Equivalent Relation between Normalized Spatial Entropy and Fractal Dimension
Chen, Yanguang
2016-01-01
Fractal dimension is defined on the base of entropy, including macro state entropy and information entropy. The generalized dimension of multifractals is based on Renyi entropy. However, the mathematical transform from entropy to fractal dimension is not yet clear in both theory and practice. This paper is devoted to revealing the equivalence relation between spatial entropy and fractal dimension using box-counting method. Based on varied regular fractals, the numerical relationship between spatial entropy and fractal dimension is examined. The results show that the ratio of actual entropy (Mq) to the maximum entropy (Mmax) equals the ratio of actual dimension (Dq) to the maximum dimension (Dmax), that is, Mq/Mmax=Dq/Dmax. For real systems, the spatial entropy and fractal dimension of complex spatial systems such as cities can be converted into one another by means of functional box-counting method. The theoretical inference is verified by observational data of urban form. A conclusion is that normalized spat...
A spatial entropy reflecting distribution of spatial objects
Youn-Kyung Jang; Byeong-Seob You; Ho-Seok Kim; Kyoung-Bae Kim; Hae-Young Bae
2007-01-01
Decision trees are mainly used to classify data and predict data classes. A spatial decision tree has been designed using Euclidean distance between objects for reflecting spatial data characteristic. Even though this method explains the distance of objects in spatial dimension, it fails to represent distributions of spatial data and their relationships. But distributions of spatial data and relationships with their neighborhoods are very important in real world. This paper proposes decision tree based on spatial entropy that represents distributions of spatial data with dispersion and dissimilarity. The rate of dispersion by dissimilarity presents how related distribution of spatial data and non-spatial attributes. The experiment evaluates the accuracy and building time of decision tree as compared to previous methods and it shows that the proposed method makes efficient and scalable classification for spatial decision support.
Spatial Entropy and Fractal Dimension of Urban Form
Chen, Yanguang; Feng, Jian
2016-01-01
Entropy is an important concept in the studies on complex systems such as cities. Spatial patterns and processes can be described with varied entropy functions. However, spatial entropy always depends on the scale of measurement, and we cannot find a characteristic value for it. In contrast, entropy-based fractal parameters can be employed to characterize scale-free phenomena. This paper is devoted to exploring the similarities and differences between spatial entropy and fractal dimension in urban description. Drawing an analogy between cities and growing fractals, we illustrate the definitions of fractal dimension based on several entropy formulae. Three representative fractal dimensions in the multifractal dimension set, capacity dimension, information dimension, and correlation dimension, are utilized to make an empirical analysis of Beijing's and Hangzhou's urban form using functional box-counting method. The results show that the entropy values are not determinate, but the fractal dimension value is cert...
Isobaric yield ratio difference and Shannon information entropy
Chun-Wang Ma
2015-03-01
Full Text Available The Shannon information entropy theory is used to explain the recently proposed isobaric yield ratio difference (IBD probe which aims to determine the nuclear symmetry energy. Theoretically, the difference between the Shannon uncertainties carried by isobars in two different reactions (ΔIn21, is found to be equivalent to the difference between the chemical potentials of protons and neutrons of the reactions [the IBD probe, IB-Δ(βμ21, with β the reverse temperature]. From the viewpoints of Shannon information entropy, the physical meaning of the above chemical potential difference is interpreted by ΔIn21 as denoting the nuclear symmetry energy or density difference between neutrons and protons in reactions more concisely than from the statistical ablation–abrasion model.
Spatial Analysis of Cities Using Renyi Entropy and Fractal Parameters
Chen, Yanguang
2016-01-01
Spatial distributions of cities fall into groups: one is the simple distribution with characteristic scale (e.g. exponential distribution), and the other is the complex distribution without characteristic scale (e.g. power-law distribution). The latter belongs to scale-free distributions, which can be modeled with fractal geometry. However, fractal dimension is suitable for the former distribution. In contrast, spatial entropy can be used to measure any types of urban distributions. This paper is devoted to developing multifractal parameters by means of the relation between entropy and fractal dimension. A new discovery is that normalized fractal dimension is equal to normalized entropy. Based on this finding, we can define a set of spatial indexes, which bears an analogy with the multifractal parameters. These indexes can be employed to describe both the simple distributions and complex distributions. The generalized fractal parameters are applied to the spatial density of population density of Hangzhou city...
The entanglement entropy for quantum system in one spatial dimension
Wang, Honglei; Su, Yao Heng; Liang, Bo; Chen, Longcong
2015-01-01
Ground-state entanglement entropies were investigated for the one-dimension quantum two- and three-spin interaction models, the four-state Potts model, and the XXZ model with uniaxial single-ion-type anisotropy, which were obtained on an infinite-size lattice in one spatial dimension. Thus we show that the entanglement, a key concept of quantum information science, is quantified by the ground-state entanglement entropy. The relationships between ground-state entanglement entropy and quantum phase transition was analyzed. These results were obtained using the infinite matrix product state algorithm which works in the thermodynamical limit.
A Multimedia Application: Spatial Perceptual Entropy of Multichannel Audio Signals
Shuixian Chen
2010-01-01
Full Text Available Usually multimedia data have to be compressed before transmitting, and higher compression rate, or equivalently lower bitrate, relieves the load of communication channels but impacts negatively the quality. We investigate the bitrate lower bound for perceptually lossless compression of a major type of multimedia—multichannel audio signals. This bound equals to the perceptible information rate of the signals. Traditionally, Perceptual Entropy (PE, based primarily on monaural hearing measures the perceptual information rate of individual channels. But PE cannot measure the spatial information captured by binaural hearing, thus is not suitable for estimating Spatial Audio Coding (SAC bitrate bound. To measure this spatial information, we build a Binaural Cue Physiological Perception Model (BCPPM on the ground of binaural hearing, which represents spatial information in the physical and physiological layers. This model enables computing Spatial Perceptual Entropy (SPE, the lower bitrate bound for SAC. For real-world stereo audio signals of various types, our experiments indicate that SPE reliably estimates their spatial information rate. Therefore, “SPE plus PE” gives lower bitrate bounds for communicating multichannel audio signals with transparent quality.
A Multimedia Application: Spatial Perceptual Entropy of Multichannel Audio Signals
Chen Shuixian
2010-01-01
Full Text Available Usually multimedia data have to be compressed before transmitting, and higher compression rate, or equivalently lower bitrate, relieves the load of communication channels but impacts negatively the quality. We investigate the bitrate lower bound for perceptually lossless compression of a major type of multimedia—multichannel audio signals. This bound equals to the perceptible information rate of the signals. Traditionally, Perceptual Entropy (PE, based primarily on monaural hearing measures the perceptual information rate of individual channels. But PE cannot measure the spatial information captured by binaural hearing, thus is not suitable for estimating Spatial Audio Coding (SAC bitrate bound. To measure this spatial information, we build a Binaural Cue Physiological Perception Model (BCPPM on the ground of binaural hearing, which represents spatial information in the physical and physiological layers. This model enables computing Spatial Perceptual Entropy (SPE, the lower bitrate bound for SAC. For real-world stereo audio signals of various types, our experiments indicate that SPE reliably estimates their spatial information rate. Therefore, "SPE plus PE" gives lower bitrate bounds for communicating multichannel audio signals with transparent quality.
Monitoring Debris Flows Using Spatial Filtering and Entropy Determination Approaches
Hung-Ming Kao
2013-01-01
Full Text Available We developed an automatic debris flow warning system in this study. The system uses a fixed video camera mounted over mountainous streams with a high risk for debris flows. The focus of this study is to develop an automatic algorithm for detecting debris flows with a low computational effort which can facilitate real-time implementation. The algorithm is based on a moving object detection technique to detect debris flow by comparing among video frames. Background subtraction is the kernel of the algorithm to reduce the computational effort, but non-rigid properties and color similarity of the object and the background color introduces some difficulties. Therefore, we used several spatial filtering approaches to increase the performance of the background subtraction. To increase the accuracy entropy is used with histogram analysis to identify whether a debris flow occurred. The modified background subtraction approach using spatial filtering and entropy determination is adopted to overcome the error in moving detection caused by non-rigid and similarities in color properties. The results of this study show that the approach described here can improve performance and also reduce the computational effort.
A Non-Parametric Spatial Independence Test Using Symbolic Entropy
López Hernández, Fernando
2008-01-01
Full Text Available In the present paper, we construct a new, simple, consistent and powerful test forspatial independence, called the SG test, by using symbolic dynamics and symbolic entropyas a measure of spatial dependence. We also give a standard asymptotic distribution of anaffine transformation of the symbolic entropy under the null hypothesis of independencein the spatial process. The test statistic and its standard limit distribution, with theproposed symbolization, are invariant to any monotonuous transformation of the data.The test applies to discrete or continuous distributions. Given that the test is based onentropy measures, it avoids smoothed nonparametric estimation. We include a MonteCarlo study of our test, together with the well-known Moran’s I, the SBDS (de Graaffet al, 2001 and (Brett and Pinkse, 1997 non parametric test, in order to illustrate ourapproach.
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
Spatial Dynamics of Urban Growth Based on Entropy and Fractal Dimension
Chen, Yanguang
2016-01-01
The fractal dimension growth of urban form can be described with sigmoid functions such as logistic function due to squashing effect. The sigmoid curves of fractal dimension suggest a type of spatial replacement dynamics of urban evolution. How to understand the underlying rationale of the fractal dimension curves is a pending problem. This study is based on two previous findings. First, normalized fractal dimension proved to equal normalized spatial entropy; second, a sigmoid function proceeds from an urban-rural interaction model. Defining urban space-filling measurement by spatial entropy, and defining rural space-filling measurement by information gain, we can construct a new urban-rural interaction and coupling model. From this model, we can derive the logistic equation of fractal dimension growth strictly. This indicates that urban growth results from the unity of opposites between spatial entropy increase and information increase. In a city, an increase in spatial entropy is accompanied by a decrease i...
Li, Weiyao; Huang, Guanhua; Xiong, Yunwu
2016-04-01
The complexity of the spatial structure of porous media, randomness of groundwater recharge and discharge (rainfall, runoff, etc.) has led to groundwater movement complexity, physical and chemical interaction between groundwater and porous media cause solute transport in the medium more complicated. An appropriate method to describe the complexity of features is essential when study on solute transport and conversion in porous media. Information entropy could measure uncertainty and disorder, therefore we attempted to investigate complexity, explore the contact between the information entropy and complexity of solute transport in heterogeneous porous media using information entropy theory. Based on Markov theory, two-dimensional stochastic field of hydraulic conductivity (K) was generated by transition probability. Flow and solute transport model were established under four conditions (instantaneous point source, continuous point source, instantaneous line source and continuous line source). The spatial and temporal complexity of solute transport process was characterized and evaluated using spatial moment and information entropy. Results indicated that the entropy increased as the increase of complexity of solute transport process. For the point source, the one-dimensional entropy of solute concentration increased at first and then decreased along X and Y directions. As time increased, entropy peak value basically unchanged, peak position migrated along the flow direction (X direction) and approximately coincided with the centroid position. With the increase of time, spatial variability and complexity of solute concentration increase, which result in the increases of the second-order spatial moment and the two-dimensional entropy. Information entropy of line source was higher than point source. Solute entropy obtained from continuous input was higher than instantaneous input. Due to the increase of average length of lithoface, media continuity increased, flow and
Entropy Maximization and the Spatial Distribution of Species
Haegeman, Bart; Etienne, Rampal S.
2010-01-01
Entropy maximization (EM, also known as MaxEnt) is a general inference procedure that originated in statistical mechanics. It has been applied recently to predict ecological patterns, such as species abundance distributions and species-area relationships. It is well known in physics that the EM resu
Entropy Maximization and the Spatial Distribution of Species
Haegeman, Bart; Etienne, Rampal S.
Entropy maximization (EM, also known as MaxEnt) is a general inference procedure that originated in statistical mechanics. It has been applied recently to predict ecological patterns, such as species abundance distributions and species-area relationships. It is well known in physics that the EM
Tonini, A.; Pede, V.
2011-01-01
In this paper, a stochastic frontier model accounting for spatial dependency is developed using generalized maximum entropy estimation. An application is made for measuring total factor productivity in European agriculture. The empirical results show that agricultural productivity growth in Europe i
Spatial and Temporal Uncertainty of Crop Yield Aggregations
Porwollik, Vera; Mueller, Christoph; Elliott, Joshua; Chryssanthacopoulos, James; Iizumi, Toshichika; Ray, Deepak K.; Ruane, Alex C.; Arneth, Almut; Balkovic, Juraj; Ciais, Philippe; Deryng, Delphine; Folberth, Christian; Izaurralde, Robert C.; Jones, Curtis D.; Khabarov, Nikolay; Lawrence, Peter J.; Liu, Wenfeng; Pugh, Thomas A. M.; Reddy, Ashwan; Sakurai, Gen; Schmid, Erwin; Wang, Xuhui; Wu, Xiuchen; de Wit, Allard
2016-01-01
The aggregation of simulated gridded crop yields to national or regional scale requires information on temporal and spatial patterns of crop-specific harvested areas. This analysis estimates the uncertainty of simulated gridded yield time series related to the aggregation with four different harvested area data sets. We compare aggregated yield time series from the Global Gridded Crop Model Inter-comparison project for four crop types from 14 models at global, national, and regional scale to determine aggregation-driven differences in mean yields and temporal patterns as measures of uncertainty. The quantity and spatial patterns of harvested areas differ for individual crops among the four datasets applied for the aggregation. Also simulated spatial yield patterns differ among the 14 models. These differences in harvested areas and simulated yield patterns lead to differences in aggregated productivity estimates, both in mean yield and in the temporal dynamics. Among the four investigated crops, wheat yield (17% relative difference) is most affected by the uncertainty introduced by the aggregation at the global scale. The correlation of temporal patterns of global aggregated yield time series can be as low as for soybean (r = 0.28).For the majority of countries, mean relative differences of nationally aggregated yields account for10% or less. The spatial and temporal difference can be substantial higher for individual countries. Of the top-10 crop producers, aggregated national multi-annual mean relative difference of yields can be up to 67% (maize, South Africa), 43% (wheat, Pakistan), 51% (rice, Japan), and 427% (soybean, Bolivia).Correlations of differently aggregated yield time series can be as low as r = 0.56 (maize, India), r = 0.05*Corresponding (wheat, Russia), r = 0.13 (rice, Vietnam), and r = -0.01 (soybean, Uruguay). The aggregation to sub-national scale in comparison to country scale shows that spatial uncertainties can cancel out in countries with
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.
Assessment of spatial structure of groundwater quality variables based on the entropy theory
Y. Mogheir
2003-01-01
Full Text Available Fundamental to the spatial sampling design of a groundwater quality monitoring network is the spatial structure of groundwater quality variables. The entropy theory presents an alternative approach to describe this variability. A case study is presented which used groundwater quality observations (13 years; 1987-2000 from groundwater domestic wells in the Gaza Strip, Palestine. The analyses of the spatial structure used the following variables: Electrical Conductivity (EC, Total Dissolved Solids (TDS, Calcium (Ca, Magnesium (Mg, Sodium (Na, Potassium (K, Chloride (Cl, Nitrate (NO3, Sulphate (SO4, alkalinity and hardness. For all these variables the spatial structure is described by means of Transinformation as a function of distance between wells (Transinformation Model and correlation also as a function of distance (Correlation Model. The parameters of the Transinformation Model analysed were: (1 the initial value of the Transinformation; (2 the rate of information decay; (3 the minimum constant value; and (4 the distance at which the Transinformation Model reaches its minimum value. Exponential decay curves were fitted to both models. The Transinformation Model was found to be superior to the Correlation Model in representing the spatial variability (structure. The parameters of the Transinformation Model were different for some variables and similar for others. That leads to a reduction of the variables to be monitored and consequently reduces the cost of monitoring. Keywords: transinformation, correlation, spatial structure, municipal wells, groundwater monitoring, entropy
无
2009-01-01
In order to restrain the mid-spatial frequency error in magnetorheological finishing (MRF) process, a novel part-random path is designed based on the theory of maximum entropy method (MEM). Using KDMRF-1000F polishing machine, one flat work piece (98 mm in diameter) is polished. The mid-spatial frequency error in the region using part-random path is much lower than that by using common raster path. After one MRF iteration (7.46 min), peak-to-valley (PV) is 0.062 wave (1 wave =632.8 nm), root-mean-square (RMS) is 0.010 wave and no obvious mid-spatial frequency error is found. The result shows that the part-random path is a novel path, which results in a high form accuracy and low mid-spatial frequency error in MRF process.
Modeling temporal and spatial variability of crop yield
Bonetti, S.; Manoli, G.; Scudiero, E.; Morari, F.; Putti, M.; Teatini, P.
2014-12-01
In a world of increasing food insecurity the development of modeling tools capable of supporting on-farm decision making processes is highly needed to formulate sustainable irrigation practices in order to preserve water resources while maintaining adequate crop yield. The design of these practices starts from the accurate modeling of soil-plant-atmosphere interaction. We present an innovative 3D Soil-Plant model that couples 3D hydrological soil dynamics with a mechanistic description of plant transpiration and photosynthesis, including a crop growth module. Because of its intrinsically three dimensional nature, the model is able to capture spatial and temporal patterns of crop yield over large scales and under various climate and environmental factors. The model is applied to a 25 ha corn field in the Venice coastland, Italy, that has been continuously monitored over the years 2010 and 2012 in terms of both hydrological dynamics and yield mapping. The model results satisfactorily reproduce the large variability observed in maize yield (from 2 to 15 ton/ha). This variability is shown to be connected to the spatial heterogeneities of the farmland, which is characterized by several sandy paleo-channels crossing organic-rich silty soils. Salt contamination of soils and groundwater in a large portion of the area strongly affects the crop yield, especially outside the paleo-channels, where measured salt concentrations are lower than the surroundings. The developed model includes a simplified description of the effects of salt concentration in soil water on transpiration. The results seem to capture accurately the effects of salt concentration and the variability of the climatic conditions occurred during the three years of measurements. This innovative modeling framework paves the way to future large scale simulations of farmland dynamics.
Entropy Theory of Polymer Glass-Formation in Variable Spatial Dimension
Xu, Wen-Sheng; Douglas, Jack; Freed, Karl
The importance of packing frustration is broadly appreciated to be an important aspect of glass-formation. Recently, great interest has focused on using spatial dimensionality () as a theoretical tool for exploring this and other aspects of glass-forming liquids. We explore glass-formation in variable based on the generalized entropy theory, a synthesis of the Adam-Gibbs model with direct computation of the configurational entropy of polymer fluids using an established analytical statistical thermodynamic model. We find that structural relaxation in the fluid state asymptotically becomes Arrhenius in the limit and that the fluid transforms upon sufficient cooling above a critical dimension near into a dense amorphous state with a finite positive residual configurational entropy. The GET also predicts the variation with of measures of fragility and of the characteristic temperatures of glass-formation demarking the onset , middle , and end , of the broad glass transition. Direct computations of the isothermal compressibility and thermal expansion coefficient, which are physical measures of packing frustration, demonstrate that these fluid properties strongly correlate with the fragility of glass-formation. Back to three dimensions, we deduce apparently universal relationships between , a measure of the breadth of the glass-formation and both the isothermal compressibility and thermal expansion coefficient of polymer melts at .
Greilich, A.; Markus, M.; Goles, E.
2005-05-01
We investigate the control of spatiotemporal chaos by external forcing at equidistant points (pinning sites) in one-dimensional systems. A monotonic decrease of the minimum distance between pinning sites versus the spatial measure entropy (in the absence of forcing) can be obtained for an appropriate choice of the forcing procedure. Such a relation between a feature for control and the disorder of the uncontrolled system is shown for four systems: binary cellular automata, coupled logistic equations, a stick-slip model and coupled differential equations.
