is formed. The horizon, L, of the old black hole then terminates at the singularity. We show that the entropy crossing L does not exceed a quarter of the area of the old horizon. Therefore, the covariant entropy bound is satisfied in this process. (author)

  3. Entropy viscosity method for nonlinear conservation laws

    KAUST Repository

    Guermond, Jean-Luc

    2011-05-01

    A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.

  4. Remarks on Bousso's covariant entropy bound

    CERN Document Server

    Mayo, A E

    2002-01-01

    Bousso's covariant entropy bound is put to the test in the context of a non-singular cosmological solution of general relativity found by Bekenstein. Although the model complies with every assumption made in Bousso's original conjecture, the entropy bound is violated due to the occurrence of negative energy density associated with the interaction of some the matter components in the model. We demonstrate how this property allows for the test model to 'elude' a proof of Bousso's conjecture which was given recently by Flanagan, Marolf and Wald. This corroborates the view that the covariant entropy bound should be applied only to stable systems for which every matter component carries positive energy density.

  5. Emission and Absorption Entropy Generation in Semiconductors

    DEFF Research Database (Denmark)

    Reck, Kasper; Varpula, Aapo; Prunnila, Mika

    2013-01-01

    While emission and absorption entropy generation is well known in black bodies, it has not previously been studied in semiconductors, even though semiconductors are widely used for solar light absorption in modern solar cells [1]. We present an analysis of the entropy generation in semiconductor...... materials due to emission and absorption of electromagnetic radiation. It is shown that the emission and absorption entropy generation reduces the fundamental limit on the efficiency of any semiconductor solar cell even further than the Landsberg limit. The results are derived from purely thermodynamical...

  6. Entropy viscosity method for nonlinear conservation laws

    KAUST Repository

    Guermond, Jean-Luc; Pasquetti, Richard; Popov, Bojan

    2011-01-01

    A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.

  7. Permutation Entropy for Random Binary Sequences

    Directory of Open Access Journals (Sweden)

    Lingfeng Liu

    2015-12-01

    Full Text Available In this paper, we generalize the permutation entropy (PE measure to binary sequences, which is based on Shannon’s entropy, and theoretically analyze this measure for random binary sequences. We deduce the theoretical value of PE for random binary sequences, which can be used to measure the randomness of binary sequences. We also reveal the relationship between this PE measure with other randomness measures, such as Shannon’s entropy and Lempel–Ziv complexity. The results show that PE is consistent with these two measures. Furthermore, we use PE as one of the randomness measures to evaluate the randomness of chaotic binary sequences.

  8. Density estimation by maximum quantum entropy

    International Nuclear Information System (INIS)

    Silver, R.N.; Wallstrom, T.; Martz, H.F.

    1993-01-01

    A new Bayesian method for non-parametric density estimation is proposed, based on a mathematical analogy to quantum statistical physics. The mathematical procedure is related to maximum entropy methods for inverse problems and image reconstruction. The information divergence enforces global smoothing toward default models, convexity, positivity, extensivity and normalization. The novel feature is the replacement of classical entropy by quantum entropy, so that local smoothing is enforced by constraints on differential operators. The linear response of the estimate is proportional to the covariance. The hyperparameters are estimated by type-II maximum likelihood (evidence). The method is demonstrated on textbook data sets

  9. Multivariate Approach for Alzheimer's Disease Detection Using Stationary Wavelet Entropy and Predator-Prey Particle Swarm Optimization.

    Science.gov (United States)

    Zhang, Yudong; Wang, Shuihua; Sui, Yuxiu; Yang, Ming; Liu, Bin; Cheng, Hong; Sun, Junding; Jia, Wenjuan; Phillips, Preetha; Gorriz, Juan Manuel

    2017-07-17

    The number of patients with Alzheimer's disease is increasing rapidly every year. Scholars often use computer vision and machine learning methods to develop an automatic diagnosis system. In this study, we developed a novel machine learning system that can make diagnoses automatically from brain magnetic resonance images. First, the brain imaging was processed, including skull stripping and spatial normalization. Second, one axial slice was selected from the volumetric image, and stationary wavelet entropy (SWE) was done to extract the texture features. Third, a single-hidden-layer neural network was used as the classifier. Finally, a predator-prey particle swarm optimization was proposed to train the weights and biases of the classifier. Our method used 4-level decomposition and yielded 13 SWE features. The classification yielded an overall accuracy of 92.73±1.03%, a sensitivity of 92.69±1.29%, and a specificity of 92.78±1.51%. The area under the curve is 0.95±0.02. Additionally, this method only cost 0.88 s to identify a subject in online stage, after its volumetric image is preprocessed. In terms of classification performance, our method performs better than 10 state-of-the-art approaches and the performance of human observers. Therefore, this proposed method is effective in the detection of Alzheimer's disease.

  10. [Stochastic characteristics of daily precipitation and its spatiotemporal difference over China based on information entropy].

    Science.gov (United States)

    Li, Xin Xin; Sang, Yan Fang; Xie, Ping; Liu, Chang Ming

    2018-04-01

    Daily precipitation process in China showed obvious randomness and spatiotemporal variation. It is important to accurately understand the influence of precipitation changes on control of flood and waterlogging disaster. Using the daily precipitation data measured at 520 stations in China during 1961-2013, we quantified the stochastic characteristics of daily precipitation over China based on the index of information entropy. Results showed that the randomness of daily precipitation in the southeast region were larger than that in the northwest region. Moreover, the spatial distribution of stochastic characteristics of precipitation was different at various grades. Stochastic characteri-stics of P 0 (precipitation at 0.1-10 mm) was large, but the spatial variation was not obvious. The stochastic characteristics of P 10 (precipitation at 10-25 mm) and P 25 (precipitation at 25-50 mm) were the largest and their spatial difference was obvious. P 50 (precipitation ≥50 mm) had the smallest stochastic characteristics and the most obviously spatial difference. Generally, the entropy values of precipitation obviously increased over the last five decades, indicating more significantly stochastic characteristics of precipitation (especially the obvious increase of heavy precipitation events) in most region over China under the scenarios of global climate change. Given that the spatial distribution and long-term trend of entropy values of daily precipitation could reflect thespatial distribution of stochastic characteristics of precipitation, our results could provide scientific basis for the control of flood and waterlogging disaster, the layout of agricultural planning, and the planning of ecological environment.

  11. Entropies of the automata networks with additive rule

    Institute of Scientific and Technical Information of China (English)

    Guo-qingGU; GeCHEN; 等

    1996-01-01

    The matrix presentation for automata networks with additive rule are described.A set of entropy theorems of additive automata network are proved and an analytic formula of its entropy is built.For example,we proved that the topological entropy is identically equal to metric entropy for an additive antomata network.

  12. Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum.

    Science.gov (United States)

    Fradkin, Eduardo; Moore, Joel E

    2006-08-04

    The entanglement entropy of a pure quantum state of a bipartite system A union or logical sumB is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. In one dimension, the entanglement of critical ground states diverges logarithmically in the subsystem size, with a universal coefficient that for conformally invariant critical points is related to the central charge of the conformal field theory. We find that the entanglement entropy of a standard class of z=2 conformal quantum critical points in two spatial dimensions, in addition to a nonuniversal "area law" contribution linear in the size of the AB boundary, generically has a universal logarithmically divergent correction, which is completely determined by the geometry of the partition and by the central charge of the field theory that describes the critical wave function.

  13. Formation of soft magnetic high entropy amorphous alloys composites containing in situ solid solution phase

    Science.gov (United States)

    Wei, Ran; Sun, Huan; Chen, Chen; Tao, Juan; Li, Fushan

    2018-03-01

    Fe-Co-Ni-Si-B high entropy amorphous alloys composites (HEAACs), which containing high entropy solid solution phase in amorphous matrix, show good soft magnetic properties and bending ductility even in optimal annealed state, were successfully developed by melt spinning method. The crystallization phase of the HEAACs is solid solution phase with body centered cubic (BCC) structure instead of brittle intermetallic phase. In addition, the BCC phase can transformed into face centered cubic (FCC) phase with temperature rise. Accordingly, Fe-Co-Ni-Si-B high entropy alloys (HEAs) with FCC structure and a small amount of BCC phase was prepared by copper mold casting method. The HEAs exhibit high yield strength (about 1200 MPa) and good plastic strain (about 18%). Meanwhile, soft magnetic characteristics of the HEAs are largely reserved from HEAACs. This work provides a new strategy to overcome the annealing induced brittleness of amorphous alloys and design new advanced materials with excellent comprehensive properties.

  14. On the entropy variation in the scenario of entropic gravity

    Science.gov (United States)

    Xiao, Yong; Bai, Shi-Yang

    2018-05-01

    In the scenario of entropic gravity, entropy varies as a function of the location of the matter, while the tendency to increase entropy appears as gravity. We concentrate on studying the entropy variation of a typical gravitational system with different relative positions between the mass and the gravitational source. The result is that the entropy of the system doesn't increase when the mass is displaced closer to the gravitational source. In this way it disproves the proposal of entropic gravity from thermodynamic entropy. It doesn't exclude the possibility that gravity originates from non-thermodynamic entropy like entanglement entropy.