Ethiopian Wheat Yield and Yield Gap Estimation: A Spatial Small Area Integrated Data Approach
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.
Jun, Suckjoon; Mulder, Bela
2006-08-01
Despite recent progress in visualization experiments, the mechanism underlying chromosome segregation in bacteria still remains elusive. Here we address a basic physical issue associated with bacterial chromosome segregation, namely the spatial organization of highly confined, self-avoiding polymers (of nontrivial topology) in a rod-shaped cell-like geometry. Through computer simulations, we present evidence that, under strong confinement conditions, topologically distinct domains of a polymer complex effectively repel each other to maximize their conformational entropy, suggesting that duplicated circular chromosomes could partition spontaneously. This mechanism not only is able to account for the spatial separation per se but also captures the major features of the spatiotemporal organization of the duplicating chromosomes observed in Escherichia coli and Caulobacter crescentus. bacterial chromosome segregation | Caulobacter crescentus | Escherichia coli | polymer physics
Multiply scattered waves through a spatially random medium : entropy production and depolarization
Bicout, Dominique; Brosseau, Christian
1992-11-01
This paper deals with the depolarization and decoherence effects of an incident pure state of polarization and of arbitrary state of coherence by a linear scattering medium which changes randomly with position. Using symmetry arguments and a maximum entropy principle we deduce the general form of the Mueller matrix describing the scattering medium which is consistent with the explicit computation done in the context of the Bethe-Salpeter equation handled in the diffusion approximation. The main result expresses the output degree of polarization and degree of spatial coherence as a function of the number of scattering events. From these results, two main conclusions can be drawn. The first is that the entropy production per scattering due to the irreversible process of depolarization is an exponentially decreasing function of the number of scattering events. The second result obtained is that full depolarization of linearly polarized light by Rayleigh scatterers requires more scattering events (typically a factor-of-2) than are required for a circularly polarized lightwave. Dans cette étude, on considère les phénomènes de dépolarisation et de décohérence d'un faisceau d'ondes planes incident, d'état pur de polarisation et d'état arbitraire de cohérence, par intéraction avec un milieu diffusant désordonné. Par des arguments de symétrie et un principe d'entropie maximum, nous déduisons la forme de la matrice de Mueller caractérisant le milieu diffusant qui est en accord avec le calcul explicite basé sur l'équation de Bethe-Salpeter traitée dans l'approximation de la diffusion. Le résultat principal exprime les degrés de polarisation et de cohérence spatiale en fonction du nombre de diffusions. Deux faits saillants sont à noter. Le premier exprime la décroissance exponentielle de la production d'entropie due à l'irréversibilité du processus de dépolarisation, en fonction du nombre de diffusions. Le second indique que la dépolarisation compl
del Jesus, Manuel; Foti, Romano; Rinaldo, Andrea; Rodriguez-Iturbe, Ignacio
2012-12-18
The spatial organization of functional vegetation types in river basins is a major determinant of their runoff production, biodiversity, and ecosystem services. The optimization of different objective functions has been suggested to control the adaptive behavior of plants and ecosystems, often without a compelling justification. Maximum entropy production (MEP), rooted in thermodynamics principles, provides a tool to justify the choice of the objective function controlling vegetation organization. The application of MEP at the ecosystem scale results in maximum productivity (i.e., maximum canopy photosynthesis) as the thermodynamic limit toward which the organization of vegetation appears to evolve. Maximum productivity, which incorporates complex hydrologic feedbacks, allows us to reproduce the spatial macroscopic organization of functional types of vegetation in a thoroughly monitored river basin, without the need for a reductionist description of the underlying microscopic dynamics. The methodology incorporates the stochastic characteristics of precipitation and the associated soil moisture on a spatially disaggregated framework. Our results suggest that the spatial organization of functional vegetation types in river basins naturally evolves toward configurations corresponding to dynamically accessible local maxima of the maximum productivity of the ecosystem.
Leach, James M.; Coulibaly, Paulin; Guo, Yiping
2016-10-01
This study explores the inclusion of a groundwater recharge based design objective and the impact it has on the design of optimum groundwater monitoring networks. The study was conducted in the Hamilton, Halton, and Credit Valley regions of Ontario, Canada, in which the existing Ontario Provincial Groundwater Monitoring Network was augmented with additional monitoring wells. The Dual Entropy-Multiobjective Optimization (DEMO) model was used in these analyses. The value of using this design objective is rooted in the information contained within the estimated recharge. Recharge requires knowledge of climate, geomorphology, and geology of the area, thus using this objective function can help account for these physical characteristics. Two sources of groundwater recharge data were examined and compared, the first was calculated using the Precipitation-Runoff Modeling System (PRMS), and the second was an aggregation of recharge found using both the PRMS and Hydrological Simulation Program-Fortran (HSP-F). The entropy functions are used to identify optimal trade-offs between the maximum information content and the minimum shared information between the monitoring wells. The recharge objective will help to quantify hydrological characteristics of the vadose zone, and thus provide more information to the optimization algorithm. Results show that by including recharge as a design objective, the spatial coverage of the monitoring network can be improved. The study also highlights the flexibility of DEMO and its ability to incorporate additional design objectives such as the groundwater recharge.
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
Simulating the influence of crop spatial patterns on canola yield
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...
The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems
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.
Spatial variability of soybean yields under two systems cropping in savannah
Lúcio Bastos Madeiros
2009-08-01
Full Text Available The geostatistics is an important tool in analysis and description of soil variability properties. The maps of productivity are considered an excellent tool for analysis of performance at the level of agricultural property. Objective was to analyze the spatial yield variability of soybean in no-tillage e conventional-tillage. The experiment was carried out in two plots in sampling points defined accordingly to grid with dimension of 40 x 55 m, totaling 44 points spaced 5m. Statistical and geostatistical analysis were performed to monitor the range of spatial variability and spatial dependence. Soybean yield didn't present spatial dependence in none systems. The management in conventional-tillage was decisive in increase the yield of soybean in relation to no-tillage.Key-words: geostatistic; spatial dependence; management soil.
Assessing the Spatial Variability of Alfalfa Yield Using Satellite Imagery and Ground-Based Data
Kayad, Ahmed G.; Al-Gaadi, Khalid A.; Tola, ElKamil; Madugundu, Rangaswamy; Zeyada, Ahmed M.; Kalaitzidis, Chariton
2016-01-01
Understanding the temporal and spatial variability in a crop yield is viewed as one of the key steps in the implementation of precision agriculture practices. Therefore, a study on a center pivot irrigated 23.5 ha field in Saudi Arabia was conducted to assess the variability in alfalfa yield using Landsat-8 imagery and a hay yield monitor data. In addition, the study was designed to also explore the potential of predicting the alfalfa yield using vegetation indices. A calibrated yield monitor mounted on a large rectangular hay baler was used to measure the actual alfalfa yield for four alfalfa harvests performed in the period from October 2013 to May 2014. A total of 18 Landsat-8 images, representing different crop growth stages, were used to derive different vegetation indices (VIs). Data from the yield monitor was used to generate yield maps, which illustrated a definite spatial variation in alfalfa yield across the experimental field for the four studied harvests as indicated by the high spatial correlation values (0.75 to 0.97) and the low P-values (4.7E-103 to 8.9E-27). The yield monitor-measured alfalfa actual yield was compared to the predicted yield form the Vis. Results of the study showed that there was a correlation between actual and predicted yield. The highest correlations were observed between actual yield and the predicted using NIR reflectance, SAVI and NDVI with maximum correlation coefficients of 0.69, 0.68 and 0.63, respectively. PMID:27281189
Spatial variability of soil attributes and sugarcane yield in relation to topographic location
de Souza, Zigomar M.; Domingos G. P. Cerri; Paulo S. G. Magalhães; Siqueira, Diego S.
2010-01-01
Soils submitted to the same management system in places with little variation of landscape, manifest differentiated spatial variability of their attributes and crop yield. The aim of this work was to investigate the correlation between spatial variability of the soil attributes and sugarcane yield as a result of soil topography. To achieve this objective, a test area of 42 ha located at the São João Sugar Mill, in Araras, in the State of São Paulo, Brazil, was selected. Sugarcane yield was me...
Spatial variability of soil fertility and its relation with cocoa yield
Railton O. dos Santos
Full Text Available ABSTRACT The knowledge on the spatial variability of soil properties and crops is important for decision-making on agricultural management. The objective of this study was to evaluate the spatial variability of soil fertility and its relation with cocoa yield. The study was conducted over 14 months in an area cultivated with cocoa. A sampling grid was created to study soil chemical properties and cocoa yield (stratified in season, off-season and annual. The data were analyzed using descriptive and exploratory statistics, and geostatistics. The chemical attributes were classified using fuzzy logic to generate a soil fertility map, which was correlated with maps of crop yield. The soil of the area, except for the western region, showed possibilities ranging from medium to high for cocoa cultivation. Soil fertility showed positive spatial correlation with cocoa yield, and its effect was predominant only for the off-season and annual cocoa.
赵春晖; 田明华; 齐滨; 王玉磊
2016-01-01
A variation pixels identification method was proposed aiming at depressing the effect of variation pixels, which dilates the theoretical hyperspectral data simplex and misguides volume evaluation of the simplex. With integration of both spatial and spectral information, this method quantitatively defines a variation index for every pixel. The variation index is proportional to pixels local entropy but inversely proportional to pixels kernel spatial attraction. The number of pixels removed was modulated by an artificial threshold factorα. Two real hyperspectral data sets were employed to examine the endmember extraction results. The reconstruction errors of preprocessing data as opposed to the result of original data were compared. The experimental results show that the number of distinct endmembers extracted has increased and the reconstruction error is greatly reduced. 100% is an optional value for the threshold factorα when dealing with no prior knowledge hyperspectral data.
Tortuosity entropy: a measure of spatial complexity of behavioral changes in animal movement.
Liu, Xiaofeng; Xu, Ning; Jiang, Aimin
2015-01-07
The goal of animal movement analysis is to understand how organisms explore and exploit complex and varying environments. Animals usually exhibit varied and complicated movements, from apparently deterministic behaviours to highly random behaviours. It has been a common method to assess movement efficiency and foraging strategies by means of quantifying and analyzing movement trajectories. Here we introduce a tortuosity entropy (TorEn), a simple measure for quantifying the behavioral change in animal movement data. In our approach, the differences between pairwise successive track points are transformed into symbolic sequences, then we map these symbols into a group of pattern vectors and calculate the information entropy of pattern vectors. We test the algorithm on both simulated trajectories and real trajectories to show that it can accurately identify not only the mixed segments in simulated data, but also the different phases in real movement data. Tortuosity entropy can be easily applied to arbitrary real-world data, whether deterministic or stochastic, stationary or non-stationary. It could be a promising tool to reveal behavioral mechanism in movement data.
Spatial-Temporal Yield Trend of Oil Palm as Influenced by Nitrogen Fertilizer Management
Abdul R. Anuar
2008-01-01
Full Text Available One of the major challenges in oil palm (Elaeis guineensis Jacq. plantations today is proper interpretation of yield maps for site-specific management and identification and understanding of the causal factors influencing the variability of oil palm yields. A study was conducted to examine the structural yield variation in order to assess the spatial and temporal yield trends so as to interpret multi-year yield maps of oil palm as influenced by the long-term N fertilizer applications in the palm circle in fertilizer response trial in Sabah, Malaysia. Two clusters of palms were selected for the study; with and without N fertilizer applications for the past 10 years. Fresh fruit bunch (ffb yields were recorded and summarized on an annual basis. Geostatistical analysis was used to characterize the spatial structure of the semivariogram while point kriging was used to interpolate the ffb yields at unsampled locations. A classified management zone map was developed based on the spatial and temporal stability yield maps from 1992-1999. Semivariance analysis revealed that the yield variations between plots and within plots could be distinguished from the structural semivariogram. The variability between plots was relatively higher compared with within plots. The maximum range of the semivariance of both fertilizer treatments was about 6-palm distance which corresponded well to the experimental plot size of 30 (5×6 palms. It was also observed that the structure of the semivariogram was governed by the sampling pattern and the experimental plot size. The annual yield maps suggested that the application of N could sustain ffb yields above 30 t ha-1 year-1 whereas its removal could result in a drastic decline in ffb yields after 1992. Long-term N fertilizer applications reduced the annual ffb yield fluctuations to between 35 and 45% based on the coefficient of variations between years obtained from individual palms. The results further demonstrate the
SPATIAL CORRELATION ANALYSIS OF CROP YIELD IN THE MIDDLE AND WEST OF JILIN PROVINCE
LILin－yi; LIChun－lin; 等
2002-01-01
In this paper,spatial correlation of crop yield in the middle and west of Jilin province is analyzed by us-ing the method of geostatistics swmivarivogram,taking the NDVI of NOAA/AVHRR spectrum data as the regionalized vari-able,aiming to provide theory and practical basis for field sampling of crop yield estimation using remote sensing.The ratio of nugget variance and sill of semivariograms are 21.1% and9.7% in the west and middle regions in Jilin Province respectively.This shows that the crop yields are spatially correlated.The degree and range of correlation are far different in the different situations.In the west test region,the range is 49.9km and the sill is 0.00019 .In the middle test re-gion,the range is 16.5km and the sill is 0.00453.The dissimilarity in the western test region is larger than that in the middle one.The range in which the correlation existed of the former is far larger than the later.Different characteristics of spatial correlation of crop yield are decided by the environmental factors.Samples for crop yield estimation should be extracted according to the characteristic of spatial distribution of crop yield to promote the efficiency of sampling.
SPATIAL CORRELATION ANALYSIS OF CROP YIELD IN THE MIDDLE AND WEST OF JILIN PROVINCE
无
2002-01-01
In this paper, spatial correlation of crop yield in the middle and west of Jilin Province is analyzed by using the method of geostatistics semivariogram, taking the NDVI of NOAA/AVHRR spectrum data as the regionalized variable, aiming to provide theory and practical basis for field sampling of crop yield estimation using remote sensing. The ratio of nugget variance and sill of semivariograms are 21.1% and 9.7% in the west and middle regions in Jilin Province respectively. This shows that the crop yields are spatially correlated. The degree and range of correlation are far different in the different situations. In the west test region, the range is 49.9km and the sill is 0.00019. In the middle test region, the range is 16.5km and the sill is 0.00453. The dissimilarity in the western test region is larger than that in the middle one. The range in which the correlation existed of the former is far larger than the later. Different characteristics of spatial correlation of crop yield are decided by the environmental factors. Samples for crop yield estimation should be extracted according to the characteristic of spatial distribution of crop yield to promote the efficiency of sampling.
The Temporal and Spatial Evolution of Water Yield in Dali County
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.
Impact of Spatial Soil and Climate Input Data Aggregation on Regional Yield Simulations.
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.
Effect of Spatial Arrangement on Growth and Yield of Cowpea in a Cowpea-maize Intercrop
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.
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.
Yield and spatial supply of bioenergy poplar and willow short-rotation coppice in the UK.
Aylott, Matthew J; Casella, E; Tubby, I; Street, N R; Smith, P; Taylor, Gail
2008-01-01
Limited information on likely supply and spatial yield of bioenergy crops exists for the UK. Here, productivities are reported of poplar (Populus spp.) and willow (Salix spp.) grown as short-rotation coppice (SRC), using data from a large 49-site yield trial network. A partial least-squares regression technique was used to upscale actual field trial observations across England and Wales. Spatial productivity was then assessed under different land-use scenarios. Mean modelled yields ranged between 4.9 and 10.7 oven-dry tonnes (odt) ha(-1) yr(-1). Yields were generally higher in willow than in poplar, reflecting the susceptibility of older poplar genotypes to rust and their tendency for single stem dominance. Replacing 10% of arable land, 20% of improved grassland and 100% of set-aside grassland in England and Wales with the three most productive genotypes would yield 13 Modt of biomass annually (supplying 7% of UK electricity production or 48% of UK combined heat and power (CHP) production). Results show existing SRC genotypes have the immediate potential to be an important component of a mixed portfolio of renewables and that, in future, as new and improved genotypes become available, higher yields could extend this potential further.
A spectral-spatial-dynamic hierarchical Bayesian (SSD-HB) model for estimating soybean yield
Kazama, Yoriko; Kujirai, Toshihiro
2014-10-01
A method called a "spectral-spatial-dynamic hierarchical-Bayesian (SSD-HB) model," which can deal with many parameters (such as spectral and weather information all together) by reducing the occurrence of multicollinearity, is proposed. Experiments conducted on soybean yields in Brazil fields with a RapidEye satellite image indicate that the proposed SSD-HB model can predict soybean yield with a higher degree of accuracy than other estimation methods commonly used in remote-sensing applications. In the case of the SSD-HB model, the mean absolute error between estimated yield of the target area and actual yield is 0.28 t/ha, compared to 0.34 t/ha when conventional PLS regression was applied, showing the potential effectiveness of the proposed model.
Bailey, J S; Wang, K; Jordan, C; Higgins, A
2001-01-01
Spatial variability in N uptake and utilisation by swards within uniformly managed field units could be responsible for a significant proportion of the NH3, N2O, NO3- and NOx (NO and NO2) 'pollutants' generated by agriculture and released to the environment. An investigation was commenced, therefore, to quantify, map and explain the spatial variability in sward N yield in a 'large' silage field and to assess the potential for managing this variability using some of the latest precision agriculture technology. Sward dry matter (DM) and N yields were predicted from the results of plant tissue analyses using mathematical models. Sward N yields were found to vary greatly across the field seemingly because of differences in net soil N mineralisation, but the pattern of variability appeared to remain constant with time. Conventional soil analysis of a range of soil chemical and physical properties, however, failed to explain this variability. It was concluded that the N-yield distribution map might be used in place of soil analysis as the basis for varying the rates of N application to different parts of the field with the twin objectives of maximising fertiliser use efficiency and minimising N emissions to air and water.
Simulating maize yield and bomass with spatial variability of soil field capacity
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.
2015-09-29
understanding of high entropy alloys from phase diagram calculations. Calphad 45, 1–10 (2014). 29. Santodonato, L. et al. Deviation from high-entropy...exist, which exhibit them. Inspired by research activities in the metal alloy communities and fundamental principles of thermodynamics we extend the...yields a single- phase material. The second experiment uses five individual phase diagrams to explore the configurational entropy versus composition trend
Spatial Variability of Soil Properties and Rice Yield Along Two Catenas in Southeast China
B. R(U)TH; B. LENNARTZ
2008-01-01
In the light of an increasing demand for staple food, especially rice, in southeast China, investigations on the specific site potential expressed as the relationship between soil and crop yield parameters gain increasing importance. Soil texture and several soil chemical parameters as well as plant properties such as crop height, biomass and grain yield were investigated along two terraced catenas with contrasting soil textures cropped with wet rice. We were aiming at identifying correlative relationships between soil and crop properties. Data were analyzed both statistically and geostatistically on the basis of semivariograms. Statistical analysis indicated a significant influence of the relief position on the spatial distribution of soil texture, total carbon and total nitrogen contents. Significant correlations were found for the catena located in a sandstone area (Catena A) between rice yield and silt as well as total nitrogen content. Corresponding relationships were not detectable for paddy fields that developed from Quaternary clays (Catena B). As suggested by the nugget to sill ratio,spatial variability of soil texture, total carbon and nitrogen was mainly controlled by intrinsic factors, which might be attributed to the erosional transport of fine soil constituents, indicating the importance of the relief position and slope in soil development even in landscapes that are terraced. The crop parameters exhibited short ranges of influence and about one third of their variability was unexplained. Comparable ranges of selected crop and soil parameters, found only for Catena A, are indicative of close spatial interactions between rice yield and soil features. Our findings show that especially in sandstone-dominated areas, a site-specific management can contribute to an environmentally safe rice production increase.
Interannual and spatial variability of maple syrup yield as related to climatic factors
Louis Duchesne
2014-06-01
Full Text Available 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.
A Sivasena Reddy; M Janga Reddy
2015-10-01
Digital elevation model (DEM) of a watershed forms key basis for hydrologic modelling and its resolution plays a key role in accurate prediction of various hydrological processes. This study appraises the effect of different DEMs with varied spatial resolutions (namely TOPO 20 m, CARTO 30 m, ASTER 30 m, SRTM 90 m, GEO-AUS 500 m and USGS 1000 m) on hydrological response of watershed using Soil and Water Assessment Tool (SWAT) and applied for a case study of Kaddam watershed in India for estimating runoff and sediment yield. From the results of case study, it was observed that reach lengths, reach slopes, minimum and maximum elevations, sub-watershed areas, land use mapping areas within the sub-watershed and number of HRUs varied substantially due to DEM resolutions, and consequently resulted in a considerable variability in estimated daily runoff and sediment yields. It was also observed that, daily runoff values have increased (decreased) on low (high) rainy days respectively with coarser resolution of DEM. The daily sediment yield values from each sub-watershed decreased with coarser resolution of the DEM. The study found that the performance of SWAT model prediction was not influenced much for finer resolution DEMs up to 90 m for estimation of runoff, but it certainly influenced the estimation of sediment yields. The DEMs of TOPO 20 m and CARTO 30 m provided better estimates of sub-watershed areas, runoff and sediment yield values over other DEMs.
Black hole entropy quantization
Corichi, A; Fernandez-Borja, E; Corichi, Alejandro; Diaz-Polo, Jacobo; Fernandez-Borja, Enrique
2006-01-01
Ever since the pioneer works of Bekenstein and Hawking, black hole entropy has been known to have a quantum origin. Furthermore, it has long been argued by Bekenstein that entropy should be quantized in discrete (equidistant) steps given its identification with horizon area in (semi-)classical general relativity and the properties of area as an adiabatic invariant. This lead to the suggestion that black hole area should also be quantized in equidistant steps to account for the discrete black hole entropy. Here we shall show that loop quantum gravity, in which area is not quantized in equidistant steps can nevertheless be consistent with Bekenstein's equidistant entropy proposal in a subtle way. For that we perform a detailed analysis of the number of microstates compatible with a given area and show that an observed oscillatory behavior in the entropy-area relation, when properly interpreted yields an entropy that has discrete, equidistant values that are consistent with the Bekenstein framework.
Effect of spatial arrangement on the production components and yield of sunflower
Francisco Thiago Coelho Bezerra
2016-04-01
Full Text Available ABSTRACT The sunflower plant is an oilseed crop that has aroused a great interest in the Brazilian and international scenery especillay because of the possibility of using its oil for biodiesel production. The objective of this study was to evaluate productivity and yield components of Embrapa 122 sunflower according to the spatial arrangement. Treatments were arranged in 4 x 4 factorial arrangement, which are the four spacings between rows (0.30; 0.50; 0.70 and 0.90 m and four sowing densities (30,000; 45,000; 60,000 and 75,000 plants ha-1. The experiment was carried out in a complete randomized block design with four replications. The experiments were conducted in the experimental area of the Plant Science Department in Fortaleza, State of Ceará-Brazil and on the Curu Vale Experimental Farm in Pentecoste, State of Ceará-Brazil. Productivity and the following production components were analyzed in the end of the crop cycle: harvested capitula, capitulum diameter, capitulum mass, achene mass per capitulum, mass of 100 achenes, achenes per capitulum, harvest index and oil content in the achenes. The experiments were analyzed jointly in relation to the cropping area and the data submitted to analysis of variance and quantitative factors tested by polynomial regression. The variables, spacing, density and cropping area did not interact with these variables and the spatial arrangement of the plants affected only the components. The cropping area influences the productive behavior of sunflower Embrapa 122. The spatial arrangement of the plants of sunflower of variety Embrapa 122 influences yield components but does not affect productivity.
ESMAEILZADEH, S; AMINPANAH, H
2015-01-01
ABSTRACTTo evaluate the effect of planting date and spatial pattern on common bean yield under weed-free and weed-infested conditions, an experiment was conducted in Kelachay, Northern Iran, in 2013...
Shi, Z. H.
2014-12-01
There are strong ties between land use and sediment yield in watersheds. Many studies have used multivariate regression techniques to explore the response of sediment yield to land-use compositions and spatial configurations in watersheds. However, one issue with the use of conventional statistical methods to address relationships between land-use compositions and spatial configurations and sediment yield is multicollinearity. This paper examines the combined effects of land-use compositions and land-use spatial configurations of the watershed on the specific sediment yield of the Upper Du River watershed (8,973 km2) in China using the Soil and Water Assessment Tool (SWAT) and partial least-squares regression (PLSR). The land-use compositions and spatial configurations of the watershed were calculated at the sub-watershed scale. The sediment yields from sub-watershed were evaluated using SWAT model. The first-order factors were identified by calculating the variable importance for the projection (VIP). The results revealed that the land-use compositions exerted the largest effects on the specific sediment yield and explained 61.2% of the variation in the specific sediment yield. Land-use spatial configurations were also found to have a large effect on the specific sediment yield and explained 21.7% of the observed variation in the specific sediment yield. The following are the dominant first-order factors of the specific sediment yield at the sub-watershed scale: the areal percentages of agriculture and forest, patch density, value of the Shannon's diversity index, contagion. The VIP values suggested that the Shannon's diversity index and contagion are important factors for sediment delivery.
Solution of the spatial neutral model yields new bounds on the Amazonian species richness
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).
Spatial Patterns of Suspended Sediment Yield in the Upper Indus River Basin, Northern Pakistan
Ali, K.; de Boer, D. H.; Martz, L. W.
2004-05-01
The Indus River is one of the world`s largest rivers in term of water discharge and sediment loads, and the backbone of Pakistan`s economy for agriculture and hydropower. Much of its flow originates in the mountains of the Himalayas, Karakoram and Hindu Kush. The suspended sediment load, which constitutes the main portion of the total load in mountain rivers, creates major water resources management problems such as siltation of reservoirs, damage to turbines, and a reduction in water quality. An understanding of the spatial pattern of suspended sediment yield in the upper Indus River basin is, therefore, essential for effective water resources development in northern Pakistan. Discharge and suspended sediment concentration records are available for 17 active and discontinued hydrological stations (with drainage areas ranging from 600 to 166,000 km2) operated by the Pakistan Water and Power Development Authority. The objective of this study is to delineate the spatial pattern of suspended sediment yield in the basin by analyzing the available hydrological database. Sediment yields have been calculated by constructing sediment rating curves. Physiographic characteristics, hydrologic regimes and climatic patterns of the basin have also been investigated. The results show that the upper Indus River basin can be subdivided into three regions based on suspended sediments yield. This division reflects the contrasting hydrological regimes of the basin. Region 1 comprises the high elevation, glacierized areas of the Karakoram Mountains in the northernmost part of the basin. This region extends downstream to Partab Bridge on the Indus River, and excludes areas around Nanga Parbat, which acts as a barrier to the monsoon. The sediments are mainly derived from the Shyok, Shigar, Hunza and Gilgit sub-basins during the period of increasing summer runoff in June. This runoff is caused by the melt of glaciers and permanent snow pack, and peaks in July and August, when almost the
Bekenstein Entropy is String Entropy
Halyo, Edi
2009-01-01
We argue that Bekenstein entropy can be interpreted as the entropy of an effective string with a rescaled tension. Using the AdS/CFT correspondence we show that the Bekenstein entropy on the boundary CFT is given by the entropy of a string at the stretched horizon of the AdS black hole in the bulk. The gravitationally redshifted tension and energy of the string match those required to reproduce Bekenstein entropy.
Parada, N. D. J. (Principal Investigator); Dutra, L. V.; Mascarenhas, N. D. A.; Mitsuo, Fernando Augusta, II
1984-01-01
A study area near Ribeirao Preto in Sao Paulo state was selected, with predominance in sugar cane. Eight features were extracted from the 4 original bands of LANDSAT image, using low-pass and high-pass filtering to obtain spatial features. There were 5 training sites in order to acquire the necessary parameters. Two groups of four channels were selected from 12 channels using JM-distance and entropy criterions. The number of selected channels was defined by physical restrictions of the image analyzer and computacional costs. The evaluation was performed by extracting the confusion matrix for training and tests areas, with a maximum likelihood classifier, and by defining performance indexes based on those matrixes for each group of channels. Results show that in spatial features and supervised classification, the entropy criterion is better in the sense that allows a more accurate and generalized definition of class signature. On the other hand, JM-distance criterion strongly reduces the misclassification within training areas.
Root proliferation and seed yield in response to spatial heterogeneity of below-ground competition.
O'Brien, Erin E; Gersani, Mordechai; Brown, Joel S
2005-11-01
Here, we tested the predictions of a 'tragedy of the commons' model of below-ground plant competition in annual plants that experience spatial heterogeneity in their competitive environment. Under interplant competition, the model predicts that a plant should over-proliferate roots relative to what would maximize the collective yield of the plants. We predict that a plant will tailor its root proliferation to local patch conditions, restraining root production when alone and over-proliferating in the presence of other plants. A series of experiments were conducted using pairs of pea (Pisum sativum) plants occupying two or three pots in which the presence or absence of interplant root competition was varied while nutrient availability per plant was held constant. In two-pot experiments, competing plants produced more root mass and less pod mass per individual than plants grown in isolation. In three-pot experiments, peas modulated this response to conditions at the scale of individual pots. Root proliferation in the shared pot was higher compared with the exclusively occupied pot. Plants appear to display sophisticated nutrient foraging with outcomes that permit insights into interplant competition.
Liu Yu
2015-03-01
Full Text Available The aim of this study is to provide assistance decision for grain yield in China, which can provide basis for reasonable layout of grain production project. Based on the statistical data of 2301 counties in China, using spatial autocorrelation analysis method, spatial changes of grain yield per unit area at county level in China during 1990-2010 were discussed and then the increase potential of grain yield per hectare and total yield at regional scale were calculated. The results showed that: (1 Grain yield per unit area at county level showed the evident pattern “High in the northern while low in the southern” and “High in the eastern and western while low in the middle”; The average grain yield per hectare increased by 1040.74 kg/hm2 during 1990-2010 and the increment of grain yield per unit area descended from North to South at county level. (2 Grain yield per unit area at county level in China had a strong spatial autocorrelation. The counties with "High-High" and "Low-Low" correlation were the majority. Counties with significant "High-High" correlation in 2010 were mostly located in plain area, while counties with significant "Low-Low" correlation were mainly distributed in Hengduan Mountainous Area, Inner Mongolia steppe Area, etc. (3 Two thousand three hundred and one counties were divided into 41 first-grade regions and 115 sec-grade regions according to the coupled conditions of cultivation system regionalization and LISA cluster map. The total potential output of China was 1.77×108 tons.
Simple, spatial and predictive approach for cereal yield prediction in the semi-arid areas
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.
Entropy of local smeared field observables
Satz, Alejandro
2017-01-01
We re-conceptualize the usual entanglement entropy of quantum fields in a spatial region as a limiting case of a more general and well-defined quantity, the entropy of a subalgebra of smeared field observables. We introduce this notion, discuss various examples, and recover from it the area law for the entanglement entropy of a sphere in Minkowski space.
Configuration entropy of fractal landscapes
Rodríguez‐Iturbe, Ignacio; D'Odorico, Paolo; Rinaldo, Andrea
1998-01-01
.... The spatial arrangement of two‐dimensional images is found to be an effective way to characterize fractal landscapes and the configurational entropy of these arrangements imposes demanding conditions for models attempting to represent these fields.
JIANG Xiao-jian; TANG Liang; LIU Xiao-jun; CAO Wei-xing; ZHU Yan
2013-01-01
The vast area and marked variation of China make it difficult to predict the impact of climate changes on rice productivity in different regions. Therefore, analyzing the spatial and temporal characteristics of rice potential productivity and predicting the possible yield increment in main rice production regions of China is important for guiding rice production and ensuring food security. Using meteorological data of main rice production regions from 1961 to 1970 (the 1960s) and from 1996 to 2005 (the 2000s) provided by 333 stations, the potential photosynthetic, photo-thermal and climatic productivities in rice crop of the 1960s and 2000s in main rice production regions of China were predicted, and differences in the spatial and temporal distribution characteristics between two decades were analyzed. Additionally, the potential yield increment based on the high yield target and actual yield of rice in the 2000s were predicted. Compared with the 1960s, the potential photosynthetic productivity of the 2000s was seen to have decreased by 5.40%, with rates in northeastern and southwestern China found to be lower than those in central and southern China. The potential photo-thermal productivity was generally seen to decrease (2.56%) throughout main rice production regions, decreasing most in central and southern China. However, an increase was seen in northeastern and southwestern China. The potential climatic productivity was observed to be lower (7.44%) in the 2000s compared to the 1960s, but increased in parts of central and southern China. The potential yield increment from the actual yield to high yield target in the 2000s were no more than 6×103 kg ha-1 and ranged from 6×103 to 12×103 kg ha-1 in most of the single-and double-cropping rice growing regions, respectively. The yield increasing potential from the high yield target to the potential photo-thermal productivity in 2000s were less than 10×103 kg ha-1 and ranged from 10×103 to 30×103 kg ha-1 in most
Xuelin Zhang
Full Text Available Improved management of soil carbon (C and nitrogen (N storage in agro-ecosystems represents an important strategy for ensuring food security and sustainable agricultural development in China. Accurate estimates of the distribution of soil C and N stores and their relationship to crop yield are crucial to developing appropriate cropland management policies. The current study examined the spatial variation of soil organic C (SOC, total soil N (TSN, and associated variables in the surface layer (0-40 cm of soils from intensive agricultural systems in 19 counties within Henan Province, China, and compared these patterns with crop yield. Mean soil C and N concentrations were 14.9 g kg(-1 and 1.37 g kg(-1, respectively, whereas soil C and N stores were 4.1 kg m(-2 and 0.4 kg m(-2, respectively. Total crop production of each county was significantly, positively related to SOC, TSN, soil C and N store, and soil C and N stock. Soil C and N were positively correlated with soil bulk density but negatively correlated with soil porosity. These results indicate that variations in soil C could regulate crop yield in intensive agricultural systems, and that spatial patterns of C and N levels in soils may be regulated by both climatic factors and agro-ecosystem management. When developing suitable management programs, the importance of soil C and N stores and their effects on crop yield should be considered.
Scott L Hamilton
Full Text Available Fish populations vary geographically in demography and life history due to environmental and ecological processes and in response to exploitation. However, population dynamic models and stock assessments, used to manage fisheries, rarely explicitly incorporate spatial variation to inform management decisions. Here, we describe extensive geographic variation in several demographic and life history characteristics (e.g., size structure, growth, survivorship, maturation, and sex change of California sheephead (Semicossyphus pulcher, a temperate rocky reef fish targeted by recreational and commercial fisheries. Fish were sampled from nine locations throughout southern California in 2007-2008. We developed a dynamic size and age-structured model, parameterized separately for each location, to assess the potential cost or benefit in terms of fisheries yield and conservation objectives of changing minimum size limits and/or fishing mortality rates (compared to the status quo. Results indicate that managing populations individually, with location-specific regulations, could increase yield by over 26% while maintaining conservative levels of spawning biomass. While this local management approach would be challenging to implement in practice, we found statistically similar increases in yield could be achieved by dividing southern California into two separate management regions, reflecting geographic similarities in demography. To maximize yield, size limits should be increased by 90 mm in the northern region and held at current levels in the south. We also found that managing the fishery as one single stock (the status quo, but with a size limit 50 mm greater than the current regulations, could increase overall fishery yield by 15%. Increases in size limits are predicted to enhance fishery yield and may also have important ecological consequences for the predatory role of sheephead in kelp forests. This framework for incorporating demographic variation
A GIS/Simulation Framework for Assessing Change in Water Yield over Large Spatial Scales
Graham, R.; Hargrove, W.W.; Huff, D.D.; Nikolov, N.; Tharp, M.L.
1999-11-13
Recent legislation to,initiate vegetation management in the Central Sierra hydrologic region of California includes a focus on corresponding changes in water yield. This served as the impetus for developing a combined geographic information system (GIS) and simulation assessment framework. Using the existing vegetation density condition, together with proposed rules for thinning to reduce fire risk, a set of simulation model inputs were generated for examining the impact of the thinning scenario on water yield. The approach allows results to be expressed as the mean and standard deviation of change in water yield for each 1 km2 map cell that is treated. Values for groups of cells are aggregated for typical watershed units using area-weighted averaging. Wet, dry and average precipitation years were simulated over a large region. Where snow plays an important role in hydrologic processes, the simulated change in water yield was less than 0.5% of expected annual runoff for a typical water shed. Such small changes would be undetectable in the field using conventional stream flow analysis. These results suggest that use of water yield increases to help justify forest-thinning activities or offset their cost will be difficult.
Chen, Chao; Baethgen, Walter E.; Wang, Enli; Yu, Qiang
2011-12-01
Grain yields of wheat and maize were obtained from national statistics and simulated with an agricultural system model to investigate the effects of historical climate variability and irrigation on crop yield in the North China Plain (NCP). Both observed and simulated yields showed large temporal and spatial variability due to variations in climate and irrigation supply. Wheat yield under full irrigation (FI) was 8 t ha-1 or higher in 80% of seasons in the north, it ranged from 7 to 10 t ha-1 in 90% of seasons in central NCP, and less than 9 t ha-1 in 85% of seasons in the south. Reduced irrigation resulted in increased crop yield variability. Wheat yield under supplemental irrigation, i.e., to meet only 50% of irrigation water requirement [supplemental irrigation (SI)] ranged from 2.7 to 8.8 t ha-1 with the maximum frequency of seasons having the range of 4-6 t ha-1 in the north, 4-7 t ha-1 in central NCP, and 5-8 t ha-1 in the south. Wheat yield under no irrigation (NI) was lower than 1 t ha-1 in about 50% of seasons. Considering the NCP as a whole, simulated maize yield under FI ranged from 3.9 to 11.8 t ha-1 with similar frequency distribution in the range of 6-11.8 t ha-1 with the interval of 2 t ha-1. It ranged from 0 to 11.8 t ha-1, uniformly distributed into the range of 4-10 t ha-1 under SI, and NI. The results give an insight into the levels of regional crop production affected by climate and water management strategies.
Grogan, D. S.; Zhang, F.; Li, C.; Frolking, S.
2011-12-01
Irrigated agriculture is an important part of China's population and economic growth. Currently, water needed to irrigate crops can be drawn from surface runoff, streams, reservoirs, renewable groundwater, or fossil groundwater. Fossil groundwater is not sustainable over long time periods, and therefore regions that rely on this source for irrigation water could face water shortages in the future, and may already be experiencing water stress today. This study uses two models, one to calculate water balance and the other to simulate crop yields, to address the question: how much unsustainable water is currently used for irrigation in China, and by how much would the use of only sustainable water reduce crop yields? The amount of sustainable water available for irrigation is determined using the WBMplus model. This model uses precipitation and temperature drivers, along with gridded data of soils, cropping, and irrigation, to simulate soil moisture, potential evapotranspiration, surface runoff, stream flow, and reservoir storage, in 30 min grid cells. The model also computes demand for irrigation water, and the capacity of various sources to supply that demand in each grid cell. The DNDC model, which has been evaluated against crop yield in a number of studies in China, is used to predict crop yield for ~50 crop types involved in ~100 cropping systems across China, under zero and full irrigation for each grid cell. Yields using only the sustainable irrigation water capacity will be calculated by weighing the zero and full irrigation yields based on the water availability results of WBMplus for each grid cell. With this methodology, we estimate how national-scale food production would be changed by limiting agricultural water use.