  15. Entropy production in a cell and reversal of entropy flow as an anticancer therapy

    Institute of Scientific and Technical Information of China (English)

    Liao-fu LUO

    2009-01-01

    The entropy production rate of cancer cells is always higher than healthy cells in the case where no external field is applied. Different entropy production between two kinds of cells determines the direction of entropy flow among cells. The entropy flow is the carrier of information flow. The entropy flow from cancerous cells to healthy cells takes along the harmful information of cancerous cells, propagating its toxic action to healthy tissues. We demonstrate that a low-frequency and low- intensity electromagnetic field or ultrasound irradiation may increase the entropy production rate of a cell in normal tissue than that in cancer and consequently re- verse the direction of entropy current between two kinds of cells. The modification of the PH value of cells may also cause the reversal of the direction of entropy flow between healthy and cancerous cells. Therefore, the bio- logical tissue under the irradiation of an electromagnetic field or ultrasound or under the appropriate change of cell acidity can avoid the propagation of harmful infor- marion from cancer cells. We suggest that this entropy mechanism possibly provides a basis for a novel approach to anticancer therapy.

  16. Logarithmic black hole entropy corrections and holographic Rényi entropy

    Science.gov (United States)

    Mahapatra, Subhash

    2018-01-01

    The entanglement and Rényi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Rényi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order GD^0. The entropic c-function and the inequalities of the Rényi entropy are also satisfied even with the correction terms.

  17. Entropy of Vaidya-deSitter Spacetime

    Institute of Scientific and Technical Information of China (English)

    LI Xiang; ZHAO Zheng

    2001-01-01

    As a statistical model of black hole entropy, the brick-wall method based on the thermal equilibrium in a large scale cannot be applied to the cases out of equilibrium, such as the non-static hole or the case with two horizons.However, the leading term of hole entropy called the Bekenstein-Hawking entropy comes from the contribution of the field near the horizon. According to this idea, the entropy of Vaidya-deSitter spacetime is calculated. A difference from the static case is that the result proportional to the area of horizon relies on a time-dependent cut-off. The condition of local equilibrium near the horizon is used as a working postulate.

  18. Linear entropy in quantum phase space

    International Nuclear Information System (INIS)

    Rosales-Zarate, Laura E. C.; Drummond, P. D.

    2011-01-01

    We calculate the quantum Renyi entropy in a phase-space representation for either fermions or bosons. This can also be used to calculate purity and fidelity, or the entanglement between two systems. We show that it is possible to calculate the entropy from sampled phase-space distributions in normally ordered representations, although this is not possible for all quantum states. We give an example of the use of this method in an exactly soluble thermal case. The quantum entropy cannot be calculated at all using sampling methods in classical symmetric (Wigner) or antinormally ordered (Husimi) phase spaces, due to inner-product divergences. The preferred method is to use generalized Gaussian phase-space methods, which utilize a distribution over stochastic Green's functions. We illustrate this approach by calculating the reduced entropy and entanglement of bosonic or fermionic modes coupled to a time-evolving, non-Markovian reservoir.

  19. Examples of algebrae with equal dynamic entropy

    International Nuclear Information System (INIS)

    Narnhofer, H.

    1988-01-01

    For given dynamical entropy we construct uncountably many examples of corresponding algebras, some of them are quantum K systems, whereas at least one explicit example is not. Consequences for cluster properties are studied. 12 refs. (Author)

  20. Thermoeconomic diagnosis and entropy generation paradox

    DEFF Research Database (Denmark)

    Sigthorsson, Oskar; Ommen, Torben Schmidt; Elmegaard, Brian

    2017-01-01

    In the entropy generation paradox, the entropy generation number, as a function of heat exchanger effectiveness, counter-intuitively approaches zero in two limits symmetrically from a single maximum. In thermoeconomic diagnosis, namely in the characteristic curve method, the exergy destruction...... to the entropy generation paradox, as a decreased heat exchanger effectiveness (as in the case of an operation anomaly in the component) can counter-intuitively result in decreased exergy destruction rate of the component. Therefore, along with an improper selection of independent variables, the heat exchanger...... increases in case of an operation anomaly in a component. The normalised exergy destruction rate as the dependent variable therefore resolves the relation of the characteristic curve method with the entropy generation paradox....

  1. Entropy Evaluation Based on Value Validity

    Directory of Open Access Journals (Sweden)

    Tarald O. Kvålseth

    2014-09-01

    Full Text Available Besides its importance in statistical physics and information theory, the Boltzmann-Shannon entropy S has become one of the most widely used and misused summary measures of various attributes (characteristics in diverse fields of study. It has also been the subject of extensive and perhaps excessive generalizations. This paper introduces the concept and criteria for value validity as a means of determining if an entropy takes on values that reasonably reflect the attribute being measured and that permit different types of comparisons to be made for different probability distributions. While neither S nor its relative entropy equivalent S* meet the value-validity conditions, certain power functions of S and S* do to a considerable extent. No parametric generalization offers any advantage over S in this regard. A measure based on Euclidean distances between probability distributions is introduced as a potential entropy that does comply fully with the value-validity requirements and its statistical inference procedure is discussed.

  2. Topological entropy for induced hyperspace maps

    International Nuclear Information System (INIS)

    Canovas Pena, Jose S.; Lopez, Gabriel Soler

    2006-01-01

    Let (X,d) be a compact metric space and let f:X->X be continuous. Let K(X) be the family of compact subsets of X endowed with the Hausdorff metric and define the extension f-bar :K(X)->K(X) by f-bar (K)=f(K) for any K-bar K(X). We prove that the topological entropy of f-bar is greater or equal than the topological entropy of f, and this inequality can be strict. On the other hand, we prove that the topological entropy of f is positive if and only if the topological entropy of f-bar is also positive

  3. Topological entropy for induced hyperspace maps

    Energy Technology Data Exchange (ETDEWEB)

    Canovas Pena, Jose S. [Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, 30203 Cartagena, Murcia (Spain)]. E-mail: Jose.canovas@upct.es; Lopez, Gabriel Soler [Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, 30203 Cartagena, Murcia (Spain)]. E-mail: Gabriel.soler@upct.es

    2006-05-15

    Let (X,d) be a compact metric space and let f:X->X be continuous. Let K(X) be the family of compact subsets of X endowed with the Hausdorff metric and define the extension f-bar :K(X)->K(X) by f-bar (K)=f(K) for any K-bar K(X). We prove that the topological entropy of f-bar is greater or equal than the topological entropy of f, and this inequality can be strict. On the other hand, we prove that the topological entropy of f is positive if and only if the topological entropy of f-bar is also positive.

  4. On the continuity of the entropy

    International Nuclear Information System (INIS)

    Lassner, G.; Lassner, G.A.

    1977-01-01

    It is shown for a quantum-mechanical system with finite degree of freedom taking into account also unbounded observables one gets physical topologies on the state-observable system with respect to which the entropy becomes a continuous function

  5. Two-dimensional maximum entropy image restoration

    International Nuclear Information System (INIS)

    Brolley, J.E.; Lazarus, R.B.; Suydam, B.R.; Trussell, H.J.

    1977-07-01

    An optical check problem was constructed to test P LOG P maximum entropy restoration of an extremely distorted image. Useful recovery of the original image was obtained. Comparison with maximum a posteriori restoration is made. 7 figures

  6. Entropy for theories with indefinite causal structure

    International Nuclear Information System (INIS)

    Markes, Sonia; Hardy, Lucien

    2011-01-01

    Any theory with definite causal structure has a defined past and future, be it defined by light cones or an absolute time scale. Entropy is a concept that has traditionally been reliant on a definite notion of causality. However, without a definite notion of causality, the concept of entropy is not all lost. Indefinite causal structure results from combining probabilistic predictions and dynamical space-time. The causaloid framework lays the mathematical groundwork to be able to treat indefinite causal structure. In this paper, we build on the causaloid mathematics and define a causally-unbiased entropy for an indefinite causal structure. In defining a causally-unbiased entropy, there comes about an emergent idea of causality in the form of a measure of causal connectedness, termed the Q factor.

  7. Minimal entropy approximation for cellular automata

    International Nuclear Information System (INIS)

    Fukś, Henryk

    2014-01-01

    We present a method for the construction of approximate orbits of measures under the action of cellular automata which is complementary to the local structure theory. The local structure theory is based on the idea of Bayesian extension, that is, construction of a probability measure consistent with given block probabilities and maximizing entropy. If instead of maximizing entropy one minimizes it, one can develop another method for the construction of approximate orbits, at the heart of which is the iteration of finite-dimensional maps, called minimal entropy maps. We present numerical evidence that the minimal entropy approximation sometimes outperforms the local structure theory in characterizing the properties of cellular automata. The density response curve for elementary CA rule 26 is used to illustrate this claim. (paper)

  8. Non-equilibrium entropy in excited nuclei

    International Nuclear Information System (INIS)

    Betak, E.

    1991-06-01

    The time-dependent behaviour of entropy in excited nuclei is investigated. In distinction to recent claims, it is shown that no self-organization is involved in pre-equilibrium nuclear reactions. (author). 9 refs.; 4 figs

  9. Effects of quantum entropy on bag constant

    International Nuclear Information System (INIS)

    Miller, D.E.; Tawfik, A.