Spatiotemporal Scaling Effect on Rainfall Network Design Using Entropy
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.
Entropy of universe as entanglement entropy
Bak, Dongsu
2012-01-01
We note that the observable part of universe at a certain time t_P is necessarily limited, when there is a beginning of universe. We argue that an appropriate spacetime region associated with an observer from t_I to t_P is the causal diamond which is the overlap of the past/future of the observer at t_P/t_I respectively. We also note that the overlap surface \\partial D of the future and the past lightcones bisects the spatial section including \\partial D into two regions D and \\bar D where D is the region inside the causal diamond and \\bar D the remaining part of the spatial section. We propose here that the entropy of universe associated with a causal diamond is given by an entanglement entropy where one is tracing over the Hilbert space associated with the region \\bar D which is not accessible by the observer. We test our proposal for various examples of cosmological spacetimes, including flat, open or closed FRW universes, by showing that the entropy as the area of \\partial D divided by 4G is a non-decreas...
Eshonkulov, Ravshan; Poyda, Arne; Ingwersen, Joachim; Streck, Thilo
2017-04-01
Assessing the spatial variability of soil physical properties is crucial for agricultural land management. We determined the spatial variability within two agricultural fields in the regions of Kraichgau and Swabian Jura in Southwest Germany. We determined soil physical properties and recorded the temporal development of soil mineral nitrogen (N) and water content as well as that of plant variables (phenology, biomass, leaf area index (LAI), N content, green vegetation fraction (GVF). The work was conducted during the vegetation periods of 2015 and 2016 in winter wheat, and winter rapeseed in Kraichgau and winter barley and silage maize on Swabian Jura. Measurements were taken in three-weekly intervals. On each field, we identified three plots with reduced plant development using high-resolution (RapidEye) satellite images ("cold spots"). Measurements taken on these cold spots were compared to those from five established (long-term) reference plots representing the average field variability. The software EXPERT-N was used to simulate the soil crop system at both cold spots and reference plots. Sensitivity analyses were conducted to identify the most important parameters for the determination of spatial variability in crop growth dynamics.
Stabilization of ground movement with yield rock bolts using spatial effect
Naprasnikov, S.V.; Alexandrov, S.N.; Sazhnev, V.P.; Nazimko, V.V. [Donetsk State Technical University, Donetsk (Ukraine)
1999-07-01
New rock bolting technology has been developed for stabilization of roofs and floor closures in underground openings. Yield rock bolts should be inclined 5-40{degree} to the relative direction of expected roof deflection and oriented in the plane under an angle of 5-90{degree} relative to the orthogonal cross-section of the roadway. Such an orientation increases the pullout force by 2% and enhances stability of a roadway. 3 refs., 2 figs., 1 tab.
Astuti, Valerio; Rovelli, Carlo
2016-01-01
Building on a technical result by Brunnemann and Rideout on the spectrum of the Volume operator in Loop Quantum Gravity, we show that the dimension of the space of the quadrivalent states --with finite-volume individual nodes-- describing a region with total volume smaller than $V$, has \\emph{finite} dimension, bounded by $V \\log V$. This allows us to introduce the notion of "volume entropy": the von Neumann entropy associated to the measurement of volume.
Entropy, Its Language, and Interpretation
Leff, Harvey S.
2007-12-01
The language of entropy is examined for consistency with its mathematics and physics, and for its efficacy as a guide to what entropy means. Do common descriptors such as disorder, missing information, and multiplicity help or hinder understanding? Can the language of entropy be helpful in cases where entropy is not well defined? We argue in favor of the descriptor spreading, which entails space, time, and energy in a fundamental way. This includes spreading of energy spatially during processes and temporal spreading over accessible microstates states in thermodynamic equilibrium. Various examples illustrate the value of the spreading metaphor. To provide further support for this metaphor’s utility, it is shown how a set of reasonable spreading properties can be used to derive the entropy function. A main conclusion is that it is appropriate to view entropy’s symbol S as shorthand for spreading.
Wang, Xinbing; Zhou, Baoyuan; Sun, Xuefang; Yue, Yang; Ma, Wei; Zhao, Ming
2015-01-01
The spatial distribution of the root system through the soil profile has an impact on moisture and nutrient uptake by plants, affecting growth and productivity. The spatial distribution of the roots, soil moisture, and fertility are affected by tillage practices. The combination of high soil density and the presence of a soil plow pan typically impede the growth of maize (Zea mays L.).We investigated the spatial distribution coordination of the root system, soil moisture, and N status in response to different soil tillage treatments (NT: no-tillage, RT: rotary-tillage, SS: subsoiling) and the subsequent impact on maize yield, and identify yield-increasing mechanisms and optimal soil tillage management practices. Field experiments were conducted on the Huang-Huai-Hai plain in China during 2011 and 2012. The SS and RT treatments significantly reduced soil bulk density in the top 0-20 cm layer of the soil profile, while SS significantly decreased soil bulk density in the 20-30 cm layer. Soil moisture in the 20-50 cm profile layer was significantly higher for the SS treatment compared to the RT and NT treatment. In the 0-20 cm topsoil layer, the NT treatment had higher soil moisture than the SS and RT treatments. Root length density of the SS treatment was significantly greater than density of the RT and NT treatments, as soil depth increased. Soil moisture was reduced in the soil profile where root concentration was high. SS had greater soil moisture depletion and a more concentration root system than RT and NT in deep soil. Our results suggest that the SS treatment improved the spatial distribution of root density, soil moisture and N states, thereby promoting the absorption of soil moisture and reducing N leaching via the root system in the 20-50 cm layer of the profile. Within the context of the SS treatment, a root architecture densely distributed deep into the soil profile, played a pivotal role in plants' ability to access nutrients and water. An optimal
K B Athreya
2009-09-01
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 $\\int fh_id_=_i$ for $i=1,2,\\ldots,\\ldots k$ the maximizer of entropy is an $f_0$ that is proportional to $\\exp(\\sum c_i h_i)$ for some choice of $c_i$. An extension of this to a continuum of constraints and many examples are presented.
Structural information in two-dimensional patterns: entropy convergence and excess entropy.
Feldman, David P; Crutchfield, James P
2003-05-01
We develop information-theoretic measures of spatial structure and pattern in more than one dimension. As is well known, the entropy density of a two-dimensional configuration can be efficiently and accurately estimated via a converging sequence of conditional entropies. We show that the manner in which these conditional entropies converge to their asymptotic value serves as a measure of global correlation and structure for spatial systems in any dimension. We compare and contrast entropy convergence with mutual-information and structure-factor techniques for quantifying and detecting spatial structure.
Waliszewski, Przemyslaw
2016-01-01
...) and the local connected fractal dimension (LCFD), Shannon entropy H and lacunarity λ were measured using computer algorithms in digitalized images of both the reference set (n = 60) and the test set (n = 208...
Regulski, Wojciech; Szumbarski, Jacek
2016-01-01
In this paper, the performance of two lattice Boltzmann method formulations for yield-stress (i.e. viscoplastic) fluids has been investigated. The first approach is based on the popular Papanastasiou regularisation of the fluid rheology in conjunction with explicit modification of the lattice Boltzmann relaxation rate. The second approach uses a locally-implicit formulation to simultaneously solve for the fluid stress and the underlying particle distribution functions. After investigating issues related to the lattice symmetry and non-hydrodynamic Burnett stresses, the two models were compared in terms of spatial convergence and their behaviour in transient and inertial flows. The choice of lattice and the presence of Burnett stresses was found to influence the results of both models, however the latter did not significantly degrade the velocity field. Using Bingham flows in ducts and synthetic porous media, it was found that the implicitly-regularised model was superior in capturing transient and inertial fl...
Przemyslaw eWaliszewski
2016-02-01
Full Text Available Background: Tumor grading, PSA concentration, and stage determine a risk of prostate cancer patients with accuracy of about 70%. An approach based on the fractal geometrical model was proposed to eliminate subjectivity from the evaluation of tumor aggressiveness and to improve the prediction. This study was undertaken to validate classes of equivalence for the spatial distribution of cancer cell nuclei in a larger, independent set of prostate carcinomas.Methods: The global fractal capacity D0, information D1 and correlation D2 dimension, the local fractal dimension (LFD and the local connected fractal dimension (LCFD, Shannon entropy H and lacunarity were measured using computer algorithms in digitalized images of both the reference set (n = 60 and the test set (n = 208 of prostate carcinomas.Results: Prostate carcinomas were re-stratified into seven classes of equivalence. The cut-off D0 values 1.5450, 1.5820, 1.6270, 1.6490, 1.6980, 1.7640 defined the classes from C1 to C7, respectively. The other measures but the D1 failed to define the same classes of equivalence. The pairs (D0, LFD, (D0, H, (D0, , (D1, LFD, (D1, H, (D1, characterized the spatial distribution of cancer cell nuclei in each class. The co-application of those measures enabled the subordination of prostate carcinomas to one out of three clusters associated with different tumor aggressiveness. For D0 0.8, the class C1 or C2 contains low complexity low aggressive carcinomas exclusively. For D0 > 1.6980, LFD > 1.7644, LCFD > 1.7051, H > 0.9, and < 0.7, the class C6 or C7 contains high complexity high aggressive carcinomas. Conclusions: The cut-off D0 values defining the classes of equivalence were validated in this study. The cluster analysis suggested that the number of the subjective Gleason grades and the number of the objective classes of equivalence could be decreased from seven to three without a loss of clinically relevant information. Two novel quantitative
Waliszewski, Przemyslaw
2016-01-01
Tumor grading, PSA concentration, and stage determine a risk of prostate cancer patients with accuracy of about 70%. An approach based on the fractal geometrical model was proposed to eliminate subjectivity from the evaluation of tumor aggressiveness and to improve the prediction. This study was undertaken to validate classes of equivalence for the spatial distribution of cancer cell nuclei in a larger, independent set of prostate carcinomas. The global fractal capacity D 0, information D 1 and correlation D 2 dimension, the local fractal dimension (LFD) and the local connected fractal dimension (LCFD), Shannon entropy H and lacunarity λ were measured using computer algorithms in digitalized images of both the reference set (n = 60) and the test set (n = 208) of prostate carcinomas. Prostate carcinomas were re-stratified into seven classes of equivalence. The cut-off D 0-values 1.5450, 1.5820, 1.6270, 1.6490, 1.6980, 1.7640 defined the classes from C1 to C7, respectively. The other measures but the D 1 failed to define the same classes of equivalence. The pairs (D 0, LFD), (D 0, H), (D 0, λ), (D 1, LFD), (D 1, H), (D 1, λ) characterized the spatial distribution of cancer cell nuclei in each class. The co-application of those measures enabled the subordination of prostate carcinomas to one out of three clusters associated with different tumor aggressiveness. For D 0 1.5, H 0.8, the class C1 or C2 contains low complexity low aggressive carcinomas exclusively. For D 0 > 1.6980, LFD > 1.7644, LCFD > 1.7051, H > 0.9, and λ < 0.7, the class C6 or C7 contains high complexity high aggressive carcinomas. The cut-off D 0-values defining the classes of equivalence were validated in this study. The cluster analysis suggested that the number of the subjective Gleason grades and the number of the objective classes of equivalence could be decreased from seven to three without a loss of clinically relevant information. Two novel quantitative criteria based on the complexity
Universal entropy relations: entropy formulae and entropy bound
Liu, Hang; Xu, Wei; Zhu, Bin
2016-01-01
We survey the applications of universal entropy relations in black holes with multi-horizons. In sharp distinction to conventional entropy product, the entropy relationship here not only improve our understanding of black hole entropy but was introduced as an elegant technique trick for handling various entropy bounds and sum. Despite the primarily technique role, entropy relations have provided considerable insight into several different types of gravity, including massive gravity, Einstein-Dilaton gravity and Horava-Lifshitz gravity. We present and discuss the results for each one.
Wilson, Marcelo; Sasal, María Carolina; Oszust, José; Gabioud, Emmanuel; Melchiori, Ricardo
2013-04-01
The soil penetration resistance (PR) is used to identify and characterize soil layers densified by effects of tilling, and the results obtained are related to root growth and crop productivity. The aims of this work were: (i) to analyze the spatial variation in PR through resistance isolines in an Aquic Argiudoll with different long-term cropping sequences under no tillage (NT), (ii) to compare the information generated from the lines with the same PR values with the analysis of the cultural profile and (iii) to study the spatial variability in the PR and the bulk density (BD) in a 10-ha plot, and their relationship with soybean crop yield. An experiment was carried out in an Aquic Argiudoll in 100-m2 plots (4 m wide x 25 m long), with different long-term cropping sequences, under NT for 15 years. The treatments tested were: soybean and maize monocultures, wheat/soybean, wheat/soybean-maize and a permanent pasture as a reference. A digital penetrologger Eijkelkamp ® was used to take 20 measurements of the PR in each plot, through the design of a grid 5 m long and 0.66 m wide, centimeter-wise until 20 cm, totaling n= 400. In addition, an observation well (1 m wide by 30 cm deep) was analyzed by means of the technique of the cultural profiles. Besides, two sampling grids in a 10-ha plot with maize-wheat/soybean sequence were used to measure PR every 30 m and BD every 60 m. The variability in the soil properties was assessed using descriptive statistical analysis, determining normality and spatial variability with the adjustment to the theoretical semivariograms. At 10-15 and 15-20 cm, wheat/soybean-maize and wheat/soybean showed the highest PR values, differentiating from the soybeans and maize monocultures and pasture. The lines with the same PR values allowed observing structural changes in the soil profile, such as surface granular structures and subsequent layers of laminar structure, sometimes discontinuous, from 1.0 to 1.5 MPa between 5 and 8 cm in depth, and
Kruglikov, Boris; Rypdal, Martin
2005-01-01
The topological entropy of piecewise affine maps is studied. It is shown that singularities may contribute to the entropy only if there is angular expansion and we bound the entropy via the expansion rates of the map. As a corollary we deduce that non-expanding conformal piecewise affine maps have zero topological entropy. We estimate the entropy of piecewise affine skew-products. Examples of abnormal entropy growth are provided.
Lynch J.P.
2017-09-01
Full Text Available Although Irish winter wheat yields are among the highest globally, increases in the profitability of this crop are required to maintain its economic viability. However, in order to determine if efforts to further increase Irish wheat yields are likely to be successful, an accurate estimation of the yield potential is required for different regions within Ireland. A winter wheat yield potential model (WWYPM was developed, which estimates the maximum water-limited yield achievable, within the confines of current genetic resources and technologies, using parameters for winter wheat growth and development observed recently in Ireland and a minor amount of daily meteorological input (maximum and minimum daily temperature, total daily rainfall and total daily incident radiation. The WWYPM is composed of three processes: (i an estimation of potential green area index, (ii an estimation of light interception and biomass accumulation and (iii an estimation of biomass partitioning to grain yield. Model validation indicated that WWYPM estimations of water-limited yield potential (YPw were significantly related to maximum yields recorded in variety evaluation trials as well as regional average and maximum farm yields, reflecting the model’s sensitivity to alterations in the climatic environment with spatial and seasonal variations. Simulations of YPw for long-term average weather data at 12 sites located at spatially contrasting regions of Ireland indicated that the typical YPw varied between 15.6 and 17.9 t/ha, with a mean of 16.7 t/ha at 15% moisture content. These results indicate that the majority of sites in Ireland have the potential to grow high-yielding crops of winter wheat when the effects of very high rainfall and other stresses such as disease incidence and nutrient deficits are not considered.
The minimum entropy principle and task performance.
Guastello, Stephen J; Gorin, Hillary; Huschen, Samuel; Peters, Natalie E; Fabisch, Megan; Poston, Kirsten; Weinberger, Kelsey
2013-07-01
According to the minimum entropy principle, efficient cognitive performance is produced with a neurocognitive strategy that involves a minimum of degrees of freedom. Although high performance is often regarded as consistent performance as well, some variability in performance still remains which allows the person to adapt to changing goal conditions or fatigue. The present study investigated the connection between performance, entropy in performance, and four task-switching strategies. Fifty-one undergraduates performed 7 different computer-based cognitive tasks producing sets of 49 responses under instructional conditions requiring task quotas or no quotas. The temporal patterns of performance were analyzed using orbital decomposition to extract pattern types and lengths, which were then compared with regard to Shannon entropy, topological entropy, and overall performance. Task switching strategies from a previous study were available for the same participants as well. Results indicated that both topological entropy and Shannon entropy were negatively correlated with performance. Some task-switching strategies produced lower entropy in performance than others. Stepwise regression showed that the top three predictors of performance were Shannon entropy and arithmetic and spatial abilities. Additional implications for the prediction of work performance with cognitive ability measurements and the applicability of the minimum entropy principle to multidimensional performance criteria and team work are discussed.
Relative entropy and torsion coupling
Ning, Bo; Lin, Feng-Li
2016-12-01
We evaluate the relative entropy on a ball region near the UV fixed point of a holographic conformal field theory deformed by a fermionic operator of nonzero vacuum expectation value. The positivity of the relative entropy considered here is implied by the expected monotonicity of the decrease of quantum entanglement under the renormalization group flow. The calculations are done in the perturbative framework of Einstein-Cartan gravity in four-dimensional asymptotic anti-de Sitter space with a postulated standard bilinear coupling between the axial fermion current and torsion. By requiring positivity of relative entropy, our result yields a constraint on axial current-torsion coupling, fermion mass, and equation of state.
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.
Maximum Entropy in Drug Discovery
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.
Bekenstein-Hawking Entropy as Entanglement Entropy
Feng, Yu-Lei
2015-01-01
We show that the Bekenstein-Hawking entropy $S_{BH}$ should be treated as an entanglement entropy, provided that the formation and evaporation of a black hole can be described by quantum unitary evolutions. To confirm this statement, we derive statistical mechanics from quantum mechanics effectively by means of open quantum systems. Then a new definition of Boltzmann entropy for a quantum closed system is given to count microstates in a way consistent with the superposition principle. In particular, this new Boltzmann entropy is a constant that depends only on the dimension of the system's relevant Hilbert subspace. Based on this new definition, some kind of "detailed balance" condition is obtained to stabilize the thermal equilibrium between two macroscopic subsystems within a larger closed system. However, the required "detailed balance" condition between black hole and matter would be broken, if the Bekenstein-Hawking entropy was treated as Boltzmann entropy together with the Hawking temperature as thermal...
Singh, Priti; Chakraborty, Abhishek; Manoj, B. S.
2017-01-01
In this paper we propose a new metric, Link Influence Entropy (LInE), which describes importance of each node based on the influence of each link present in a network. Influence of a link can neither be effectively estimated using betweenness centrality nor using degree based probability measures. The proposed LInE metric which provides an effective way to estimate the influence of a link in the network and incorporates this influence to identify nodal characteristics, performs better compared to degree based entropy. We found that LInE can differentiate various network types which degree-based or betweenness centrality based node influence metrics cannot. Our findings show that spatial wireless networks and regular grid networks, respectively, have lowest and highest LInE values. Finally, performance analysis of LInE is carried out on a real-world network as well as on a wireless mesh network testbed to study the influence of our metric as well as influence stability of nodes in dynamic networks.
Coherent states measurement entropy
Kwapien, J; Zyczkowski, K; Kwapien, Jaroslaw; Slomczynski, Wojciech; Zyczkowski, Karol
1996-01-01
Coherent states (CS) quantum entropy can be split into two components. The dynamical entropy is linked with the dynamical properties of a quantum system. The measurement entropy, which tends to zero in the semiclassical limit, describes the unpredictability induced by the process of a quantum approximate measurement. We study the CS--measurement entropy for spin coherent states defined on the sphere discussing different methods dealing with the time limit n \\to \\infty. In particular we propose an effective technique of computing the entropy by iterated function systems. The dependence of CS--measurement entropy on the character of the partition of the phase space is analysed.