    2012-01-01

    The effects of quantum entropy on the bag constant are studied at low temperatures and for small chemical potentials. The inclusion of the quantum entropy of the quarks in the equation of state provides the hadronic bag with an additional heat which causes a decrease in the effective latent heat inside the bag. We have considered two types of baryonic bags, Δ and Ω - . In both cases we have found that the bag constant without the quantum entropy almost does not change with temperature and quark chemical potential. The contribution from the quantum entropy to the equation of state clearly decreases the value of the bag constant. Furthermore, we construct states densities for quarks using the 'Thomas Fermi model' and take into consideration a thermal potential for the interaction. (author)

  10. Linear entropy in quantum phase space

    Energy Technology Data Exchange (ETDEWEB)

    Rosales-Zarate, Laura E. C.; Drummond, P. D. [Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne 3122 (Australia)

    2011-10-15

    We calculate the quantum Renyi entropy in a phase-space representation for either fermions or bosons. This can also be used to calculate purity and fidelity, or the entanglement between two systems. We show that it is possible to calculate the entropy from sampled phase-space distributions in normally ordered representations, although this is not possible for all quantum states. We give an example of the use of this method in an exactly soluble thermal case. The quantum entropy cannot be calculated at all using sampling methods in classical symmetric (Wigner) or antinormally ordered (Husimi) phase spaces, due to inner-product divergences. The preferred method is to use generalized Gaussian phase-space methods, which utilize a distribution over stochastic Green's functions. We illustrate this approach by calculating the reduced entropy and entanglement of bosonic or fermionic modes coupled to a time-evolving, non-Markovian reservoir.

  11. Entropy estimates for simple random fields

    DEFF Research Database (Denmark)

    Forchhammer, Søren; Justesen, Jørn

    1995-01-01

    We consider the problem of determining the maximum entropy of a discrete random field on a lattice subject to certain local constraints on symbol configurations. The results are expected to be of interest in the analysis of digitized images and two dimensional codes. We shall present some examples...... of binary and ternary fields with simple constraints. Exact results on the entropies are known only in a few cases, but we shall present close bounds and estimates that are computationally efficient...

  12. Growth rate, population entropy, and perturbation theory.

    OpenAIRE

    Demetrius, L.

    1989-01-01

    This paper is concerned with the connection between two classes of population variables: measures of population growth rate—the Malthusian parameter, the net reproduction rate, the gross reproduction rate, and the mean life expectancy; and measures of demographic heterogeneity—population entropy. It is shown that the entropy functions predict the response of the growth rate parameters to perturbations in the age-specific fecundity and mortality schedule. These results are invoked to introduce...

  13. Differences and implications in biogeochemistry from maximizing entropy production locally versus globally

    Directory of Open Access Journals (Sweden)

    J. J. Vallino

    2011-06-01

    Full Text Available In this manuscript we investigate the use of the maximum entropy production (MEP principle for modeling biogeochemical processes that are catalyzed by living systems. Because of novelties introduced by the MEP approach, many questions need to be answered and techniques developed in the application of MEP to describe biological systems that are responsible for energy and mass transformations on a planetary scale. In previous work we introduce the importance of integrating entropy production over time to distinguish abiotic from biotic processes under transient conditions. Here we investigate the ramifications of modeling biological systems involving one or more spatial dimensions. When modeling systems over space, entropy production can be maximized either locally at each point in space asynchronously or globally over the system domain synchronously. We use a simple two-box model inspired by two-layer ocean models to illustrate the differences in local versus global entropy maximization. Synthesis and oxidation of biological structure is modeled using two autocatalytic reactions that account for changes in community kinetics using a single parameter each. Our results show that entropy production can be increased if maximized over the system domain rather than locally, which has important implications regarding how biological systems organize and supports the hypothesis for multiple levels of selection and cooperation in biology for the dissipation of free energy.

  14. Quantum Entropy of Black Hole with Internal Global Monopole

    Institute of Scientific and Technical Information of China (English)

    HAN Yi-Wen; YANG Shu-Zheng; LIU Wen-Biao

    2005-01-01

    Using the generalized uncertainty relation, the new equation of state density is obtained, and then the entropy of black hole with an internal global monopole is discussed. The divergence that appears in black hole entropy calculation through original brick-wall model is overcome. The result of the direct proportion between black hole entropy and its event horizon area is drawn and given. The result shows that the black hole entropy must be the entropy of quantum state near the event horizon.

  15. EEG entropy measures indicate decrease of cortical information processing in Disorders of Consciousness.

    Science.gov (United States)

    Thul, Alexander; Lechinger, Julia; Donis, Johann; Michitsch, Gabriele; Pichler, Gerald; Kochs, Eberhard F; Jordan, Denis; Ilg, Rüdiger; Schabus, Manuel

    2016-02-01

    Clinical assessments that rely on behavioral responses to differentiate Disorders of Consciousness are at times inapt because of some patients' motor disabilities. To objectify patients' conditions of reduced consciousness the present study evaluated the use of electroencephalography to measure residual brain activity. We analyzed entropy values of 18 scalp EEG channels of 15 severely brain-damaged patients with clinically diagnosed Minimally-Conscious-State (MCS) or Unresponsive-Wakefulness-Syndrome (UWS) and compared the results to a sample of 24 control subjects. Permutation entropy (PeEn) and symbolic transfer entropy (STEn), reflecting information processes in the EEG, were calculated for all subjects. Participants were tested on a modified active own-name paradigm to identify correlates of active instruction following. PeEn showed reduced local information content in the EEG in patients, that was most pronounced in UWS. STEn analysis revealed altered directed information flow in the EEG of patients, indicating impaired feed-backward connectivity. Responses to auditory stimulation yielded differences in entropy measures, indicating reduced information processing in MCS and UWS. Local EEG information content and information flow are affected in Disorders of Consciousness. This suggests local cortical information capacity and feedback information transfer as neural correlates of consciousness. The utilized EEG entropy analyses were able to relate to patient groups with different Disorders of Consciousness. Copyright © 2015 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

  16. Measuring the quality of a quantum reference frame: The relative entropy of frameness

    International Nuclear Information System (INIS)

    Gour, Gilad; Marvian, Iman; Spekkens, Robert W.

    2009-01-01

    In the absence of a reference frame for transformations associated with group G, any quantum state that is noninvariant under the action of G may serve as a token of the missing reference frame. We here present a measure of the quality of such a token: the relative entropy of frameness. This is defined as the relative entropy distance between the state of interest and the nearest G-invariant state. Unlike the relative entropy of entanglement, this quantity is straightforward to calculate, and we find it to be precisely equal to the G-asymmetry, a measure of frameness introduced by Vaccaro et al. It is shown to provide an upper bound on the mutual information between the group element encoded into the token and the group element that may be extracted from it by measurement. In this sense, it quantifies the extent to which the token successfully simulates a full reference frame. We also show that despite a suggestive analogy from entanglement theory, the regularized relative entropy of frameness is zero and therefore does not quantify the rate of interconversion between the token and some standard form of quantum reference frame. Finally, we show how these investigations yield an approach to bounding the relative entropy of entanglement.

  17. The relative entropy in the quantum mechanics

    International Nuclear Information System (INIS)

    Lecomte Montes, A.

    1983-06-01

    Relative Entropy is a generalization of entropy which substitutes the Liouville measure from classical mechanics or the trace from quantum mechanics by an arbitrary state. There are many different defintions of it in quantum mechanics because the algebra of observables is not commutative. In this work, three known defintions of the quantum relative entropy are studied and compared but specifically their common properties are presented. The best known defintion was proposed many years ago by Umegaki and later on by Lindblad. This defintion can be realized through a functional calculus for quadratic forms introduced by Pusz and Woronowicz, for two arbitrary states on a Csup(*)-algebra. The two other definitions investigated are the Naudt's entropy and the inference function of Marchand and Wyss. The first one can be expressed through the functional calculus too, it has then almost the same properties as the Umegaki-Lindblad defintion. The inference function can be considered only as some kind of 1/2-relative entropy. The function is nevertheless very important because it can be expressed as the logarithm of the transition probability between the basis state and the actual state. A general theory which includes the three defintions is not found yet, but it is shown that the functional calculus provides a great family of relative entropies. This is important for a unified theory of all defintions and their properties. (Author)

  18. A review of entropy generation in microchannels

    Directory of Open Access Journals (Sweden)

    Mohamed M Awad

    2015-12-01

    Full Text Available In this study, a critical review of thermodynamic optimum of microchannels based on entropy generation analysis is presented. Using entropy generation analysis as evaluation parameter of microchannels has been reported by many studies in the literature. In these studies, different working fluids such as nanofluids, air, water, engine oil, aniline, ethylene glycol, and non-Newtonian fluids have been used. For the case of nanofluids, “nanoparticles” has been used in various kinds such as Al2O3 and Cu, and “base fluid” has been used in various kinds such as water and ethylene glycol. Furthermore, studies on thermodynamic optimum of microchannels based on entropy generation analysis are summarized in a table. At the end, recommendations of future work for thermodynamic optimum of microchannels based on entropy generation analysis are given. As a result, this article can not only be used as the starting point for the researcher interested in entropy generation in microchannels, but it also includes recommendations for future studies on entropy generation in microchannels.

  19. Trajectories entropy in dynamical graphs with memory

    Directory of Open Access Journals (Sweden)

    Francesco eCaravelli

    2016-04-01

    Full Text Available In this paper we investigate the application of non-local graph entropy to evolving and dynamical graphs. The measure is based upon the notion of Markov diffusion on a graph, and relies on the entropy applied to trajectories originating at a specific node. In particular, we study the model of reinforcement-decay graph dynamics, which leads to scale free graphs. We find that the node entropy characterizes the structure of the network in the two parameter phase-space describing the dynamical evolution of the weighted graph. We then apply an adapted version of the entropy measure to purely memristive circuits. We provide evidence that meanwhile in the case of DC voltage the entropy based on the forward probability is enough to characterize the graph properties, in the case of AC voltage generators one needs to consider both forward and backward based transition probabilities. We provide also evidence that the entropy highlights the self-organizing properties of memristive circuits, which re-organizes itself to satisfy the symmetries of the underlying graph.

  20. Entanglement entropy and nonabelian gauge symmetry

    International Nuclear Information System (INIS)

    Donnelly, William

    2014-01-01

    Entanglement entropy has proven to be an extremely useful concept in quantum field theory. Gauge theories are of particular interest, but for these systems the entanglement entropy is not clearly defined because the physical Hilbert space does not factor as a tensor product according to regions of space. Here we review a definition of entanglement entropy that applies to abelian and nonabelian lattice gauge theories. This entanglement entropy is obtained by embedding the physical Hilbert space into a product of Hilbert spaces associated to regions with boundary. The latter Hilbert spaces include degrees of freedom on the entangling surface that transform like surface charges under the gauge symmetry. These degrees of freedom are shown to contribute to the entanglement entropy, and the form of this contribution is determined by the gauge symmetry. We test our definition using the example of two-dimensional Yang–Mills theory, and find that it agrees with the thermal entropy in de Sitter space, and with the results of the Euclidean replica trick. We discuss the possible implications of this result for more complicated gauge theories, including quantum gravity. (paper)

  1. Gradient Dynamics and Entropy Production Maximization

    Science.gov (United States)

    Janečka, Adam; Pavelka, Michal

    2018-01-01

    We compare two methods for modeling dissipative processes, namely gradient dynamics and entropy production maximization. Both methods require similar physical inputs-how energy (or entropy) is stored and how it is dissipated. Gradient dynamics describes irreversible evolution by means of dissipation potential and entropy, it automatically satisfies Onsager reciprocal relations as well as their nonlinear generalization (Maxwell-Onsager relations), and it has statistical interpretation. Entropy production maximization is based on knowledge of free energy (or another thermodynamic potential) and entropy production. It also leads to the linear Onsager reciprocal relations and it has proven successful in thermodynamics of complex materials. Both methods are thermodynamically sound as they ensure approach to equilibrium, and we compare them and discuss their advantages and shortcomings. In particular, conditions under which the two approaches coincide and are capable of providing the same constitutive relations are identified. Besides, a commonly used but not often mentioned step in the entropy production maximization is pinpointed and the condition of incompressibility is incorporated into gradient dynamics.

  2. On variational definition of quantum entropy

    International Nuclear Information System (INIS)

    Belavkin, Roman V.

    2015-01-01

    Entropy of distribution P can be defined in at least three different ways: 1) as the expectation of the Kullback-Leibler (KL) divergence of P from elementary δ-measures (in this case, it is interpreted as expected surprise); 2) as a negative KL-divergence of some reference measure ν from the probability measure P; 3) as the supremum of Shannon’s mutual information taken over all channels such that P is the output probability, in which case it is dual of some transportation problem. In classical (i.e. commutative) probability, all three definitions lead to the same quantity, providing only different interpretations of entropy. In non-commutative (i.e. quantum) probability, however, these definitions are not equivalent. In particular, the third definition, where the supremum is taken over all entanglements of two quantum systems with P being the output state, leads to the quantity that can be twice the von Neumann entropy. It was proposed originally by V. Belavkin and Ohya [1] and called the proper quantum entropy, because it allows one to define quantum conditional entropy that is always non-negative. Here we extend these ideas to define also quantum counterpart of proper cross-entropy and cross-information. We also show inequality for the values of classical and quantum information

  3. Entropy as a collective variable

    Science.gov (United States)

    Parrinello, Michele

    Sampling complex free energy surfaces that exhibit long lived metastable states separated by kinetic bottlenecks is one of the most pressing issues in the atomistic simulations of matter. Not surprisingly many solutions to this problem have been suggested. Many of them are based on the identification of appropriate collective variables that span the manifold of the slow varying modes of the system. While much effort has been put in devising and even constructing on the fly appropriate collective variables there is still a cogent need of introducing simple, generic, physically transparent, and yet effective collective variables. Motivated by the physical observation that in many case transitions between one metastable state and another result from a trade off between enthalpy and entropy we introduce appropriate collective variables that are able to represent in a simple way these two physical properties. We use these variables in the context of the recently introduced variationally enhanced sampling and apply it them with success to the simulation of crystallization from the liquid and to conformational transitions in protein. Department of Chemistry and Applied Biosciences, ETH Zurich, and Facolta' di Informatica, Istituto di Scienze Computazionali, Universita' della Svizzera Italiana, Via G. Buffi 13, 6900 Lugano, Switzerland.

  4. Entropy in an expanding universe

    International Nuclear Information System (INIS)

    Frautschi, S.C.

    1986-01-01

    The present picture of the evolution of the universe, based on the Big Bang, suggests a remarkably different and more interesting situation. In the beginning there is a hot gas, nearly homogeneous and in thermal equilibrium [the 3 0 blackbody radiation, reaching us isotropically from all directions, is a relic of, and evidence for, this early state]. The picture of cosmic evolution, seemingly paradoxical in the light of the law of thermodynamics, motivates the questions the author considers in this paper: How can disequilibrium, order, and in particular the free energy supplies which enable life to maintain its organization, emerge from an apparently chaotic early universe in thermal and chemical equilibrium; will free energy supplies continue to become available and be utilized in the future, or will some sort of heat death eventually settle in? The evolution of free energy and entropy in the universe could not be treated accurately on the basis of physics known in the 19th century. However, various 20th century discoveries and ideas make informed discussion of such issues possible, even though definitive answers are not yet in hand. The author discusses some of the ideas which are quite recent, and are currently undergoing rapid development

  5. Mechanical Entropy and Its Implications

    Directory of Open Access Journals (Sweden)

    Pharis E. Williams

    2001-06-01

    Full Text Available Abstract: It is shown that the classical laws of thermodynamics require that mechanical systems must exhibit energy that becomes unavailable to do useful work. In thermodynamics, this type of energy is called entropy. It is further shown that these laws require two metrical manifolds, equations of motion, field equations, and Weyl's quantum principles. Weyl's quantum principle requires quantization of the electrostatic potential of a particle and that this potential be non-singular. The interactions of particles through these non-singular electrostatic potentials are analyzed in the low velocity limit and in the relativistic limit. It is shown that writing the two particle interactions for unlike particles allows an examination in two limiting cases: large and small separations. These limits are shown to have the limiting motions of: all motions are ABOUT the center of mass or all motion is OF the center of mass. The first limit leads to the standard Dirac equation. The second limit is shown to have equations of which the electroweak theory is a subset. An extension of the gauge principle into a five-dimensional manifold, then restricting the generality of the five-dimensional manifold by using the conservation principle, shows that the four-dimensional hypersurface that is embedded within the 5-D manifold is required to obey Einstein's field equations. The 5-D gravitational quantum equations of the solar system are presented.

  6. Maximum entropy and Bayesian methods

    International Nuclear Information System (INIS)

    Smith, C.R.; Erickson, G.J.; Neudorfer, P.O.

    1992-01-01

    Bayesian probability theory and Maximum Entropy methods are at the core of a new view of scientific inference. These 'new' ideas, along with the revolution in computational methods afforded by modern computers allow astronomers, electrical engineers, image processors of any type, NMR chemists and physicists, and anyone at all who has to deal with incomplete and noisy data, to take advantage of methods that, in the past, have been applied only in some areas of theoretical physics. The title workshops have been the focus of a group of researchers from many different fields, and this diversity is evident in this book. There are tutorial and theoretical papers, and applications in a very wide variety of fields. Almost any instance of dealing with incomplete and noisy data can be usefully treated by these methods, and many areas of theoretical research are being enhanced by the thoughtful application of Bayes' theorem. Contributions contained in this volume present a state-of-the-art overview that will be influential and useful for many years to come

  7. Entropy and the Magic Flute

    Science.gov (United States)

    Morowitz, Harold J.

    1996-10-01

    Harold Morowitz has long been highly regarded both as an eminent scientist and as an accomplished science writer. The essays in The Wine of Life , his first collection, were hailed by C.P. Snow as "some of the wisest, wittiest and best informed I have ever read," and Carl Sagan called them "a delight to read." In later volumes he established a reputation for a wide-ranging intellect, an ability to see unexpected connections and draw striking parallels, and a talent for communicating scientific ideas with optimism and wit. With Entropy and the Magic Flute , Morowitz once again offers an appealing mix of brief reflections on everything from litmus paper to the hippopotamus to the sociology of Palo Alto coffee shops. Many of these pieces are appreciations of scientists that Morowitz holds in high regard, while others focus on health issues, such as America's obsession with cheese toppings. There is also a fascinating piece on the American Type Culture Collection, a zoo or warehouse for microbes that houses some 11,800 strains of bacteria, and over 3,000 specimens of protozoa, algae, plasmids, and oncogenes. Here then are over forty light, graceful essays in which one of our wisest experimental biologists comments on issues of science, technology, society, philosophy, and the arts.