Lee, Jeongseog; Safdi, Benjamin R
2014-01-01
Entanglement entropy in even dimensional conformal field theories (CFTs) contains well-known universal terms arising from the conformal anomaly. Renyi entropies are natural generalizations of the entanglement entropy that are much less understood. Above two spacetime dimensions, the universal terms in the Renyi entropies are unknown for general entangling geometries. We conjecture a new structure in the dependence of the four-dimensional Renyi entropies on the intrinsic and extrinsic geometry of the entangling surface. We provide evidence for this conjecture by direct numerical computations in the free scalar and fermion field theories. The computation involves relating the four-dimensional free massless Renyi entropies across cylindrical entangling surfaces to corresponding three-dimensional massive Renyi entropies across circular entangling surfaces. Our numerical technique also allows us to directly probe other interesting aspects of three-dimensional Renyi entropy, including the massless renormalized Reny...
Gagie, Travis
2007-01-01
We trace the history of empirical entropy, touching briefly on its relation to Markov processes, normal numbers, Shannon entropy, the Chomsky hierarchy, Kolmogorov complexity, Ziv-Lempel compression, de Bruijn sequences and stochastic complexity.
2016-01-01
We propose an entropy function for simplicial complices. Its value gives the expected cost of the optimal encoding of sequences of vertices of the complex, when any two vertices belonging to the same simplex are indistinguishable. We show that the proposed entropy function can be computed efficiently. By computing the entropy of several complices consisting of hundreds of simplices, we show that the proposed entropy function can be used in the analysis of the large sequences of simplicial com...
Entropy of Baker's Transformation
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.
Physical entropy, information entropy and their evolution equations
无
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.
Balian, Roger
We review at a tutorial level the many aspects of the concept of entropy and their interrelations, in thermodynamics, information theory, probability theory and statistical physics. The consideration of relevant entropies and the identification of entropy with missing information enlighten the paradoxes of irreversibility and of Maxwell's demon.
Chirikjian, Gregory S
2011-01-01
Proteins fold from a highly disordered state into a highly ordered one. Traditionally, the folding problem has been stated as one of predicting "the" tertiary structure from sequential information. However, new evidence suggests that the ensemble of unfolded forms may not be as disordered as once believed, and that the native form of many proteins may not be described by a single conformation, but rather an ensemble of its own. Quantifying the relative disorder in the folded and unfolded ensembles as an entropy difference may therefore shed light on the folding process. One issue that clouds discussions of "entropy" is that many different kinds of entropy can be defined: entropy associated with overall translational and rotational Brownian motion, configurational entropy, vibrational entropy, conformational entropy computed in internal or Cartesian coordinates (which can even be different from each other), conformational entropy computed on a lattice, each of the above with different solvation and solvent models, thermodynamic entropy measured experimentally, etc. The focus of this work is the conformational entropy of coil/loop regions in proteins. New mathematical modeling tools for the approximation of changes in conformational entropy during transition from unfolded to folded ensembles are introduced. In particular, models for computing lower and upper bounds on entropy for polymer models of polypeptide coils both with and without end constraints are presented. The methods reviewed here include kinematics (the mathematics of rigid-body motions), classical statistical mechanics, and information theory.
Entropy Is Simple, Qualitatively.
Lambert, Frank L.
2002-01-01
Suggests that qualitatively, entropy is simple. Entropy increase from a macro viewpoint is a measure of the dispersal of energy from localized to spread out at a temperature T. Fundamentally based on statistical and quantum mechanics, this approach is superior to the non-fundamental "disorder" as a descriptor of entropy change. (MM)
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.)
Entropy power inequalities for qudits
Audenaert, Koenraad; Datta, Nilanjana; Ozols, Maris
2016-05-01
Shannon's entropy power inequality (EPI) can be viewed as a statement of concavity of an entropic function of a continuous random variable under a scaled addition rule: f ( √{ a } X + √{ 1 - a } Y ) ≥ a f ( X ) + ( 1 - a ) f ( Y ) ∀ a ∈ [ 0 , 1 ] . Here, X and Y are continuous random variables and the function f is either the differential entropy or the entropy power. König and Smith [IEEE Trans. Inf. Theory 60(3), 1536-1548 (2014)] and De Palma, Mari, and Giovannetti [Nat. Photonics 8(12), 958-964 (2014)] obtained quantum analogues of these inequalities for continuous-variable quantum systems, where X and Y are replaced by bosonic fields and the addition rule is the action of a beam splitter with transmissivity a on those fields. In this paper, we similarly establish a class of EPI analogues for d-level quantum systems (i.e., qudits). The underlying addition rule for which these inequalities hold is given by a quantum channel that depends on the parameter a ∈ [0, 1] and acts like a finite-dimensional analogue of a beam splitter with transmissivity a, converting a two-qudit product state into a single qudit state. We refer to this channel as a partial swap channel because of the particular way its output interpolates between the states of the two qudits in the input as a is changed from zero to one. We obtain analogues of Shannon's EPI, not only for the von Neumann entropy and the entropy power for the output of such channels, but also for a much larger class of functions. This class includes the Rényi entropies and the subentropy. We also prove a qudit analogue of the entropy photon number inequality (EPnI). Finally, for the subclass of partial swap channels for which one of the qudit states in the input is fixed, our EPIs and EPnI yield lower bounds on the minimum output entropy and upper bounds on the Holevo capacity.
Entropy of uremia and dialysis technology.
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.
Mainardi, J. T.; Jung, L. H.; Correa, A. R.; Pellin, D. M. P.; Souza, B. R. F.; Roque, C. G.; Teixeira, R. B.; Minotto, V.; Montanari, R.
2012-04-01
In Brazil, the common bean (Phaseolus vulgaris L.) is in one of the most representative farms, not only by the area under cultivation as well as the value of production. Thus, in the agricultural year 2010/2011, the Foundation of the Federal University of Mato Grosso do Sul (UFMS) Campus de Chapadão do Sul, we studied the variability and spatial dependence between physical properties of the soil and grain yield common bean under conventional tillage in Oxisol of Chapadão do Sul, Northeast region of Mato Grosso do Sul, Brazil. We also studied the linear and spatial correlations between these attributes, investigating conditions that provide increased agricultural productivity. For this, the area with the cultivation of common bean under conventional tillage installed a mesh containing 121 sampling points, with spacing of 5.0 x 5.0 m between them, a total area of 1600 m2. The grain yield common bean, with high variability, was found to average national standards. However, variability in soil physical attributes was higher, indicating that conventional tillage is a system that generates the heterogeneity of the environment, and the total porosity at a depth of 0.00 to 0.10 m is the attribute that might explain the average variability of grain yield. Index terms: soil management, conventional tillage, soil physical attributes.
Brissaud, Jean-Bernard
2005-03-01
Entropy is a basic physical quantity that led to various, and sometimes apparently conflicting interpretations. It has been successively assimilated to different concepts such as disorder and information. In this paper we're going to revisit these conceptions, and establish the three following results: Entropy measures lack of information; it also measures information. These two conceptions are complementary. Entropy measures freedom, and this allows a coherent interpretation of entropy formulas and of experimental facts. To associate entropy and disorder implies defining order as absence of freedom. Disorder or agitation is shown to be more appropriately linked with temperature.
Jean-Bernard Brissaud
2005-02-01
Full Text Available Abstract: Entropy is a basic physical quantity that led to various, and sometimes apparently conflicting interpretations. It has been successively assimilated to different concepts such as disorder and information. In this paper we're going to revisit these conceptions, and establish the three following results: Entropy measures lack of information; it also measures information. These two conceptions are complementary. Entropy measures freedom, and this allows a coherent interpretation of entropy formulas and of experimental facts. To associate entropy and disorder implies defining order as absence of freedom. Disorder or agitation is shown to be more appropriately linked with temperature.
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.
王兆礼; 赖成光; 陈晓宏
2012-01-01
基于灾害系统理论构建了东江流域洪灾风险评价指标体系,针对各指标的模糊性和不确定性,将信息论中的熵值理论应用于洪灾风险评价中,借助GIS技术建立了基于熵权的洪灾风险空间模糊综合评价模型。实际应用结果表明：东江流域洪灾风险度最高的地方为河源市区、惠州市区、惠阳以及龙岗等经济较发达地区;而安全区域则位于流域中上游经济发展较为落后的山区;评价结果与流域风险实际情况吻合较好,验证了本文所提出的模型科学可靠,结果相对客观可信。%Entropy theory was used to combine with traditional fuzzy comprehensive assessment method to develop a spatially fuzzy model for flood hazard risk in this work. To improve weight allocation, weight coefficients of evaluation factors were derived from the available data reflecting information entropy. Application with GIS to the Dongjiang river basin indicates that the highest risk of this basin appears in the regions of Heyuan city, Huizhou city, Huiyang district, Dongguan city and Bao'an and Longgang, while the relatively safe region covers mountainous areas less economically developed in the lower-middle Dongjiang. Comparison with a few historical floods of the basin shows that the assessment map agrees well with the observed flood risk and it provides a reference for flood control and disaster assessment.
RNA Thermodynamic Structural Entropy.
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
RNA Thermodynamic Structural Entropy.
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
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.
Multidimensional entropy landscape of quantum criticality
Grube, K.; Zaum, S.; Stockert, O.; Si, Q.; Löhneysen, H. V.
2017-08-01
The third law of thermodynamics states that the entropy of any system in equilibrium has to vanish at absolute zero temperature. At nonzero temperatures, on the other hand, matter is expected to accumulate entropy near a quantum critical point, where it undergoes a continuous transition from one ground state to another. Here, we determine, based on general thermodynamic principles, the spatial-dimensional profile of the entropy S near a quantum critical point and its steepest descent in the corresponding multidimensional stress space. We demonstrate this approach for the canonical quantum critical compound CeCu 6-xAux near its onset of antiferromagnetic order. We are able to link the directional stress dependence of S to the previously determined geometry of quantum critical fluctuations. Our demonstration of the multidimensional entropy landscape provides the foundation to understand how quantum criticality nucleates novel phases such as high-temperature superconductivity.
Entanglement Entropy in Jammed CFTs
Mefford, Eric
2016-01-01
We construct solutions to the Einstein equations for asymptotically locally Anti-de Sitter spacetimes with four, five, and six dimensional Reissner-Nordstr\\"om boundary metrics. These spacetimes are gravitational duals to "jammed" CFTs on those backgrounds at infinite N and strong coupling. For these spacetimes, we calculate the boundary stress tensor as well as compute entanglement entropies for ball shaped regions as functions of the boundary black hole temperature $T_{BH}$. From this, we see how the CFT prevents heat flow from the black hole to the vacuum at spatial infinity. We also compute entanglement entropies for a three dimensional boundary black hole using the AdS C-metric. We compare our results to previous work done in similar spacetimes.
Applications of quantum entropy to statistics
Silver, R.N.; Martz, H.F.
1994-07-01
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.
Entropy of Movement Outcome in Space-Time.
Lai, Shih-Chiung; Hsieh, Tsung-Yu; Newell, Karl M
2015-07-01
Information entropy of the joint spatial and temporal (space-time) probability of discrete movement outcome was investigated in two experiments as a function of different movement strategies (space-time, space, and time instructional emphases), task goals (point-aiming and target-aiming) and movement speed-accuracy constraints. The variance of the movement spatial and temporal errors was reduced by instructional emphasis on the respective spatial or temporal dimension, but increased on the other dimension. The space-time entropy was lower in targetaiming task than the point aiming task but did not differ between instructional emphases. However, the joint probabilistic measure of spatial and temporal entropy showed that spatial error is traded for timing error in tasks with space-time criteria and that the pattern of movement error depends on the dimension of the measurement process. The unified entropy measure of movement outcome in space-time reveals a new relation for the speed-accuracy.
Relative entropy equals bulk relative entropy
Jafferis, Daniel L; Maldacena, Juan; Suh, S Josephine
2015-01-01
We consider the gravity dual of the modular Hamiltonian associated to a general subregion of a boundary theory. We use it to argue that the relative entropy of nearby states is given by the relative entropy in the bulk, to leading order in the bulk gravitational coupling. We also argue that the boundary modular flow is dual to the bulk modular flow in the entanglement wedge, with implications for entanglement wedge reconstruction.
Checa-Garcia, Ramiro
2013-01-01
The main challenges of measuring precipitation are related to the spatio-temporal variability of the drop-size distribution, to the uncertainties that condition the modeling of that distribution, and to the instrumental errors present in the in situ estimations. This PhD dissertation proposes advances in all these questions. The relevance of the spatial variability of the drop-size distribution for remote sensing measurements and hydro-meteorology field studies is asserted by analyzing the measurement of a set of disdrometers deployed on a network of 5 squared kilometers. This study comprises the spatial variability of integral rainfall parameters, the ZR relationships, and the variations within the one moment scaling method. The modeling of the drop-size distribution is analyzed by applying the MaxEnt method and comparing it with the methods of moments and the maximum likelihood. The instrumental errors are analyzed with a compressive comparison of sampling and binning uncertainties that affect actual device...
Black hole entropy and entropy of entanglement
Kabat, D
1995-01-01
We compute the one-loop correction to the entropy of a very massive black hole, by evaluating the partition function in the presence of a conical singularity for quantum fields of spin zero, one-half, and one. We compare the results to the entropy of entanglement, defined by the density matrix which describes the ground state of the field as seen from one side of a boundary in Minkowski space. Fields of spin zero and one-half contribute an entropy to the black hole which is identical to their entropy of entanglement. For spin one a contact interaction with the horizon appears in the black hole entropy but is absent from the entropy of entanglement. Expressed as a particle path integral the contact term is an integral over paths which begin and end on the horizon; it is the field theory limit of the interaction proposed by Susskind and Uglum which couples a closed string to an open string stranded on the horizon.
Absence of log correction in entropy of large black holes
Ghosh, A
2014-01-01
Earlier calculations of black hole entropy in loop quantum gravity have led to a dominant term proportional to the area, but there was a correction involving the logarithm of the area. We find however that calculations yield an entropy proportional to the area eigenvalue with no such correction if the area eigenvalue is taken to be much larger than the classical area.
Yield and spatial distributions of femtosecond laser-produced protons%飞秒激光作用下质子产额及空间分布
唐翠明; 王昌军; 王亚平; 王光昶; 张建炜; 郑志坚
2012-01-01
在超短超强激光装置SILEX-Ⅰ上,利用HD810辐射变色膜在靶背法线方向测量了质子产额及空间分布.测量结果显示:光学密度与质子流量密切相关,光学密度越大,质子流量就越大；当C8H8厚度相同,Cu厚度增加时,质子产额随辐射变色膜的光学密度平均值减小而减小；当靶相同,激光功率密度越小时,光学密度平均值就越小,则质子产额也越小；实验中还得到了质子呈环状、成丝和圆盘状结构的空间分布,该空间分布的大小与激光焦斑大小无关.%For studying the yield and spatial distributions of protons produced in the interaction of femtosecond laser with plasmas, protons behavior at the normal direction of the rear surface of the target irradiated by ultra-intensity pulse laser irradiated solid targets was explored on SILEX-I laser facility. The yield and .spatial distributions of the protons with different target thicknesses were recorded by radiochromic film (RCF) HD810. The results show that the optics density (OD) is closely correlated with the protons flux, OD values increase with the increasing of proton beam flux; For fixed thickness of C8 H8 layer, the proton beam flux and yield of protons and OD of RCF decrease with the increasing Cu layer thickness; for the same thickness of targets, the OD and yield of protons decrease with the decreases of laser intensity; And the corresponding spatial profile of proton beam shows ring-, filament-, and disc-like distribution. The size of the distribution is independent of laser focus.
Hubeny, Veronika E
2014-01-01
A recently explored interesting quantity in AdS/CFT, dubbed 'residual entropy', characterizes the amount of collective ignorance associated with either boundary observers restricted to finite time duration, or bulk observers who lack access to a certain spacetime region. However, the previously-proposed expression for this quantity involving variation of boundary entanglement entropy (subsequently renamed to 'differential entropy') works only in a severely restrictive context. We explain the key limitations, arguing that in general, differential entropy does not correspond to residual entropy. Given that the concept of residual entropy as collective ignorance transcends these limitations, we identify two correspondingly robust, covariantly-defined constructs: a 'strip wedge' associated with boundary observers and a 'rim wedge' associated with bulk observers. These causal sets are well-defined in arbitrary time-dependent asymptotically AdS spacetimes in any number of dimensions. We discuss their relation, spec...
Rosser, J. Barkley
2016-12-01
Entropy is a central concept of statistical mechanics, which is the main branch of physics that underlies econophysics, the application of physics concepts to understand economic phenomena. It enters into econophysics both in an ontological way through the Second Law of Thermodynamics as this drives the world economy from its ecological foundations as solar energy passes through food chains in dissipative process of entropy rising and production fundamentally involving the replacement of lower entropy energy states with higher entropy ones. In contrast the mathematics of entropy as appearing in information theory becomes the basis for modeling financial market dynamics as well as income and wealth distribution dynamics. It also provides the basis for an alternative view of stochastic price equilibria in economics, as well providing a crucial link between econophysics and sociophysics, keeping in mind the essential unity of the various concepts of entropy.
Information Entropy of Fullerenes.
Sabirov, Denis Sh; Ōsawa, Eiji
2015-08-24
The reasons for the formation of the highly symmetric C60 molecule under nonequilibrium conditions are widely discussed as it dominates over numerous similar fullerene structures. In such conditions, evolution of structure rather than energy defines the processes. We have first studied the diversity of fullerenes in terms of information entropy. Sorting 2079 structures from An Atlas of Fullerenes [ Fowler , P. W. ; Manolopoulos , D. E. An Atlas of Fullerenes ; Oxford : Clarendon , 1995 . ], we have found that the information entropies of only 14 fullerenes (entropy, i.e., an exclusive compound among the other members of the fullerene family. Such an efficient sorting demonstrates possible relevance of information entropy to chemical processes. For this reason, we have introduced an algorithm for calculating changes in information entropy at chemical transformations. The preliminary calculations of changes in information entropy at the selected fullerene reactions show good agreement with thermochemical data.
Special Issue: Tsallis Entropy
Anastasios Anastasiadis
2012-01-01
One of the crucial properties of the Boltzmann-Gibbs entropy in the context of classical thermodynamics is extensivity, namely proportionality with the number of elements of the system. The Boltzmann-Gibbs entropy satisfies this prescription if the subsystems are statistically (quasi-) independent, or typically if the correlations within the system are essentially local. In such cases the energy of the system is typically extensive and the entropy is additive. In general, however, the situati...
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. =
Quantum Thermodynamics and Quantum Entanglement Entropies in an Expanding Universe
Farahmand, Mehrnoosh; Mehri-Dehnavi, Hossein
2016-01-01
We investigate an asymptotically spatially flat Robertson-Walker spacetime from two different perspectives. First, using von Neumann entropy, we evaluate the entanglement generation due to the encoded information in spacetime. Then, we work out the entropy of particle creation based on the quantum thermodynamics of the scalar field on the underlying spacetime. We show that the general behavior of both entropies are the same. Therefore, the entanglement can be applied to the customary quantum thermodynamics of the universe. Also, using these entropies, we can recover some information about the parameters of spacetime.
P. Mitra
1994-01-01
In the talk different definitions of the black hole entropy are discussed and compared. It is shown that the Bekenstein-Hawking entropy $S^{BH}$ (defined by the response of the free energy of a system containing a black hole on the change of the temperature) differs from the statistical- mechanical entropy $S^{SM}=-\\mbox{Tr}(\\hat{\\rho}\\ln \\hat{\\rho})$ (defined by counting internal degrees of freedom of a black hole). A simple explanation of the universality of the Bekenstein-Hawking entropy (...