  8. Calculation of Configurational Entropy in Complex Landscapes

    Directory of Open Access Journals (Sweden)

    Samuel A Cushman

    2018-04-01

    Full Text Available Entropy and the second law of thermodynamics are fundamental concepts that underlie all natural processes and patterns. Recent research has shown how the entropy of a landscape mosaic can be calculated using the Boltzmann equation, with the entropy of a lattice mosaic equal to the logarithm of the number of ways a lattice with a given dimensionality and number of classes can be arranged to produce the same total amount of edge between cells of different classes. However, that work seemed to also suggest that the feasibility of applying this method to real landscapes was limited due to intractably large numbers of possible arrangements of raster cells in large landscapes. Here I extend that work by showing that: (1 the proportion of arrangements rather than the number with a given amount of edge length provides a means to calculate unbiased relative configurational entropy, obviating the need to compute all possible configurations of a landscape lattice; (2 the edge lengths of randomized landscape mosaics are normally distributed, following the central limit theorem; and (3 given this normal distribution it is possible to fit parametric probability density functions to estimate the expected proportion of randomized configurations that have any given edge length, enabling the calculation of configurational entropy on any landscape regardless of size or number of classes. I evaluate the boundary limits (4 for this normal approximation for small landscapes with a small proportion of a minority class and show it holds under all realistic landscape conditions. I further (5 demonstrate that this relationship holds for a sample of real landscapes that vary in size, patch richness, and evenness of area in each cover type, and (6 I show that the mean and standard deviation of the normally distributed edge lengths can be predicted nearly perfectly as a function of the size, patch richness and diversity of a landscape. Finally, (7 I show that the

  9. Scintigraphic acquisition entropy (2). A new approach in the quality control of the scintillation camera performances

    International Nuclear Information System (INIS)

    Elloumi, I.; Bouhdima, M.S.

    2002-01-01

    A new approach in the survey of the performances of gamma camera based on the entropy associated to the scintigraphic acquisition is presented. We take into account the sensitivity, the variation of the collimator response in function of the depth, the uncertainty on the number of counts, the multiplex effect and the spatial uncertainty. This entropy function is expressed in function of all the acquisition parameters: intrinsic crystal resolution, collimator characteristics, emitter object parameters and the source activity. The application of this method to the study of the influence of the collimation shows that the entropy associated to a collimator permits a best appreciation of the quality of the acquisition and therefore a better analysis of collimator performances. Likewise, the evolution of the entropy associated to the acquisition of a uniform source image is in agreement with the variation of the quality of image histogram. One shows, thus, that nor the spatial resolution, nor the sensitivity and nor the signal to noise ratio are able detect a variation of the image quality, when analysed one by one. (author)

  10. The High Temperature Tensile and Creep Behaviors of High Entropy Superalloy.

    Science.gov (United States)

    Tsao, Te-Kang; Yeh, An-Chou; Kuo, Chen-Ming; Kakehi, Koji; Murakami, Hideyuki; Yeh, Jien-Wei; Jian, Sheng-Rui

    2017-10-04

    This article presents the high temperature tensile and creep behaviors of a novel high entropy alloy (HEA). The microstructure of this HEA resembles that of advanced superalloys with a high entropy FCC matrix and L1 2 ordered precipitates, so it is also named as "high entropy superalloy (HESA)". The tensile yield strengths of HESA surpass those of the reported HEAs from room temperature to elevated temperatures; furthermore, its creep resistance at 982 °C can be compared to those of some Ni-based superalloys. Analysis on experimental results indicate that HESA could be strengthened by the low stacking-fault energy of the matrix, high anti-phase boundary energy of the strengthening precipitate, and thermally stable microstructure. Positive misfit between FCC matrix and precipitate has yielded parallel raft microstructure during creep at 982 °C, and the creep curves of HESA were dominated by tertiary creep behavior. To the best of authors' knowledge, this article is the first to present the elevated temperature tensile creep study on full scale specimens of a high entropy alloy, and the potential of HESA for high temperature structural application is discussed.

  11. Maximum entropy principal for transportation

    International Nuclear Information System (INIS)

    Bilich, F.; Da Silva, R.

    2008-01-01

    In this work we deal with modeling of the transportation phenomenon for use in the transportation planning process and policy-impact studies. The model developed is based on the dependence concept, i.e., the notion that the probability of a trip starting at origin i is dependent on the probability of a trip ending at destination j given that the factors (such as travel time, cost, etc.) which affect travel between origin i and destination j assume some specific values. The derivation of the solution of the model employs the maximum entropy principle combining a priori multinomial distribution with a trip utility concept. This model is utilized to forecast trip distributions under a variety of policy changes and scenarios. The dependence coefficients are obtained from a regression equation where the functional form is derived based on conditional probability and perception of factors from experimental psychology. The dependence coefficients encode all the information that was previously encoded in the form of constraints. In addition, the dependence coefficients encode information that cannot be expressed in the form of constraints for practical reasons, namely, computational tractability. The equivalence between the standard formulation (i.e., objective function with constraints) and the dependence formulation (i.e., without constraints) is demonstrated. The parameters of the dependence-based trip-distribution model are estimated, and the model is also validated using commercial air travel data in the U.S. In addition, policy impact analyses (such as allowance of supersonic flights inside the U.S. and user surcharge at noise-impacted airports) on air travel are performed.

  12. Entropy of balance - some recent results

    Directory of Open Access Journals (Sweden)

    Laxåback Gerd

    2010-07-01

    Full Text Available Abstract Background Entropy when applied to biological signals is expected to reflect the state of the biological system. However the physiological interpretation of the entropy is not always straightforward. When should high entropy be interpreted as a healthy sign, and when as marker of deteriorating health? We address this question for the particular case of human standing balance and the Center of Pressure data. Methods We have measured and analyzed balance data of 136 participants (young, n = 45; elderly, n = 91 comprising in all 1085 trials, and calculated the Sample Entropy (SampEn for medio-lateral (M/L and anterior-posterior (A/P Center of Pressure (COP together with the Hurst self-similariy (ss exponent α using Detrended Fluctuation Analysis (DFA. The COP was measured with a force plate in eight 30 seconds trials with eyes closed, eyes open, foam, self-perturbation and nudge conditions. Results 1 There is a significant difference in SampEn for the A/P-direction between the elderly and the younger groups Old > young. 2 For the elderly we have in general A/P > M/L. 3 For the younger group there was no significant A/P-M/L difference with the exception for the nudge trials where we had the reverse situation, A/P Eyes Open. 5 In case of the Hurst ss-exponent we have for the elderly, M/L > A/P. Conclusions These results seem to be require some modifications of the more or less established attention-constraint interpretation of entropy. This holds that higher entropy correlates with a more automatic and a less constrained mode of balance control, and that a higher entropy reflects, in this sense, a more efficient balancing.

  13. Phonon broadening in high entropy alloys

    Science.gov (United States)

    Körmann, Fritz; Ikeda, Yuji; Grabowski, Blazej; Sluiter, Marcel H. F.

    2017-09-01

    Refractory high entropy alloys feature outstanding properties making them a promising materials class for next-generation high-temperature applications. At high temperatures, materials properties are strongly affected by lattice vibrations (phonons). Phonons critically influence thermal stability, thermodynamic and elastic properties, as well as thermal conductivity. In contrast to perfect crystals and ordered alloys, the inherently present mass and force constant fluctuations in multi-component random alloys (high entropy alloys) can induce significant phonon scattering and broadening. Despite their importance, phonon scattering and broadening have so far only scarcely been investigated for high entropy alloys. We tackle this challenge from a theoretical perspective and employ ab initio calculations to systematically study the impact of force constant and mass fluctuations on the phonon spectral functions of 12 body-centered cubic random alloys, from binaries up to 5-component high entropy alloys, addressing the key question of how chemical complexity impacts phonons. We find that it is crucial to include both mass and force constant fluctuations. If one or the other is neglected, qualitatively wrong results can be obtained such as artificial phonon band gaps. We analyze how the results obtained for the phonons translate into thermodynamically integrated quantities, specifically the vibrational entropy. Changes in the vibrational entropy with increasing the number of elements can be as large as changes in the configurational entropy and are thus important for phase stability considerations. The set of studied alloys includes MoTa, MoTaNb, MoTaNbW, MoTaNbWV, VW, VWNb, VWTa, VWNbTa, VTaNbTi, VWNbTaTi, HfZrNb, HfMoTaTiZr.

  14. Quantum statistical entropy for Kerr-de Sitter black hole

    Institute of Scientific and Technical Information of China (English)

    Zhang Li-Chun; Wu Yue-Qin; Zhao Ren

    2004-01-01

    Improving the membrane model by which the entropy of the black hole is studied, we study the entropy of the black hole in the non-thermal equilibrium state. To give the problem stated here widespread meaning, we discuss the (n+2)-dimensional de Sitter spacetime. Through discussion, we obtain that the black hole's entropy which contains two horizons (a black hole's horizon and a cosmological horizon) in the non-thermal equilibrium state comprises the entropy corresponding to the black hole's horizon and the entropy corresponding to the cosmological horizon. Furthermore, the entropy of the black hole is a natural property of the black hole. The entropy is irrelevant to the radiation field out of the horizon. This deepens the understanding of the relationship between black hole's entropy and horizon's area. A way to study the bosonic and fermionic entropy of the black hole in high non-thermal equilibrium spacetime is given.

  15. Progress in Preparation and Research of High Entropy Alloys

    Directory of Open Access Journals (Sweden)

    CHEN Yong-xing

    2017-11-01

    Full Text Available The current high entropy alloys' studies are most in block, powder, coating, film and other areas. There are few studies of high entropy alloys in other areas and they are lack of unified classification. According to the current high entropy alloys' research situation, The paper has focused on the classification on all kinds of high entropy alloys having been researched, introduced the selecting principle of elements, summarized the preparation methods, reviewed the research institutions, research methods and research contents of high entropy alloys, prospected the application prospect of high entropy alloys, put forward a series of scientific problems of high entropy alloys, including less research on mechanism, incomplete performance research, unsystematic thermal stability study, preparation process parameters to be optimized, lightweight high entropy alloys' design, the expansion on the research field, etc, and the solutions have been given. Those have certain guiding significance for the expansion of the application of high entropy alloys subjects in the future research direction.

  16. Variations mechanism in entropy of wave height field and its relation with thermodynamic entropy

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    This paper gives a brief description of annual period and seasonal variation in the wave height field entropy in the northeastern Pacific. A calculation of the quantity of the, received by lithosphere systems in the northern hemisphere is introduced. The wave heat field entropy is compared with the difference in the quantity of the sun's radiation heat. Analysis on the transfer method, period and lag of this seasonal variation led to the conclusion that the annual period and seasonal variation in the entropy of the wave height field in the Northwestern Pacific is due to the seasonal variation of the sun's radiation heat. Furthermore, the inconsistency between thermodynamic entropy and information entropy was studied.

  17. Entanglement entropy of ABJM theory and entropy of topological black hole

    Science.gov (United States)

    Nian, Jun; Zhang, Xinyu

    2017-07-01

    In this paper we discuss the supersymmetric localization of the 4D N = 2 offshell gauged supergravity on the background of the AdS4 neutral topological black hole, which is the gravity dual of the ABJM theory defined on the boundary {S}^1× H^2 . We compute the large- N expansion of the supergravity partition function. The result gives the black hole entropy with the logarithmic correction, which matches the previous result of the entanglement entropy of the ABJM theory up to some stringy effects. Our result is consistent with the previous on-shell one-loop computation of the logarithmic correction to black hole entropy. It provides an explicit example of the identification of the entanglement entropy of the boundary conformal field theory with the bulk black hole entropy beyond the leading order given by the classical Bekenstein-Hawking formula, which consequently tests the AdS/CFT correspondence at the subleading order.

  18. Properties of Risk Measures of Generalized Entropy in Portfolio Selection

    Directory of Open Access Journals (Sweden)

    Rongxi Zhou

    2017-12-01

    Full Text Available This paper systematically investigates the properties of six kinds of entropy-based risk measures: Information Entropy and Cumulative Residual Entropy in the probability space, Fuzzy Entropy, Credibility Entropy and Sine Entropy in the fuzzy space, and Hybrid Entropy in the hybridized uncertainty of both fuzziness and randomness. We discover that none of the risk measures satisfy all six of the following properties, which various scholars have associated with effective risk measures: Monotonicity, Translation Invariance, Sub-additivity, Positive Homogeneity, Consistency and Convexity. Measures based on Fuzzy Entropy, Credibility Entropy, and Sine Entropy all exhibit the same properties: Sub-additivity, Positive Homogeneity, Consistency, and Convexity. These measures based on Information Entropy and Hybrid Entropy, meanwhile, only exhibit Sub-additivity and Consistency. Cumulative Residual Entropy satisfies just Sub-additivity, Positive Homogeneity, and Convexity. After identifying these properties, we develop seven portfolio models based on different risk measures and made empirical comparisons using samples from both the Shenzhen Stock Exchange of China and the New York Stock Exchange of America. The comparisons show that the Mean Fuzzy Entropy Model performs the best among the seven models with respect to both daily returns and relative cumulative returns. Overall, these results could provide an important reference for both constructing effective risk measures and rationally selecting the appropriate risk measure under different portfolio selection conditions.

  19. Extended statistical entropy analysis as a quantitative management tool for water resource systems

    Science.gov (United States)

    Sobantka, Alicja; Rechberger, Helmut

    2010-05-01

    The use of entropy in hydrology and water resources has been applied to various applications. As water resource systems are inherently spatial and complex, a stochastic description of these systems is needed, and entropy theory enables development of such a description by providing determination of the least-biased probability distributions with limited knowledge and data. Entropy can also serve as a basis for risk and reliability analysis. The relative entropy has been variously interpreted as a measure freedom of choice, uncertainty and disorder, information content, missing information or information gain or loss. In the analysis of empirical data, entropy is another measure of dispersion, an alternative to the variance. Also, as an evaluation tool, the statistical entropy analysis (SEA) has been developed by previous workers to quantify the power of a process to concentrate chemical elements. Within this research programme the SEA is aimed to be extended for application to chemical compounds and tested for its deficits and potentials in systems where water resources play an important role. The extended SEA (eSEA) will be developed first for the nitrogen balance in waste water treatment plants (WWTP). Later applications on the emission of substances to water bodies such as groundwater (e.g. leachate from landfills) will also be possible. By applying eSEA to the nitrogen balance in a WWTP, all possible nitrogen compounds, which may occur during the water treatment process, are taken into account and are quantified in their impact towards the environment and human health. It has been shown that entropy reducing processes are part of modern waste management. Generally, materials management should be performed in a way that significant entropy rise is avoided. The entropy metric might also be used to perform benchmarking on WWTPs. The result out of this management tool would be the determination of the efficiency of WWTPs. By improving and optimizing the efficiency

  20. Fast estimate of Hartley entropy in image sharpening

    Science.gov (United States)

    Krbcová, Zuzana; Kukal, Jaromír.; Svihlik, Jan; Fliegel, Karel

    2016-09-01

    Two classes of linear IIR filters: Laplacian of Gaussian (LoG) and Difference of Gaussians (DoG) are frequently used as high pass filters for contextual vision and edge detection. They are also used for image sharpening when linearly combined with the original image. Resulting sharpening filters are radially symmetric in spatial and frequency domains. Our approach is based on the radial approximation of unknown optimal filter, which is designed as a weighted sum of Gaussian filters with various radii. The novel filter is designed for MRI image enhancement where the image intensity represents anatomical structure plus additive noise. We prefer the gradient norm of Hartley entropy of whole image intensity as a measure which has to be maximized for the best sharpening. The entropy estimation procedure is as fast as FFT included in the filter but this estimate is a continuous function of enhanced image intensities. Physically motivated heuristic is used for optimum sharpening filter design by its parameter tuning. Our approach is compared with Wiener filter on MRI images.

  1. Transfer entropy in physical systems and the arrow of time

    Science.gov (United States)

    Spinney, Richard E.; Lizier, Joseph T.; Prokopenko, Mikhail

    2016-08-01

    Recent developments have cemented the realization that many concepts and quantities in thermodynamics and information theory are shared. In this paper, we consider a highly relevant quantity in information theory and complex systems, the transfer entropy, and explore its thermodynamic role by considering the implications of time reversal upon it. By doing so we highlight the role of information dynamics on the nuanced question of observer perspective within thermodynamics by relating the temporal irreversibility in the information dynamics to the configurational (or spatial) resolution of the thermodynamics. We then highlight its role in perhaps the most enduring paradox in modern physics, the manifestation of a (thermodynamic) arrow of time. We find that for systems that process information such as those undergoing feedback, a robust arrow of time can be formulated by considering both the apparent physical behavior which leads to conventional entropy production and the information dynamics which leads to a quantity we call the information theoretic arrow of time. We also offer an interpretation in terms of optimal encoding of observed physical behavior.

  2. Entropy Parameter M in Modeling a Flow Duration Curve

    Directory of Open Access Journals (Sweden)

    Yu Zhang

    2017-12-01

    Full Text Available A flow duration curve (FDC is widely used for predicting water supply, hydropower, environmental flow, sediment load, and pollutant load. Among different methods of constructing an FDC, the entropy-based method, developed recently, is appealing because of its several desirable characteristics, such as simplicity, flexibility, and statistical basis. This method contains a parameter, called entropy parameter M, which constitutes the basis for constructing the FDC. Since M is related to the ratio of the average streamflow to the maximum streamflow which, in turn, is related to the drainage area, it may be possible to determine M a priori and construct an FDC for ungauged basins. This paper, therefore, analyzed the characteristics of M in both space and time using streamflow data from 73 gauging stations in the Brazos River basin, Texas, USA. Results showed that the M values were impacted by reservoir operation and possibly climate change. The values were fluctuating, but relatively stable, after the operation of the reservoirs. Parameter M was found to change inversely with the ratio of average streamflow to the maximum streamflow. When there was an extreme event, there occurred a jump in the M value. Further, spatially, M had a larger value if the drainage area was small.

  3. Isotope yield ratios as a probe of the reaction dynamics

    International Nuclear Information System (INIS)

    Trautmann, W.; Hildenbrand, K.D.; Lynen, U.; Mueller, W.F.J.; Rabe, H.J.; Sann, H.; Stelzer, H.; Trockel, R.; Wada, R.; Brummund, N.; Glasow, R.; Kampert, K.H.; Santo, R.; Eckert, E.M.; Pochodzalla, J.; Bock, I.; Pelte, D.

    1987-04-01

    Isotopically resolved yields of particles and complex fragments from 12 C and 18 O induced reactions on 53 Ni, 54 Ni, Ag, and 197 Au in the intermediate range of bombarding energies 30 MeV ≤ E/A ≤ 84 MeV were measured. The systematic variation of the deduced isotope yield ratios with projectile and target is used to determine the degree of N/Z equilibration achieved and to establish time scales for the reaction process. A quantum statistical model is employed in order to derive entropies of the emitting systems from the measured isotope yield ratios. (orig.)