Frolov, V
1994-01-01
In the talk different definitions of the black hole entropy are discussed and compared. It is shown that the Bekenstein-Hawking entropy S^{BH} (defined by the response of the free energy of a system containing a black hole on the change of the temperature) differs from the statistical- mechanical entropy S^{SM}=-\\mbox{Tr}(\\hat{\\rho}\\ln \\hat{\\rho}) (defined by counting internal degrees of freedom of a black hole). A simple explanation of the universality of the Bekenstein-Hawking entropy (i.e. its independence of the number and properties of the fields which might contribute to S^{SM}) is given.
Entropy localization in magnetic compounds and thin-film nanostructures
Skomski, R.; Binek, Ch.; Michalski, S.; Mukherjee, T.; Enders, A.; Sellmyer, D. J.
2010-05-01
The effect of nanostructuring on the magnetic entropy of materials for room-temperature magnetic cooling is investigated by model calculations. The materials are structurally inhomogeneous with a large number of nonequivalent crystallographic sites. In the mean-field Heisenberg model, the entropy density is a unique function of the local magnetization so that the coupled set of nonlinear mean-field equations yields not only the magnetization but also the entropy density. Since most of the entropy is localized near grain boundaries, nanomagnetic cooling requires small feature sizes. Magnetic anisotropy is a substantial complication, even on a mean-field level, but the corresponding corrections are often very small.
ENTROPY FUNCTIONAL FOR CONTINUOUS SYSTEMS OF FINITE ENTROPY
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.
Projective Power Entropy and Maximum Tsallis Entropy Distributions
Shinto Eguchi; Shogo Kato; Osamu Komori
2011-01-01
We discuss a one-parameter family of generalized cross entropy between two distributions with the power index, called the projective power entropy. The cross entropy is essentially reduced to the Tsallis entropy if two distributions are taken to be equal. Statistical and probabilistic properties associated with the projective power entropy are extensively investigated including a characterization problem of which conditions uniquely determine the projective power entropy up to the power index...
Topological entropy of autonomous flows
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.
Cheeseman, Peter; Stutz, John
2005-01-01
A long standing mystery in using Maximum Entropy (MaxEnt) is how to deal with constraints whose values are uncertain. This situation arises when constraint values are estimated from data, because of finite sample sizes. One approach to this problem, advocated by E.T. Jaynes [1], is to ignore this uncertainty, and treat the empirically observed values as exact. We refer to this as the classic MaxEnt approach. Classic MaxEnt gives point probabilities (subject to the given constraints), rather than probability densities. We develop an alternative approach that assumes that the uncertain constraint values are represented by a probability density {e.g: a Gaussian), and this uncertainty yields a MaxEnt posterior probability density. That is, the classic MaxEnt point probabilities are regarded as a multidimensional function of the given constraint values, and uncertainty on these values is transmitted through the MaxEnt function to give uncertainty over the MaXEnt probabilities. We illustrate this approach by explicitly calculating the generalized MaxEnt density for a simple but common case, then show how this can be extended numerically to the general case. This paper expands the generalized MaxEnt concept introduced in a previous paper [3].
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 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 between two abundant rainfalls during the growing season led to a significant change in yield (0.5 t ha-1 on average). Our results highlight the importance of using fine
Entropy of Mixing of Distinguishable Particles
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,…
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
Renyi extrapolation of Shannon entropy
Zyczkowski, K
2003-01-01
Relations between Shannon entropy and Renyi entropies of integer order are discussed. For any N-point discrete probability distribution for which the Renyi entropies of order two and three are known, we provide an lower and an upper bound for the Shannon entropy. The average of both bounds provide an explicit extrapolation for this quantity. These results imply relations between the von Neumann entropy of a mixed quantum state, its linear entropy and traces.
Quantification of entanglement entropy in helium by the Schmidt-Slater decomposition method
Lin, Chien-Hao
2014-01-01
In this work, we present an investigation on the spatial entanglement entropies in the helium atom by using highly correlated Hylleraas functions to represent the S-wave states. Singlet-spin 1sns 1Se states (with n = 1 to 6) and triplet-spin 1sns 3Se states (with n = 2 to 6) are investigated. As a measure on the spatial entanglement, von Neumann entropy and linear entropy are calculated. Furthermore, we apply the Schmidt-Slater decomposition method on the two-electron wave functions, and obtain eigenvalues of the one-particle reduced density matrix, from which the linear entropy and von Neumann entropy can be determined.
Marder, Daniel
The Second Law of Thermodynamics demonstrates the idea of entropy, the tendency of ordered energy to free itself and thus break apart the system that contains it and dissipate that system into chaos. When applied to communications theory, entropy increases not only with noise but with the density of information--particles of possible meaning…
New multifactor spatial prediction method based on Bayesian maximum entropy%基于贝叶斯最大熵的多因子空间属性预测新方法
杨勇; 张楚天; 贺立源
2013-01-01
Summary The spatial distributions of soil properties (e.g.,organic matter and heavy metal content) are vital to soil quality evaluation and regional environment assessment.Currently,the spatial distribution of soil properties is usually predicted with classical geostatistics or environmental correlation.These two methods are different in theory.Geostatistics is based on spatial correlation of sampling points.However,it contains some deficiencies, such as the lack of effective utilization of environmental information,the smoothing effect of predicted results, difficult to meet the assumption of single point to multipoint Gaussian distribution etc .On the other hand,the theoretical basis of environmental correlation is based on the relationship between soil and environment,but it ignores the spatial correlation among sampling points.These two methods complement each other.Thus,it is very important to study how to integrate these two methods,so that the spatial correlation among sampling points and the relationship between soil and environmental factors can both be used to improve the prediction accuracy. We propose a new spatial prediction method based on the theory of Bayesian maximum entropy (BME), which is one of the most well-known modern spatiotemporal geostatistical techniques.The main objective is to incorporate the results of classical geostatistics and quantitative soil-landscape model in the BME framework. The result of ordinary Kriging was taken as the priori probability density function (pdf),as well as the sampling data as hard data,and the results of environmental correlation as soft data.Posterior pdf is calculated with priori pdf,hard data and soft data.According to the posterior pdf,the predicted values of non-sampling points could be obtained,which not only contained the spatial correlation between sample points,but also took into account the relationship between soil properties and the environment.Meanwhile,the soil organic matter contents in
Entropy and Digital Installation
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.
Entropy, Perception, and Relativity
Jaeger, Stefan
2008-01-01
In this paper, I expand Shannon's definition of entropy into a new form of entropy that allows integration of information from different random events. Shannon's notion of entropy is a special case of my more general definition of entropy. I define probability using a so-called performance function, which is de facto an exponential distribution. Assuming that my general notion of entropy reflects the true uncertainty about a probabilistic event, I understand that our perceived uncertainty differs. I claim that our perception is the result of two opposing forces similar to the two famous antagonists in Chinese philosophy: Yin and Yang. Based on this idea, I show that our perceived uncertainty matches the true uncertainty in points determined by the golden ratio. I demonstrate that the well-known sigmoid function, which we typically employ in artificial neural networks as a non-linear threshold function, describes the actual performance. Furthermore, I provide a motivation for the time dilation in Einstein's Sp...
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
Nonsymmetric entropy I: basic concepts and results
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.
Entropy Coherent and Entropy Convex Measures of Risk
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, respe
Entropy coherent and entropy convex measures of risk
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 measur
Entropy of the Mixture of Sources and Entropy Dimension
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.
Greg F. Naterer
2009-07-01
Full Text Available An experimental design is presented for an optical method of measuring spatial variations of flow irreversibilities in laminar viscous fluid motion. Pulsed laser measurements of fluid velocity with PIV (Particle Image Velocimetry are post-processed to determine the local flow irreversibilities. The experimental technique yields whole-field measurements of instantaneous entropy production with a non-intrusive, optical method. Unlike point-wise methods that give measured velocities at single points in space, the PIV method is used to measure spatial velocity gradients over the entire problem domain. When combined with local temperatures and thermal irreversibilities, these velocity gradients can be used to find local losses of energy availability and exergy destruction. This article focuses on the frictional portion of entropy production, which leads to irreversible dissipation of mechanical energy to internal energy through friction. Such effects are significant in various technological applications, ranging from power turbines to internal duct flows and turbomachinery. Specific problems of a rotational stirring tank and channel flow are examined in this paper. By tracking the local flow irreversibilities, designers can focus on problem areas of highest entropy production to make local component modifications, thereby improving the overall energy efficiency of the system.
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.
Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems
Dagmar Markechová
2016-01-01
Full Text Available In the paper we define three kinds of entropy of a fuzzy dynamical system using different entropies of fuzzy partitions. It is shown that different definitions of the entropy of fuzzy partitions lead to different notions of entropies of fuzzy dynamical systems. The relationships between these entropies are studied and connections with the classical case are mentioned as well. Finally, an analogy of the Kolmogorov–Sinai Theorem on generators is proved for fuzzy dynamical systems.
Kevin H. Knuth
2014-01-01
Full Text Available In 2013, Entropy instituted the “Best Paper” award to recognize outstanding papers in the area of entropy and information studies published in Entropy [1]. We are pleased to announce the “Entropy Best Paper Award” for 2014. Nominations were selected by the Editor-in-Chief and designated Editorial Board Members from all the papers published in 2010.
Quantum geometry and microscopic black hole entropy
Corichi, Alejandro [Instituto de Matematicas, Universidad Nacional Autonoma de Mexico, A Postal 61-3, Morelia, Michoacan 58090 (Mexico); DIaz-Polo, Jacobo [Departamento de AstronomIa y AstrofIsica, Universidad de Valencia, Burjassot-46100, Valencia (Spain); Fernandez-Borja, Enrique [Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Universidad de Valencia, Burjassot-46100, Valencia (Spain)
2007-01-07
Quantum black holes within the loop quantum gravity (LQG) framework are considered. The number of microscopic states that is consistent with a black hole of a given horizon area A{sub 0} are counted and the statistical entropy, as a function of the area, is obtained for A{sub 0} up to 550l{sup 2}{sub Pl}. The results are consistent with an asymptotic linear relation and a logarithmic correction with a coefficient equal to -1/2. The Barbero-Immirzi parameter that yields the asymptotic linear relation compatible with the Bekenstein-Hawking entropy is shown to coincide with a value close to {gamma} = 0.274, which has been previously obtained analytically. However, a new and oscillatory functional form for the entropy is found for small, Planck size, black holes that calls for a physical interpretation.
Entropy of international trades
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.
Kyle, Benjamin G.
1988-01-01
Illustrates qualitative and metaphoric applications of entropy in the areas of cosmology, the birth and death of the universe and time; life and evolution; literature and art; and social science. (RT)
Multifractals and Entropy Computing
Slomczynski, W; Zyczkowski, K; Slomczynski, Wojciech; Kwapien, Jaroslaw; Zyczkowski, Karol
1998-01-01
We discuss the properties of invariant measures corresponding to iterated function systems (IFSs) with place-dependent probabilities and compute their shown that with certain dynamical systems one can associate the corresponding IFSs in such a way that their generalized entropies are equal. We use this method to compute entropy of some classical and quantum dynamical systems. Numerical techniques are based on integration over fractal measures.
Entropy and environmental mystery.
Stamps, Arthur E
2007-06-01
Two studies are reported regarding the effects of entropy, lighting, and occlusion on impressions of mystery in physical environments. The theoretical context of this study was the "informational theory" of environmental preference, which, among other claims, holds that mystery can be measured by the extent to which people perceive a promise of more information if they move deeper into an environment. Entropy, in the context of this article, is visual diversity as measured using information theory. Mystery was measured by a semantic differential scale. The definition of mystery was left up to each individual participant. Entropy of occluded objects was used to obtain an objective, experimentally manipulatable and operational definition of "promise of more information." Exp. 1 had 12 stimuli and 15 participants. Exp. 2 had 12 stimuli and 16 participants. Entropy of occluded objects ranged from 0 to 6 bits. Entropy of occluded objects was used to measure the promise that there would be more information if one moved deeper into an environment. Overall, amount of light had the strongest effect on responses of mystery (r = -.63, darker was more mysterious), followed by occlusion (r = .26, occluding objects made a scene seem more mysterious), and by the promise of more information if one moved about in the scene (r = .13), the more entropy in occluded objects, the greater the impression of mystery). The theoretical contribution of this work is that a relationship between subjective impressions of mystery and an objective measure of "promise of more information" was found.
Special Issue: Tsallis Entropy
Anastasios Anastasiadis
2012-02-01
Full Text Available One of the crucial properties of the Boltzmann-Gibbs entropy in the context of classical thermodynamics is extensivity, namely proportionality with the number of elements of the system. The Boltzmann-Gibbs entropy satisfies this prescription if the subsystems are statistically (quasi- independent, or typically if the correlations within the system are essentially local. In such cases the energy of the system is typically extensive and the entropy is additive. In general, however, the situation is not of this type and correlations may be far from negligible at all scales. Tsallis in 1988 introduced an entropic expression characterized by an index q which leads to a non-extensive statistics. Tsallis entropy, Sq, is the basis of the so called non-extensive statistical mechanics, which generalizes the Boltzmann-Gibbs theory. Tsallis statistics have found applications in a wide range of phenomena in diverse disciplines such as physics, chemistry, biology, medicine, economics, geophysics, etc. The focus of this special issue of Entropy was to solicit contributions that apply Tsallis entropy in various scientific fields. [...
Francisco Nogara Neto
2011-06-01
insumos sejam aplicados nas dosagens adequadas em partes específicas da gleba, e não uniformemente em toda a gleba, alterando positivamente a produtividade dessas partes. Quando as tomadas de decisão sobre o manejo são auxiliadas por ferramentas estatísticas apropriadas, a agricultura de precisão é viável tecnicamente para o manejo de atributos químicos do solo, proporcionando assim a otimização no uso de insumos e, potencialmente, contribuindo para o rendimento economicamente ideal.Precision agriculture can increase efficiency and sustainability of grain crops in Brazil, especially in support of soil and crop management. In this study the importance of spatially-variable soil and crop attributes on the variability of grain crop yield and the use of this information to improve management decisions was examined. The study used data from the 2005/6 corn growing season of a 18 ha commercial field on a clayey Latossolo Bruno (FAO: Ferralsol. Soil (0-0.10 m layer and crop properties were sampled at a density of two per ha. Spatially distributed crop yield was determined with a grain sensor on the harvester. Yield variability (average of 12.4 Mg ha-1, amplitude between 11.1 and 14.0 Mg ha-1 was related to the soil properties - P Mehlich, Mg2+, sum of bases and Ca:Mg, Mg:K and Mg:CEC ratios - but not with crop attributes, according to the results of a Spearman correlation matrix. Regression analysis identified a critical value of Magnesium saturation (Mg:CEC of 0.10, and a critical Mg:K ratio of 2.3, as the most significant soil properties. Below the critical values, yields were reduced. Cluster analysis confirmed the results obtained by the two previous statistical techniques, and their combined interpretation supported the conclusion that P and Mg were the two nutrients for which spatial management is most needed. Compared to the traditional fixed-rate, whole-field application, using variable rate application would require, for the whole field, 6.6 Mg of additional
On the Conditional Rényi Entropy
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 ve
On the Conditional Rényi Entropy
Fehr, S.; Berens, S.
2014-01-01
The 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 versions have
EEG entropy measures in anesthesia
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.
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.
Kersting, E.; von Seggern, H.
2017-08-01
A new production route for europium doped cesium bromide (CsBr:Eu2+) imaging plates has been developed, synthesizing CsBr:Eu2+ powder from a precipitation reaction of aqueous CsBr solution with ethanol. This new route allows the control of features like homogeneous grain size and grain shape of the obtained powder. After drying and subsequent compacting the powder, disk-like samples were fabricated, and their resulting photostimulated luminescence (PSL) properties like yield and spatial resolution were determined. It will be shown that hydration of such disks causes the CsBr:Eu2+ powder to recrystallize starting from the humidity exposed surfaces to the sample interior up to a completely polycrystalline sample resulting in a decreasing PSL yield and an increasing resolution. Subsequent annealing leads to grain refinement combined with a large PSL yield increment and a minor effect on the spatial resolution. By first annealing the "as made" disk, one observes a strong increment of the PSL yield and almost no effect on the spatial resolution. During subsequent hydration, the recrystallization is hindered by minor structural changes of the grains. The related PSL yield drops slightly with increasing hydration time, and the spatial resolution drops considerably. The obtained PSL properties with respect to structure will be discussed with a simple model.
Baker, Ronald J.; Wieben, Christine M.; Lathrop, Richard G.; Nicholson, Robert S.
2014-01-01
Concentrations, loads, and yields of nutrients (total nitrogen and total phosphorus) were calculated for the Barnegat Bay-Little Egg Harbor (BB-LEH) watershed for 1989–2011 at annual and seasonal (growing and nongrowing) time scales. Concentrations, loads, and yields were calculated at three spatial scales: for each of the 81 subbasins specified by 14-digit hydrologic unit codes (HUC-14s); for each of the three BB-LEH watershed segments, which coincide with segmentation of the BB-LEH estuary; and for the entire BB-LEH watershed. Base-flow and runoff values were calculated separately and were combined to provide total values. Available surface-water-quality data for all streams in the BB-LEH watershed for 1980–2011 were compiled from existing datasets and quality assured. Precipitation and streamflow data were used to distinguish between water-quality samples that were collected during base-flow conditions and those that were collected during runoff conditions. Base-flow separation of hydrographs of six streams in the BB-LEH watershed indicated that base flow accounts for about 72 to 94 percent of total flow in streams in the watershed. Base-flow mean concentrations (BMCs) of total nitrogen (TN) and total phosphorus (TP) for each HUC-14 subbasin were calculated from relations between land use and measured base-flow concentrations. These relations were developed from multiple linear regression models determined from water-quality data collected at sampling stations in the BB-LEH watershed under base-flow conditions and land-use percentages in the contributing drainage basins. The total watershed base-flow volume was estimated for each year and season from continuous streamflow records for 1989–2011 and relations between precipitation and streamflow during base-flow conditions. For each year and season, the base-flow load and yield were then calculated for each HUC-14 subbasin from the BMCs, total base-flow volume, and drainage area. The watershed
Statistical Entropy of the Kaluza－Klein Black Hole from the Horizon Conformal Field Theory
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.
Comparisons of Black Hole Entropy
Kupferman, Judy
2016-01-01
In this thesis I examine several different concepts of black hole entropy in order to understand whether they describe the same quantity. I look at statistical and entanglement entropies, Wald entropy and Carlip's entropy from conformal field theory, and compare their behavior in a few specific aspects: divergence at the BH horizon, dependence on space time curvature and behavior under a geometric variation. I find that statistical and entanglement entropy may be similar but they seem to differ from the entropy of Wald and Carlip. Chapters 2 and 3 overlap with 1010.4157 and 1310.3938. Chapter 4 does not appear elsewhere.
Entropy, color, and color rendering.
Price, Luke L A
2012-12-01
The Shannon entropy [Bell Syst. Tech J.27, 379 (1948)] of spectral distributions is applied to the problem of color rendering. With this novel approach, calculations for visual white entropy, spectral entropy, and color rendering are proposed, indices that are unreliant on the subjectivity inherent in reference spectra and color samples. The indices are tested against real lamp spectra, showing a simple and robust system for color rendering assessment. The discussion considers potential roles for white entropy in several areas of color theory and psychophysics and nonextensive entropy generalizations of the entropy indices in mathematical color spaces.
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.
System Entropy Measurement of Stochastic Partial Differential Systems
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.