  4. Entropy, baryon asymmetry and dark matter from heavy neutrino decays

    International Nuclear Information System (INIS)

    Buchmueller, W.; Schmitz, K.; Vertongen, G.

    2011-01-01

    The origin of the hot phase of the early universe remains so far an unsolved puzzle. A viable option is entropy production through the decays of heavy Majorana neutrinos whose lifetimes determine the initial temperature. We show that baryogenesis and the production of dark matter are natural by-products of this mechanism. As is well known, the cosmological baryon asymmetry can be accounted for by leptogenesis for characteristic neutrino mass parameters. We find that thermal gravitino production then automatically yields the observed amount of dark matter, for the gravitino as the lightest superparticle and typical gluino masses. As an example, we consider the production of heavy Majorana neutrinos in the course of tachyonic preheating associated with spontaneous B-L breaking. A quantitative analysis leads to constraints on the superparticle masses in terms of neutrino masses: For a light neutrino mass of 10 -5 eV the gravitino mass can be as small as 200 MeV, whereas a lower neutrino mass bound of 0.01 eV implies a lower bound of 9 GeV on the gravitino mass. The measurement of a light neutrino mass of 0.1 eV would rule out heavy neutrino decays as the origin of entropy, visible and dark matter.

  5. Query construction, entropy, and generalization in neural-network models

    Science.gov (United States)

    Sollich, Peter

    1994-05-01

    We study query construction algorithms, which aim at improving the generalization ability of systems that learn from examples by choosing optimal, nonredundant training sets. We set up a general probabilistic framework for deriving such algorithms from the requirement of optimizing a suitable objective function; specifically, we consider the objective functions entropy (or information gain) and generalization error. For two learning scenarios, the high-low game and the linear perceptron, we evaluate the generalization performance obtained by applying the corresponding query construction algorithms and compare it to training on random examples. We find qualitative differences between the two scenarios due to the different structure of the underlying rules (nonlinear and ``noninvertible'' versus linear); in particular, for the linear perceptron, random examples lead to the same generalization ability as a sequence of queries in the limit of an infinite number of examples. We also investigate learning algorithms which are ill matched to the learning environment and find that, in this case, minimum entropy queries can in fact yield a lower generalization ability than random examples. Finally, we study the efficiency of single queries and its dependence on the learning history, i.e., on whether the previous training examples were generated randomly or by querying, and the difference between globally and locally optimal query construction.

  6. Entropy, baryon asymmetry and dark matter from heavy neutrino decays

    Energy Technology Data Exchange (ETDEWEB)

    Buchmueller, W.; Schmitz, K.; Vertongen, G.

    2011-04-15

    The origin of the hot phase of the early universe remains so far an unsolved puzzle. A viable option is entropy production through the decays of heavy Majorana neutrinos whose lifetimes determine the initial temperature. We show that baryogenesis and the production of dark matter are natural by-products of this mechanism. As is well known, the cosmological baryon asymmetry can be accounted for by lepto- genesis for characteristic neutrino mass parameters. We nd that thermal gravitino production then automatically yields the observed amount of dark matter, for the gravitino as the lightest superparticle and typical gluino masses. As an example, we consider the production of heavy Majorana neutrinos in the course of tachyonic preheating associated with spontaneous B-L breaking. A quantitative analysis leads to contraints on the superparticle masses in terms of neutrino masses: For a light neutrino mass of 10{sup -5} eV the gravitino mass can be as small as 200 MeV, whereas a lower neutrino mass bound of 0.01 eV implies a lower bound of 9 GeV on the gravitino mass. The measurement of a light neutrino mass of 0.1 eV would rule out heavy neutrino decays as the origin of entropy, visible and dark matter. (orig.)

  7. Maximum entropy production rate in quantum thermodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Beretta, Gian Paolo, E-mail: beretta@ing.unibs.i [Universita di Brescia, via Branze 38, 25123 Brescia (Italy)

    2010-06-01

    In the framework of the recent quest for well-behaved nonlinear extensions of the traditional Schroedinger-von Neumann unitary dynamics that could provide fundamental explanations of recent experimental evidence of loss of quantum coherence at the microscopic level, a recent paper [Gheorghiu-Svirschevski 2001 Phys. Rev. A 63 054102] reproposes the nonlinear equation of motion proposed by the present author [see Beretta G P 1987 Found. Phys. 17 365 and references therein] for quantum (thermo)dynamics of a single isolated indivisible constituent system, such as a single particle, qubit, qudit, spin or atomic system, or a Bose-Einstein or Fermi-Dirac field. As already proved, such nonlinear dynamics entails a fundamental unifying microscopic proof and extension of Onsager's reciprocity and Callen's fluctuation-dissipation relations to all nonequilibrium states, close and far from thermodynamic equilibrium. In this paper we propose a brief but self-contained review of the main results already proved, including the explicit geometrical construction of the equation of motion from the steepest-entropy-ascent ansatz and its exact mathematical and conceptual equivalence with the maximal-entropy-generation variational-principle formulation presented in Gheorghiu-Svirschevski S 2001 Phys. Rev. A 63 022105. Moreover, we show how it can be extended to the case of a composite system to obtain the general form of the equation of motion, consistent with the demanding requirements of strong separability and of compatibility with general thermodynamics principles. The irreversible term in the equation of motion describes the spontaneous attraction of the state operator in the direction of steepest entropy ascent, thus implementing the maximum entropy production principle in quantum theory. The time rate at which the path of steepest entropy ascent is followed has so far been left unspecified. As a step towards the identification of such rate, here we propose a possible

  8. Objective Bayesianism and the Maximum Entropy Principle

    Directory of Open Access Journals (Sweden)

    Jon Williamson

    2013-09-01

    Full Text Available Objective Bayesian epistemology invokes three norms: the strengths of our beliefs should be probabilities; they should be calibrated to our evidence of physical probabilities; and they should otherwise equivocate sufficiently between the basic propositions that we can express. The three norms are sometimes explicated by appealing to the maximum entropy principle, which says that a belief function should be a probability function, from all those that are calibrated to evidence, that has maximum entropy. However, the three norms of objective Bayesianism are usually justified in different ways. In this paper, we show that the three norms can all be subsumed under a single justification in terms of minimising worst-case expected loss. This, in turn, is equivalent to maximising a generalised notion of entropy. We suggest that requiring language invariance, in addition to minimising worst-case expected loss, motivates maximisation of standard entropy as opposed to maximisation of other instances of generalised entropy. Our argument also provides a qualified justification for updating degrees of belief by Bayesian conditionalisation. However, conditional probabilities play a less central part in the objective Bayesian account than they do under the subjective view of Bayesianism, leading to a reduced role for Bayes’ Theorem.

  9. An entropy-assisted musculoskeletal shoulder model.

    Science.gov (United States)

    Xu, Xu; Lin, Jia-Hua; McGorry, Raymond W

    2017-04-01

    Optimization combined with a musculoskeletal shoulder model has been used to estimate mechanical loading of musculoskeletal elements around the shoulder. Traditionally, the objective function is to minimize the summation of the total activities of the muscles with forces, moments, and stability constraints. Such an objective function, however, tends to neglect the antagonist muscle co-contraction. In this study, an objective function including an entropy term is proposed to address muscle co-contractions. A musculoskeletal shoulder model is developed to apply the proposed objective function. To find the optimal weight for the entropy term, an experiment was conducted. In the experiment, participants generated various 3-D shoulder moments in six shoulder postures. The surface EMG of 8 shoulder muscles was measured and compared with the predicted muscle activities based on the proposed objective function using Bhattacharyya distance and concordance ratio under different weight of the entropy term. The results show that a small weight of the entropy term can improve the predictability of the model in terms of muscle activities. Such a result suggests that the concept of entropy could be helpful for further understanding the mechanism of muscle co-contractions as well as developing a shoulder biomechanical model with greater validity. Copyright © 2017 Elsevier Ltd. All rights reserved.

  10. Enzyme catalysis by entropy without Circe effect.

    Science.gov (United States)

    Kazemi, Masoud; Himo, Fahmi; Åqvist, Johan

    2016-03-01

    Entropic effects have often been invoked to explain the extraordinary catalytic power of enzymes. In particular, the hypothesis that enzymes can use part of the substrate-binding free energy to reduce the entropic penalty associated with the subsequent chemical transformation has been very influential. The enzymatic reaction of cytidine deaminase appears to be a distinct example. Here, substrate binding is associated with a significant entropy loss that closely matches the activation entropy penalty for the uncatalyzed reaction in water, whereas the activation entropy for the rate-limiting catalytic step in the enzyme is close to zero. Herein, we report extensive computer simulations of the cytidine deaminase reaction and its temperature dependence. The energetics of the catalytic reaction is first evaluated by density functional theory calculations. These results are then used to parametrize an empirical valence bond description of the reaction, which allows efficient sampling by molecular dynamics simulations and computation of Arrhenius plots. The thermodynamic activation parameters calculated by this approach are in excellent agreement with experimental data and indeed show an activation entropy close to zero for the rate-limiting transition state. However, the origin of this effect is a change of reaction mechanism compared the uncatalyzed reaction. The enzyme operates by hydroxide ion attack, which is intrinsically associated with a favorable activation entropy. Hence, this has little to do with utilization of binding free energy to pay the entropic penalty but rather reflects how a preorganized active site can stabilize a reaction path that is not operational in solution.

  11. Differential effects of gender on entropy perception

    Science.gov (United States)

    Satcharoen, Kleddao

    2017-12-01

    The purpose of this research is to examine differences in perception of entropy (color intensity) between male and female computer users. The objectives include identifying gender-based differences in entropy intention and exploring the potential effects of these differences (if any) on user interface design. The research is an effort to contribute to an emerging field of interest in gender as it relates to science, engineering and technology (SET), particularly user interface design. Currently, there is limited evidence on the role of gender in user interface design and in use of technology generally, with most efforts at gender-differentiated or customized design based on stereotypes and assumptions about female use of technology or the assumption of a default position based on male preferences. Image entropy was selected as a potential characteristic where gender could be a factor in perception because of known differences in color perception acuity between male and female individuals, even where there is no known color perception abnormality (which is more common with males). Although the literature review suggested that training could offset differences in color perception and identification, tests in untrained subject groups routinely show that females are more able to identify, match, and differentiate colors, and that there is a stronger emotional and psychosocial association of color for females. Since image entropy is associated with information content and image salience, the ability to identify areas of high entropy could make a difference in user perception and technological capabilities.

  12. Entropy and black-hole thermodynamics

    International Nuclear Information System (INIS)

    Wald, R.M.

    1979-01-01

    The concept of entropy is examined with an eye toward gaining insight into the nature of black-hole thermodynamics. Definitions of entropy are given for ordinary classical and quantum-mechanical systems which lead to plausibility arguments for the ordinary laws of thermodynamics. The treatment of entropy for a classical system is in the spirit of the information-theory viewpoint, but by explicitly incorporating the coarse-grained observable into the definition of entropy, we eliminate any nonobjective features. The definition of entropy for a quantum-mechanical system is new, but directly parallels the classical treatment. We then apply these ideas to a self-gravitating quantum system which contains a black hole. Under some assumptions: which, although nontrivial, are by no means exotic: about the nature of such a system, it is seen that the same plausibility arguments which lead to the ordinary laws of thermodynamics for ordinary systems now lead to the laws of black-hole mechanics, including the generalized second law of thermodynamics. Thus, it appears perfectly plausible that black-hole thermodynamics is nothing more than ordinary thermodynamics applied to a self-gravitating quantum system

  13. Entropy Measurement for Biometric Verification Systems.

    Science.gov (United States)

    Lim, Meng-Hui; Yuen, Pong C

    2016-05-01

    Biometric verification systems are designed to accept multiple similar biometric measurements per user due to inherent intrauser variations in the biometric data. This is important to preserve reasonable acceptance rate of genuine queries and the overall feasibility of the recognition system. However, such acceptance of multiple similar measurements decreases the imposter's difficulty of obtaining a system-acceptable measurement, thus resulting in a degraded security level. This deteriorated security needs to be measurable to provide truthful security assurance to the users. Entropy is a standard measure of security. However, the entropy formula is applicable only when there is a single acceptable possibility. In this paper, we develop an entropy-measuring model for biometric systems that accepts multiple similar measurements per user. Based on the idea of guessing entropy, the proposed model quantifies biometric system security in terms of adversarial guessing effort for two practical attacks. Excellent agreement between analytic and experimental simulation-based measurement results on a synthetic and a benchmark face dataset justify the correctness of our model and thus the feasibility of the proposed entropy-measuring approach.

  14. Entropy and Entanglement of the Electromagnetically Induced Transparency System

    Institute of Scientific and Technical Information of China (English)

    LIU Xiao-Juan; FANG Mao-Fa; ZHOU Qing-Ping

    2004-01-01

    @@ We study the entropy and the entanglement of an electromagnetically induced transparency system. The quantum entanglement between the atom and the two quantized laser fields is discussed by using quantum reduced entropy and that between the two quantized laser fields by using quantum relative entropy. We also examine whether influences of EIT on entropy and quantum entanglement of the system considered occur or not. Our results show that the minimum value of the atomic reduced entropy may be regarded as an entropy criterion on the electromagnetically induced transparency occurring.

  15. Holographic entropy inequalities and gapped phases of matter

    Energy Technology Data Exchange (ETDEWEB)

    Bao, Ning [Institute for Quantum Information and Matter, California Institute of Technology,Pasadena, CA 91125 (United States); Walter Burke Institute for Theoretical Physics, California Institute of Technology,Pasadena, CA 91125 (United States); Cao, ChunJun [Walter Burke Institute for Theoretical Physics, California Institute of Technology,Pasadena, CA 91125 (United States); Walter, Michael [Stanford Institute for Theoretical Physics,Stanford University, Stanford, CA 94305 (United States); Wang, Zitao [Institute for Quantum Information and Matter, California Institute of Technology,Pasadena, CA 91125 (United States); Walter Burke Institute for Theoretical Physics, California Institute of Technology,Pasadena, CA 91125 (United States)

    2015-09-29

    We extend our studies of holographic entropy inequalities to gapped phases of matter. For any number of regions, we determine the linear entropy inequalities satisfied by systems in which the entanglement entropy satisfies an exact area law. In particular, we find that all holographic entropy inequalities are valid in such systems. In gapped systems with topological order, the “cyclic inequalities” derived recently for the holographic entanglement entropy generalize the Kitaev-Preskill formula for the topological entanglement entropy. Finally, we propose a candidate linear inequality for general 4-party quantum states.

  16. Holographic entropy inequalities and gapped phases of matter

    International Nuclear Information System (INIS)

    Bao, Ning; Cao, ChunJun; Walter, Michael; Wang, Zitao

    2015-01-01

    We extend our studies of holographic entropy inequalities to gapped phases of matter. For any number of regions, we determine the linear entropy inequalities satisfied by systems in which the entanglement entropy satisfies an exact area law. In particular, we find that all holographic entropy inequalities are valid in such systems. In gapped systems with topological order, the “cyclic inequalities” derived recently for the holographic entanglement entropy generalize the Kitaev-Preskill formula for the topological entanglement entropy. Finally, we propose a candidate linear inequality for general 4-party quantum states.

  17. Information-theoretical aspects of quantum-mechanical entropy

    International Nuclear Information System (INIS)

    Wehrl, A.

    1990-01-01

    Properties of the quantum ( = von Neumann) entropy S(ρ) -k Trρ lnρ, ρ being a compact operator, are proved first, and differences against the classical case, e.g. the Shannon entropy, are worked out. The main result is on the strong subadditivity of this quantum entropy. Then another entropy, a function not of the state but of the dynamics of the system, is considered as a quantum analogue of the classical Kolmogorov-Sinai-entropy. An attempt in defining such a quantity had only recently sucess in a paper of Connes, Narnhofer and Thirring. A definition of this entropy is given. 34 refs

  18. Quantification of entanglement entropies for doubly excited resonance states in two-electron atomic systems

    International Nuclear Information System (INIS)

    Ho, Yew Kam; Lin, Chien-Hao

    2015-01-01

    In this work, we study the quantum entanglement for doubly excited resonance states in two-electron atomic systems such as the H - and Ps - ions and the He atom by using highly correlated Hylleraas type functions The resonance states are determined by calculation of density of resonance states with the stabilization method. The spatial (electron-electron orbital) entanglement entropies (linear and von Neumann) for the low-lying doubly excited states are quantified using the Schmidt-Slater decomposition method. (paper)

  19. Bias correction for magnetic resonance images via joint entropy regularization.

    Science.gov (United States)

    Wang, Shanshan; Xia, Yong; Dong, Pei; Luo, Jianhua; Huang, Qiu; Feng, Dagan; Li, Yuanxiang

    2014-01-01

    Due to the imperfections of the radio frequency (RF) coil or object-dependent electrodynamic interactions, magnetic resonance (MR) images often suffer from a smooth and biologically meaningless bias field, which causes severe troubles for subsequent processing and quantitative analysis. To effectively restore the original signal, this paper simultaneously exploits the spatial and gradient features of the corrupted MR images for bias correction via the joint entropy regularization. With both isotropic and anisotropic total variation (TV) considered, two nonparametric bias correction algorithms have been proposed, namely IsoTVBiasC and AniTVBiasC. These two methods have been applied to simulated images under various noise levels and bias field corruption and also tested on real MR data. The test results show that the proposed two methods can effectively remove the bias field and also present comparable performance compared to the state-of-the-art methods.

  20. Holographic entanglement entropy of surface defects

    Energy Technology Data Exchange (ETDEWEB)

    Gentle, Simon A.; Gutperle, Michael; Marasinou, Chrysostomos [Department of Physics and Astronomy, University of California,Los Angeles, CA 90095 (United States)

    2016-04-12

    We calculate the holographic entanglement entropy in type IIB supergravity solutions that are dual to half-BPS disorder-type surface defects in N=4 supersymmetric Yang-Mills theory. The entanglement entropy is calculated for a ball-shaped region bisected by a surface defect. Using the bubbling supergravity solutions we also compute the expectation value of the defect operator. Combining our result with the previously-calculated one-point function of the stress tensor in the presence of the defect, we adapt the calculation of Lewkowycz and Maldacena http://dx.doi.org/10.1007/JHEP05(2014)025 to obtain a second expression for the entanglement entropy. Our two expressions agree up to an additional term, whose possible origin and significance is discussed.