ENTROPY FLOW CHARACTERISTICS ANALYSIS OF TYPHOON MATSA (0509)
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.
Entropy budget of the earth,atmosphere and ocean system
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.
Quantum Statistical Entropy of Spherical Black Holes in Higher Dimensions
XU Dian-Yan
2000-01-01
The free energy and entropy of a general spherically symmetry black hole are calculated by quantum statistic method with brick wall model Two different kinds of approximation are used to calculate the number of states in transverse spatial space. The final results are approximately equal except a rational numerical constant. The formulas of free energy and entropy, evaluated by each one of the two different kinds of approximation, are the same except some numerical constants. The free energy and entropy are dependent on the spacetime dimensionsD. When D = 4, they reduce to the usual well known results.
Entropy-Based Credit Evaluation for Mobile Telephone Customers
Yang Zong-Chang
2013-10-01
Full Text Available The arrears problem puzzled most mobile communication corporations in China. In information theory, the Shannon entropy is a measure of the uncertainty in a signal or random event. Motivated by entropy theory especially the Shannon Entropy, in this study, one called customer information entropy is defined and proposed to credit evaluation for arrearage customers of cellular telephone. The proposed customer information entropy is based on customer’s behavior attributes. Arrearage customers often include malevolent ones and non-malevolent ones. 52364 arrearage customers among a total number of 400000 ones in a mobile communication corporation are chosen for experiment. The proposed measure yields good results in its application of credit evaluation for 52364 arrearage customers in August and September. Its correct evaluation rates for malevolent and non-malevolent of the 52364 arrearage ones both are over 90.0%: among the 52364 arrearage customers, 90.75% of the non-malevolent ones, whose entropy changes is less than zero, while for the entropy changes of the malevolent ones, 95.36% is equal to zero and 1.57% is more than zero. The experimental results indicate that the entropy changes of the non-malevolent ones could be considered as negative and nonnegative for the malevolent ones. The proposed show its potential practicality.
Routes to fractality and entropy in Liesegang systems
Kalash, Leen; Sultan, Rabih, E-mail: rsultan@aub.edu.lb [Department of Chemistry, American University of Beirut, Riad El Solh, 1107 2020 Beirut (Lebanon)
2014-06-01
Liesegang bands are formed when solutions of co-precipitate ions interdiffuse in a 1D gel matrix. In a recent study [R. F. Sultan, Acta. Mech. Sin. 27, 119 (2011)], Liesegang patterns have been characterized as fractal structures. In addition to experimentally obtained patterns, geometric Liesegang patterns were constructed in conformity with the well-known empirical laws. Both mathematical fractal dimensions and box count dimensions for images of PbF{sub 2} and PbI{sub 2} Liesegang patterns have been calculated. Liesegang patterns can also be described by the entropy state function, and categorized as more or less ordered structures. We revisit the relation between entropy and fractal dimension, and apply it to simulated geometrical Liesegang patterns. We have resort to three different routes for the estimation of the entropy of a Liesegang pattern. The HarFA software enabled the calculation of the Hausdorff dimension and the topological entropy, then the information dimension and the Shannon entropy. In a third pathway, analytical calculations were carried out by estimating the probability of occurrence of a fractal element or coverage. The product of Shannon entropy and Boltzmann constant yields the thermodynamic entropy. The values for PbF{sub 2} and PbI{sub 2} Liesegang patterns attained the order of magnitude of the reported Third Law entropies, but yet remained lower, in conformity with the more ordered Liesegang structures.
A modulated shear to entropy ratio
Ovdat, O
2014-01-01
We study correlation functions in an equilibrated spatially modulated phase of Einstein-Maxwell two-derivative gravity. We find that the ratio of the appropriate low frequency limit of the stress-stress two point function to the entropy density is modulated. The conductivity, the stress-current and current-stress correlation functions are also modulated. At temperatures close to the phase transition we obtain analytic expressions for some of the correlation functions.
Cardinal, Jean; Joret, Gwenaël
2008-01-01
We study graph orientations that minimize the entropy of the in-degree sequence. The problem of finding such an orientation is an interesting special case of the minimum entropy set cover problem previously studied by Halperin and Karp [Theoret. Comput. Sci., 2005] and by the current authors [Algorithmica, to appear]. We prove that the minimum entropy orientation problem is NP-hard even if the graph is planar, and that there exists a simple linear-time algorithm that returns an approximate solution with an additive error guarantee of 1 bit. This improves on the only previously known algorithm which has an additive error guarantee of log_2 e bits (approx. 1.4427 bits).
Holographic entropy production
Tian, Yu; Wu, Xiao-Ning; Zhang, Hongbao
2014-10-01
The suspicion that gravity is holographic has been supported mainly by a variety of specific examples from string theory. In this paper, we propose that such a holography can actually be observed in the context of Einstein's gravity and at least a class of generalized gravitational theories, based on a definite holographic principle where neither is the bulk space-time required to be asymptotically AdS nor the boundary to be located at conformal infinity, echoing Wilson's formulation of quantum field theory. After showing the general equilibrium thermodynamics from the corresponding holographic dictionary, in particular, we provide a rather general proof of the equality between the entropy production on the boundary and the increase of black hole entropy in the bulk, which can be regarded as strong support to this holographic principle. The entropy production in the familiar holographic superconductors/superfluids is investigated as an important example, where the role played by the holographic renormalization is explained.
Holographic Entropy Production
Tian, Yu; Zhang, Hong-Bao
2014-01-01
The suspicion that gravity is holographic has been supported mainly by a variety of specific examples from string theory. In this paper, we propose that such a holography can actually be observed in the context of Einstein's gravity and at least a class of generalized gravitational theories, based on a definite holographic principle where neither is the bulk space-time required to be asymptotically AdS nor the boundary to be located at conformal infinity, echoing Wilson's formulation of quantum field theory. After showing the general equilibrium thermodynamics from the corresponding holographic dictionary, in particular, we provide a rather general proof of the equality between the entropy production on the boundary and the increase of black hole entropy in the bulk, which can be regarded as strong support to this holographic principle. The entropy production in the familiar holographic superconductors/superfluids is investigated as an important example, where the role played by the holographic renormalizatio...
Entropy Message Passing Algorithm
Ilic, Velimir M; Branimir, Todorovic T
2009-01-01
Message passing over factor graph can be considered as generalization of many well known algorithms for efficient marginalization of multivariate function. A specific instance of the algorithm is obtained by choosing an appropriate commutative semiring for the range of the function to be marginalized. Some examples are Viterbi algorithm, obtained on max-product semiring and forward-backward algorithm obtained on sum-product semiring. In this paper, Entropy Message Passing algorithm (EMP) is developed. It operates over entropy semiring, previously introduced in automata theory. It is shown how EMP extends the use of message passing over factor graphs to probabilistic model algorithms such as Expectation Maximization algorithm, gradient methods and computation of model entropy, unifying the work of different authors.
Kay, Bernard S
2015-01-01
We give an account of the 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 new 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. We also very briefly review some recent related work on the nature of equilibrium states involving quantum black holes and point out how it promises to resolve some puzzling issues in the current version of the string theory approach to black hole entropy.
Sharp continuity bounds for entropy and conditional entropy
Chen, ZhiHua; Ma, ZhiHao; Nikoufar, Ismail; Fei, Shao-Ming
2017-02-01
The Renyi entropy plays an essential role in quantum information theory. We study the continuity estimation of the Renyi entropy. An inequality relating the Renyi entropy difference of two quantum states to their trace norm distance is derived. This inequality is shown to be tight in the sense that equality can be attained for every prescribed value of the trace norm distance. It includes the sharp Fannes inequality for von Neumann entropy as a special case.
Åqvist, Johan; Kazemi, Masoud; Isaksen, Geir Villy; Brandsdal, Bjørn Olav
2017-02-21
The role played by entropy for the enormous rate enhancement achieved by enzymes has been debated for many decades. There are, for example, several confirmed cases where the activation free energy is reduced by around 10 kcal/mol due to entropic effects, corresponding to a rate enhancement of ∼10(7) compared to the uncatalyzed reaction. However, despite substantial efforts from both the experimental and theoretical side, no real consensus has been reached regarding the origin of such large entropic contributions to enzyme catalysis. Another remarkable instance of entropic effects is found in enzymes that are adapted by evolution to work at low temperatures, near the freezing point of water. These cold-adapted enzymes invariably show a more negative entropy and a lower enthalpy of activation than their mesophilic orthologs, which counteracts the exponential damping of reaction rates at lower temperature. The structural origin of this universal phenomenon has, however, remained elusive. The basic problem with connecting macroscopic thermodynamic quantities, such as activation entropy and enthalpy derived from Arrhenius plots, to the 3D protein structure is that the underlying detailed (microscopic) energetics is essentially inaccessible to experiment. Moreover, attempts to calculate entropy contributions by computer simulations have mostly focused only on substrate entropies, which do not provide the full picture. We have recently devised a new approach for accessing thermodynamic activation parameters of both enzyme and solution reactions from computer simulations, which turns out to be very successful. This method is analogous to the experimental Arrhenius plots and directly evaluates the temperature dependence of calculated reaction free energy profiles. Hence, by extensive molecular dynamics simulations and calculations of up to thousands of independent free energy profiles, we are able to extract activation parameters with sufficient precision for making
Dimensional Equations of Entropy
Sparavigna, Amelia Carolina
2015-01-01
Entropy is a quantity which is of great importance in physics and chemistry. The concept comes out of thermodynamics, proposed by Rudolf Clausius in his analysis of Carnot cycle and linked by Ludwig Boltzmann to the number of specific ways in which a physical system may be arranged. Any physics classroom, in its task of learning physics, has therefore to face this crucial concept. As we will show in this paper, the lectures can be enriched by discussing dimensional equations linked to the entropy of some physical systems.
F. TopsÃƒÂ¸e
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
Entropy, materials, and posterity
Cloud, P.
1977-01-01
Materials and energy are the interdependent feedstocks of economic systems, and thermodynamics is their moderator. It costs energy to transform the dispersed minerals of Earth's crust into ordered materials and structures. And it costs materials to collect and focus the energy to perform work - be it from solar, fossil fuel, nuclear, or other sources. The greater the dispersal of minerals sought, the more energy is required to collect them into ordered states. But available energy can be used once only. And the ordered materials of industrial economies become disordered with time. They may be partially reordered and recycled, but only at further costs in energy. Available energy everywhere degrades to bound states and order to disorder - for though entropy may be juggled it always increases. Yet industry is utterly dependent on low entropy states of matter and energy, while decreasing grades of ore require ever higher inputs of energy to convert them to metals, with ever increasing growth both of entropy and environmental hazard. Except as we may prize a thing for its intrinsic qualities - beauty, leisure, love, or gold - low-entropy is the only thing of real value. It is worth whatever the market will bear, and it becomes more valuable as entropy increases. It would be foolish of suppliers to sell it more cheaply or in larger amounts than their own enjoyment of life requires, whatever form it may take. For this reason, and because of physical constraints on the availability of all low-entropy states, the recent energy crises is only the first of a sequence of crises to be expected in energy and materials as long as current trends continue. The apportioning of low-entropy states in a modern industrial society is achieved more or less according to the theory of competitive markets. But the rational powers of this theory suffer as the world grows increasingly polarized into rich, over-industrialized nations with diminishing resource bases and poor, supplier nations
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....
On Joint and Conditional Entropies
D. V. Gokhale
1999-05-01
Full Text Available Abstract: It is shown that if the conditional densities of a bivariate random variable have maximum entropies, subject to certain constraints, then the bivariate density also maximizes entropy, subject to appropriate constraints. Some examples are discussed.
Dynamical maximum entropy approach to flocking
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.
Entropy is a Mathematical Formula
Garai, Jozsef
2003-01-01
The microscopic explanation of entropy has been challenged from both experimental and theoretical point of view. The expression of entropy is derived from the first law of thermodynamics indicating that entropy or the second law of thermodynamics is not an independent law.
Entropie analysis of floating car data systems
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.
Higher spin entanglement entropy from CFT
Datta, Shouvik; David, Justin R. [Centre for High Energy Physics, Indian Institute of Science,C.V. Raman Avenue, Bangalore 560012 (India); Ferlaino, Michael [Department of Physics, Swansea University,Singleton Park, Swansea SA2 8PP (United Kingdom); Kumar, S. Prem [Centre for High Energy Physics, Indian Institute of Science,C.V. Raman Avenue, Bangalore 560012 (India); Department of Physics, Swansea University,Singleton Park, Swansea SA2 8PP (United Kingdom)
2014-06-17
We consider free fermion and free boson CFTs in two dimensions, deformed by a chemical potential μ for the spin-three current. For the CFT on the infinite spatial line, we calculate the finite temperature entanglement entropy of a single interval perturbatively to second order in μ in each of the theories. We find that the result in each case is given by the same non-trivial function of temperature and interval length. Remarkably, we further obtain the same formula using a recent Wilson line proposal for the holographic entanglement entropy, in holomorphically factorized form, associated to the spin-three black hole in SL(3,ℝ)×SL(3,ℝ) Chern-Simons theory. Our result suggests that the order μ{sup 2} correction to the entanglement entropy may be universal for W-algebra CFTs with spin-three chemical potential, and constitutes a check of the holographic entanglement entropy proposal for higher spin theories of gravity in AdS{sub 3}.
Relations Among Some Fuzzy Entropy Formulae
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.
Rescaling Temperature and Entropy
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…
Optimized Kernel Entropy Components.
Izquierdo-Verdiguier, Emma; Laparra, Valero; Jenssen, Robert; Gomez-Chova, Luis; Camps-Valls, Gustau
2016-02-25
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.
Rescaling Temperature and Entropy
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…
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
Entropy equilibrium equation and dynamic entropy production in environment liquid
无
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.
Use of Entropy in the Assessment of Uncertainty of River Runoff Regime in Poland
Wrzesiński, Dariusz
2016-10-01
The objective of this paper is to describe spatial differences in the uncertainty of features of the runoff regimes of Polish rivers based on entropy in Shannon's information theory. They included: the entropy of monthly river runoff and the entropy of river runoff distribution over time. An analysis of monthly flow series for the years 1951-2010 from 395 gauging stations located on 248 rivers in Poland was performed. This allowed a quantitative determination of the degree of uncertainty of two regime characteristics indirectly establishing the predictability, regularity, and stability of their appearance and their spatial variability. An analysis of relations between the calculated entropy, as well as between the entropy and the classical parameters commonly used was performed in describing the hydrological regime. The obtained grouping of rivers into four categories in terms of entropy of volume and distribution of runoff in the annual cycle clearly coincides with the types of river regime distinguished in Poland.
Kevin H. Knuth
2013-02-01
Full Text Available The journal Entropy is initiating a “Best Paper” award to recognize outstanding papers in the area of entropy and information studies published in Entropy. We are pleased to announce the first “Entropy Best Paper Award” for 2013. Nominations were selected by the Editor-in-Chief and selected Editorial Board Members from all the papers published in 2009 and evaluated by the Entropy Best Paper Award Committee. Reviews and articles were evaluated separately. A first prize is awarded to the selected review paper, and a first and second prize is awarded to the top two selected research articles.
Maximizing Entropy over Markov Processes
Biondi, Fabrizio; Legay, Axel; Nielsen, Bo Friis
2013-01-01
computation reduces to finding a model of a specification with highest entropy. Entropy maximization for probabilistic process specifications has not been studied before, even though it is well known in Bayesian inference for discrete distributions. We give a characterization of global entropy of a process...... 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...
Maximizing entropy over Markov processes
Biondi, Fabrizio; Legay, Axel; Nielsen, Bo Friis
2014-01-01
computation reduces to finding a model of a specification with highest entropy. Entropy maximization for probabilistic process specifications has not been studied before, even though it is well known in Bayesian inference for discrete distributions. We give a characterization of global entropy of a process...... 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...
Chahbi, Aicha; Zribi, Mehrez; Lili-Chabaane, Zohra
2016-04-01
In arid and semi-arid areas, population growth, urbanization, food security and climate change have an impact on agriculture in general and particular on the cereal production. Therefore to improve food security in arid countries, crop canopy monitoring and yield forecasting cereals are needed. Many models, based on the use of remote sensing or agro-meteorological models, have been developed to estimate the biomass and grain yield of cereals. Through the use of a rich database, acquired over a period of two years for more than 80 test fields, and from optical satellite SPOT/HRV images, the aim of the present study is to evaluate the feasibility of two yield prediction approaches. The first approach is based on the application of the semi-empirical growth model SAFY, developed to simulate the dynamics of the LAI and the grain yield, at the field scale. The model is able to reproduce the time evolution of the leaf area index of all fields with acceptable error. However, an inter-comparison between ground yield measurements and SAFY model simulations reveals that the yields are under-estimated by this model. We can explain the limits of the semi-empirical model SAFY by its simplicity and also by various factors that were not considered (fertilization, irrigation,...). To improve the yield estimation, a new approach is proposed: the grain yield is estimated in function of the LAI in the growth period between 25 March and 5 April. The LAI of this period is estimated by SAFY model. A linear relationship is developed between the measured grain yield and the LAI area of the maximum growth period.This approach is robust, the measured and estimated grain yields are well correlated. Following the validation of this approach, yield estimations are proposed for the entire studied site using the SPOT/HRV images.
Fractal Structure and Entropy Production within the Central Nervous System
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.
mohamad hoseyni
2009-06-01
Full Text Available With respect to effect of climatic changes on crop yields, study of long term trend of yields is conducted on the basis of statistical procedures that will be a suitable way to determine contribution of climatic factors affecting yield changes. As this trend of yield changes has been studied at regional and national levels in many parts of the world, conducting these studies will be necessary for Iran. So, with respect to economical importance and social aspect of saffron for Khorasan province and Iran, evaluation of yield trend of saffron in recent years and study of relationship of its changes to climatic changes have been purpose of this research. Findings show that yield reduction of saffron in Khorasan has been affected by changes in climatic indices particularly temperature and precipitation during the past ten years, so that among main cities of saffron cultivation in Khorasan 31 to 66 percent of yield variation can be explained by these climatic variables. In this research, from meteorological parameters, effect of precipitation compared with monthly temperature has been less and results show that precipitation has been effective only in Torbat-e-heidarieh while minimum and maximum monthly temperatures are considered as the most important variables affecting saffron yield. It was also concluded that temperatures of spring season and almost the first month of summer have highest effects on saffron yield. Patterns of increasing minimum and maximum temperatures of these months during the past ten years are related to trend of yield reduction in saffron, and It seems that this decreasing trend will be continued.
Conductivity and entanglement entropy of high dimensional holographic superconductors
Romero-Bermúdez, Aurelio
2015-01-01
We investigate the dependence of the conductivity and the entanglement entropy on the space-time dimensionality $d$ in two holographic superconductors: one dual to a quantum critical point with spontaneous symmetry breaking, and the other modeled by a charged scalar that condenses at a sufficiently low temperature in the presence of a Maxwell field. In both cases the gravity background is asymptotically Anti de Sitter (AdS). In the large $d$ limit we obtain explicit analytical results for the conductivity at zero temperature and the entanglement entropy by a $1/d$ expansion. We show that the entanglement entropy is always smaller in the broken phase and identify a novel decay of the conductivity for intermediate frequencies. As dimensionality increases, the entanglement entropy decreases, the coherence peak in the conductivity becomes narrower and the ratio between the energy gap and the critical temperature decreases. These results suggest that the condensate interactions become weaker in high spatial dimens...
Universal Features of Left-Right Entanglement Entropy.
Das, Diptarka; Datta, Shouvik
2015-09-25
We show the presence of universal features in the entanglement entropy of regularized boundary states for (1+1)D conformal field theories on a circle when the reduced density matrix is obtained by tracing over right- or left-moving modes. We derive a general formula for the left-right entanglement entropy in terms of the central charge and the modular S matrix of the theory. When the state is chosen to be an Ishibashi state, this measure of entanglement is shown to precisely reproduce the spatial entanglement entropy of a (2+1)D topological quantum field theory. We explicitly evaluate the left-right entanglement entropies for the Ising model, the tricritical Ising model and the su[over ^](2)_{k} Wess-Zumino-Witten model as examples.
Entanglement entropy in three dimensional gravity
Maxfield, Henry
2014-01-01
The Ryu-Takayanagi and covariant Hubeny-Rangamani-Takayanagi proposals relate entanglement entropy in CFTs with holographic duals to the areas of minimal or extremal surfaces in the bulk geometry. We show how, in three dimensional pure gravity, the relevant regulated geodesic lengths can be obtained by writing a spacetime as a quotients of AdS3, with the problem reduced to a simple purely algebraic calculation. We explain how this works in both Lorentzian and Euclidean formalisms, before illustrating its use to obtain novel results in a number of examples, including rotating BTZ, the RP2 geon, and several wormhole geometries. This includes spatial and temporal dependence of single-interval entanglement entropy, despite these symmetries being broken only behind an event horizon. We also discuss considerations allowing HRT to be derived from analytic continuation of Euclidean computations in certain contexts, and a related class of complexified extremal surfaces.
Entanglement entropy in three dimensional gravity
Maxfield, Henry [Centre for Particle Theory & Department of Mathematical Sciences, Durham University,South Road, Durham DH1 3LE (United Kingdom)
2015-04-07
The Ryu-Takayanagi (RT) and covariant Hubeny-Rangamani-Takayanagi (HRT) proposals relate entanglement entropy in CFTs with holographic duals to the areas of minimal or extremal surfaces in the bulk geometry. We show how, in three dimensional pure gravity, the relevant regulated geodesic lengths can be obtained by writing a spacetime as a quotient of AdS{sub 3}, with the problem reduced to a simple purely algebraic calculation. We explain how this works in both Lorentzian and Euclidean formalisms, before illustrating its use to obtain novel results in a number of examples, including rotating BTZ, the ℝℙ{sup 2} geon, and several wormhole geometries. This includes spatial and temporal dependence of single-interval entanglement entropy, despite these symmetries being broken only behind an event horizon. We also discuss considerations allowing HRT to be derived from analytic continuation of Euclidean computations in certain contexts, and a related class of complexified extremal surfaces.
Holographic Entanglement Entropy
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...
Preimage entropy dimension of topological dynamical systems
Lei LIU; 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...
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.
Quantum and Ecosystem Entropies
A. D. Kirwan
2008-06-01
Full Text Available Ecosystems and quantum gases share a number of superficial similarities including enormous numbers of interacting elements and the fundamental role of energy in such interactions. A theory for the synthesis of data and prediction of new phenomena is well established in quantum statistical mechanics. The premise of this paper is that the reason a comparable unifying theory has not emerged in ecology is that a proper role for entropy has yet to be assigned. To this end, a phase space entropy model of ecosystems is developed. Specification of an ecosystem phase space cell size based on microbial mass, length, and time scales gives an ecosystem uncertainty parameter only about three orders of magnitude larger than PlanckÃ¢Â€Â™s constant. Ecosystem equilibria is specified by conservation of biomass and total metabolic energy, along with the principle of maximum entropy at equilibria. Both Bose - Einstein and Fermi - Dirac equilibrium conditions arise in ecosystems applications. The paper concludes with a discussion of some broader aspects of an ecosystem phase space.
Holographic entanglement entropy
Rangamani, Mukund
2017-01-01
This book provides a comprehensive overview of developments in the field of holographic entanglement entropy. Within the context of the AdS/CFT correspondence, it is shown how quantum entanglement is computed by the area of certain extremal surfaces. The general lessons one can learn from this connection are drawn out for quantum field theories, many-body physics, and quantum gravity. An overview of the necessary background material is provided together with a flavor of the exciting open questions that are currently being discussed. The book is divided into four main parts. In the first part, the concept of entanglement, and methods for computing it, in quantum field theories is reviewed. In the second part, an overview of the AdS/CFT correspondence is given and the holographic entanglement entropy prescription is explained. In the third part, the time-dependence of entanglement entropy in out-of-equilibrium systems, and applications to many body physics are explored using holographic methods. The last part f...
Quantum Dynamical Entropies and Gács Algorithmic Entropy
Fabio Benatti
2012-07-01
Full Text Available Several quantum dynamical entropies have been proposed that extend the classical Kolmogorov–Sinai (dynamical entropy. The same scenario appears in relation to the extension of algorithmic complexity theory to the quantum realm. A theorem of Brudno establishes that the complexity per unit time step along typical trajectories of a classical ergodic system equals the KS-entropy. In the following, we establish a similar relation between the Connes–Narnhofer–Thirring quantum dynamical entropy for the shift on quantum spin chains and the Gács algorithmic entropy. We further provide, for the same system, a weaker linkage between the latter algorithmic complexity and a different quantum dynamical entropy proposed by Alicki and Fannes.
Generalized entanglement entropy and holography
Bizet, Nana Cabo
2015-01-01
In this work, we first introduce a generalized von Neumann entropy that depends only on the density matrix. This is based on a previous proposal by one of us modifying the Shannon entropy by considering non-equilibrium systems on stationary states, and an entropy functional depending only on the probability. We propose a generalization of the replica trick and find that the resulting modified von Neumann entropy is precisely the previous mentioned entropy that was obtained by other assumptions. Then, we address the question whether alternative entanglement entropies can play a role in the gauge/gravity duality. Our focus are 2d CFT and their gravity duals. Our results show corrections to the von Neumann entropy $S_0$ that are larger than the usual $UV$ ones and also than the corrections to the length dependent $AdS_3$ entropy which result comparable to the $UV$ ones. The correction terms due to the new entropy would modify the Ryu-Takayanagi identification between the CFT and the gravitational $AdS_3$ entropi...
Black hole entropy with and without log correction in loop quantum gravity
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.
Ansari, Mohammad H
2016-01-01
A common approach to evaluate entropy in quantum systems is to solve a master-Bloch equation to determine density matrix and substitute it in entropy definition. However, this method has been recently understood to lack many energy correlators. The new correlators make entropy evaluation to be different from the substitution method described above. The reason for such complexity lies in the nonlinearity of entropy. In this paper we present a pedagogical approach to evaluate the new correlators and explain their contribution in the analysis. We show that the inherent nonlinearity in entropy makes the second law of thermodynamics to carry new terms associated to the new correlators. Our results show important new remarks on quantum black holes. Our formalism reveals that the notion of degeneracy of states at the event horizon makes an indispensable deviation from black hole entropy in the leading order.
Entropy: From Thermodynamics to Hydrology
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.
Generalized Entropy Concentration for Counts
Oikonomou, Kostas N
2016-01-01
We consider the phenomenon of entropy concentration under linear constraints in a discrete setting, using the "balls and bins" paradigm, but without the assumption that the number of balls allocated to the bins is known. Therefore instead of \\ frequency vectors and ordinary entropy, we have count vectors with unknown sum, and a certain generalized entropy. We show that if the constraints bound the allowable sums, this suffices for concentration to occur even in this setting. The concentration can be either in terms of deviation from the maximum generalized entropy value, or in terms of the norm of the difference from the maximum generalized entropy vector. Without any asymptotic considerations, we quantify the concentration in terms of various parameters, notably a tolerance on the constraints which ensures that they are always satisfied by an integral vector. Generalized entropy maximization is not only compatible with ordinary MaxEnt, but can also be considered an extension of it, as it allows us to address...
Müller-Lennert, Martin; Dupont-Dupuis, Fréderic; Szehr, Oleg
2013-01-01
in information theory and beyond. Various generalizations of Rényi entropies to the quantum setting have been proposed, most prominently Petz's quasi-entropies and Renner's conditional min-, max-, and collision entropy. However, these quantum extensions are incompatible and thus unsatisfactory. We propose a new...... quantum generalization of the family of Rényi entropies that contains the von Neumann entropy, min-entropy, collision entropy, and the max-entropy as special cases, thus encompassing most quantum entropies in use today. We show several natural properties for this definition, including data...
Residual entropy and simulated annealing
Ettelaie, R.; Moore, M. A.
1985-01-01
Determining the residual entropy in the simulated annealing approach to optimization is shown to provide useful information on the true ground state energy. The one-dimensional Ising spin glass is studied to exemplify the procedure and in this case the residual entropy is related to the number of one-spin flip stable metastable states. The residual entropy decreases to zero only logarithmically slowly with the inverse cooling rate.
Entropy and its relationship to allometry
Shour, Robert
2008-01-01
The entropy of an organism's capacity to supply energy through its circulatory system is 4/3 the entropy of the organism's energy requirements. Organisms appear to maximize entropy. The concept of entropy enables shorter derivations of some allometric equations, further evidence of the concept's utility. Entropy helps explain emergence in social, lexical, and biological networks.
Supersymmetric Renyi entropy in CFT{sub 2} and AdS{sub 3}
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}.
Entanglement Entropy of Black Holes
Solodukhin, Sergey N.
2011-10-01
The entanglement entropy is a fundamental quantity, which characterizes the correlations between sub-systems in a larger quantum-mechanical system. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff, which regulates the short-distance correlations. The geometrical nature of entanglement-entropy calculation is particularly intriguing when applied to black holes when the entangling surface is the black-hole horizon. I review a variety of aspects of this calculation: the useful mathematical tools such as the geometry of spaces with conical singularities and the heat kernel method, the UV divergences in the entropy and their renormalization, the logarithmic terms in the entanglement entropy in four and six dimensions and their relation to the conformal anomalies. The focus in the review is on the systematic use of the conical singularity method. The relations to other known approaches such as 't Hooft's brick-wall model and the Euclidean path integral in the optical metric are discussed in detail. The puzzling behavior of the entanglement entropy due to fields, which non-minimally couple to gravity, is emphasized. The holographic description of the entanglement entropy of the blackhole horizon is illustrated on the two- and four-dimensional examples. Finally, I examine the possibility to interpret the Bekenstein-Hawking entropy entirely as the entanglement entropy.
Entanglement Entropy of Black Holes
Sergey N. Solodukhin
2011-10-01
Full Text Available The entanglement entropy is a fundamental quantity, which characterizes the correlations between sub-systems in a larger quantum-mechanical system. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff, which regulates the short-distance correlations. The geometrical nature of entanglement-entropy calculation is particularly intriguing when applied to black holes when the entangling surface is the black-hole horizon. I review a variety of aspects of this calculation: the useful mathematical tools such as the geometry of spaces with conical singularities and the heat kernel method, the UV divergences in the entropy and their renormalization, the logarithmic terms in the entanglement entropy in four and six dimensions and their relation to the conformal anomalies. The focus in the review is on the systematic use of the conical singularity method. The relations to other known approaches such as ’t Hooft’s brick-wall model and the Euclidean path integral in the optical metric are discussed in detail. The puzzling behavior of the entanglement entropy due to fields, which non-minimally couple to gravity, is emphasized. The holographic description of the entanglement entropy of the black-hole horizon is illustrated on the two- and four-dimensional examples. Finally, I examine the possibility to interpret the Bekenstein-Hawking entropy entirely as the entanglement entropy.
Entropy Generation in Regenerative Systems
Kittel, Peter
1995-01-01
Heat exchange to the oscillating flows in regenerative coolers generates entropy. These flows are characterized by oscillating mass flows and oscillating temperatures. Heat is transferred between the flow and heat exchangers and regenerators. In the former case, there is a steady temperature difference between the flow and the heat exchangers. In the latter case, there is no mean temperature difference. In this paper a mathematical model of the entropy generated is developed for both cases. Estimates of the entropy generated by this process are given for oscillating flows in heat exchangers and in regenerators. The practical significance of this entropy is also discussed.
The different paths to entropy
Benguigui, L
2012-01-01
In order to undestand how the complex concept of entropy emerged,we propose a trip towards the past reviewing the works of Clausius, Boltzmann, Gibbs and Planck. In particular, since the Gibbs's work is not very well known, we present a detailed analysis, recalling the three definitions of the entropy that Gibbs gives. May be one of the most important aspect of the entropy is to see it as a thermodynamic potential like the other thermodynamic potentials as proposed by Callen. We close with some remarks on entropy and irreversibility.
Howard, Eric M
2016-01-01
We analyze spacetimes with horizons and study the thermodynamic aspects of causal horizons, suggesting that the resemblance between gravitational and thermodynamic systems has a deeper quantum mechanical origin. We find that the observer dependence of such horizons is a direct consequence of associating a temperature and entropy to a spacetime. The geometrical picture of a horizon acting as a one-way membrane for information flow can be accepted as a natural interpretation of assigning a quantum field theory to a spacetime with boundary, ultimately leading to a close connection with thermodynamics.
Minimum Error Entropy Classification
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.
Hansen, Britt Rosendahl; Kuhn, Luise Theil; Bahl, Christian Robert Haffenden
2010-01-01
in the temperature of a magnetic material when a magnetic eld is applied or removed. For many years, experimentalists have made use of dilute paramagnetic materials to achieve milliKelvin temperatures by use of the magnetocaloric eect. Also, research is done on materials, which might be used for hydrogen, helium...... the eect: the isothermal magnetic entropy change and the adiabatic temperature change. Some of the manifestations and utilizations of the MCE will be touched upon in a general way and nally I will talk about the results I have obtained on a sample of Gadolinium Iron Garnet (GdIG, Gd3Fe5O12), which...
Nonextensive entropy interdisciplinary applications
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.
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.
The development of sensors that provide geospatial information on crop and soil conditions has been a primary success for precision agriculture. However, further developments are needed to integrate geospatial data into computer algorithms that spatially optimize crop production while considering po...
Black Hole Entropy and Finite Geometry
Lévay, Péter; Vrana, Péter; Pracna, Petr
2009-01-01
It is shown that the $E_{6(6)}$ symmetric entropy formula describing black holes and black strings in D=5 is intimately tied to the geometry of the generalized quadrangle GQ$(2,4)$ with automorphism group the Weyl group $W(E_6)$. The 27 charges correspond to the points and the 45 terms in the entropy formula to the lines of GQ$(2,4)$. Different truncations with $15, 11$ and 9 charges are represented by three distinguished subconfigurations of GQ$(2,4)$, well-known to finite geometers; these are the "doily" (i. e. GQ$(2,2)$) with 15, the "perp-set" of a point with 11, and the "grid" (i. e. GQ$(2,1)$) with 9 points, respectively. In order to obtain the correct signs for the terms in the entropy formula, we use a non- commutative labelling for the points of GQ$(2,4)$. For the 40 different possible truncations with 9 charges this labelling yields 120 Mermin squares -- objects well-known from studies concerning Bell-Kochen-Specker-like theorems. These results are connected to our previous ones obtained for the $E_...
Information Entropy Measures for Stand Structural Diversity:Joint Entropy
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.
RG flow of entanglement entropy to thermal entropy
Kim, Ki-Seok
2016-01-01
Utilizing the holographic technique, we investigate how the entanglement entropy evolves along the RG flow. After defining a new generalized entanglement temperature which satisfies the thermodynamics-like law even in the IR regime, we show that the renormalized entanglement entropy and temperature in the IR limit approach to the thermal entropy and temperature of a real thermal system. Intriguingly, the thermalization of the IR entanglement entropy generally happens regardless of the detail of a dual field theory. We check such a universality for a two-dimensional CFT, a Lifshitz field theory, and a non-conformal field theory. In addition, we also show that for a two-dimensional scale invariant theory the first quantum correction to the IR entanglement entropy leads to a logarithmic term caused by the remnant of the short distance quantum correlation near the entangling surface.
Cleavage entropy as quantitative measure of protease specificity.
Fuchs, Julian E; von Grafenstein, Susanne; Huber, Roland G; Margreiter, Michael A; Spitzer, Gudrun M; Wallnoefer, Hannes G; Liedl, Klaus R
2013-04-01
A purely information theory-guided approach to quantitatively characterize protease specificity is established. We calculate an entropy value for each protease subpocket based on sequences of cleaved substrates extracted from the MEROPS database. We compare our results with known subpocket specificity profiles for individual proteases and protease groups (e.g. serine proteases, metallo proteases) and reflect them quantitatively. Summation of subpocket-wise cleavage entropy contributions yields a measure for overall protease substrate specificity. This total cleavage entropy allows ranking of different proteases with respect to their specificity, separating unspecific digestive enzymes showing high total cleavage entropy from specific proteases involved in signaling cascades. The development of a quantitative cleavage entropy score allows an unbiased comparison of subpocket-wise and overall protease specificity. Thus, it enables assessment of relative importance of physicochemical and structural descriptors in protease recognition. We present an exemplary application of cleavage entropy in tracing substrate specificity in protease evolution. This highlights the wide range of substrate promiscuity within homologue proteases and hence the heavy impact of a limited number of mutations on individual substrate specificity.
Cleavage entropy as quantitative measure of protease specificity.
Julian E Fuchs
2013-04-01
Full Text Available A purely information theory-guided approach to quantitatively characterize protease specificity is established. We calculate an entropy value for each protease subpocket based on sequences of cleaved substrates extracted from the MEROPS database. We compare our results with known subpocket specificity profiles for individual proteases and protease groups (e.g. serine proteases, metallo proteases and reflect them quantitatively. Summation of subpocket-wise cleavage entropy contributions yields a measure for overall protease substrate specificity. This total cleavage entropy allows ranking of different proteases with respect to their specificity, separating unspecific digestive enzymes showing high total cleavage entropy from specific proteases involved in signaling cascades. The development of a quantitative cleavage entropy score allows an unbiased comparison of subpocket-wise and overall protease specificity. Thus, it enables assessment of relative importance of physicochemical and structural descriptors in protease recognition. We present an exemplary application of cleavage entropy in tracing substrate specificity in protease evolution. This highlights the wide range of substrate promiscuity within homologue proteases and hence the heavy impact of a limited number of mutations on individual substrate specificity.
On determining absolute entropy without quantum theory or the third law of thermodynamics
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.
Black Hole Radiation and Volume Statistical Entropy
Rabinowitz, M
2005-01-01
The simplest possible equations for Hawking radiation, and other black hole radiated power is derived in terms of black hole density. Black hole density also leads to the simplest possible model of a gas of elementary constituents confined inside a gravitational bottle of Schwarzchild radius at tremendous pressure, which yields identically the same functional dependence as the traditional black hole entropy. Variations of Sbh are can be obtained which depend on the occupancy of phase space cells. A relation is derived between the constituent momenta and the black hole radius RH
Weak entropy inequalities and entropic convergence
GAO FuQing; LI LiNa
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.
Weak entropy inequalities and entropic convergence
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.
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.
Entropy production by resonance decays
Ochs, S; Ochs, Stefan; Heinz, Ulrich
1996-01-01
We investigate entropy production for an expanding system of particles and resonances with isospin symmetry -- in our case pions and \\rho mesons -- within the framework of relativistic kinetic theory. A cascade code to simulate the kinetic equations is developed and results for entropy production and particle spectra are presented.
Kevin H. Knuth
2015-02-01
Full Text Available We are pleased to announce the “Entropy Best Paper Award” for 2015. Nominations were selected by the Editor-in-Chief and designated Editorial Board Members from all the papers published in 2011. Reviews and research papers were evaluated separately. We gladly announce that the following three papers have won the Entropy Best Paper Award in 2015:[...
Ignaccolo, M; Jernajczyk, W; Grigolini, P; West, B J
2009-01-01
EEG time series are analyzed using the diffusion entropy method. The resulting EEG entropy manifests short-time scaling, asymptotic saturation and an attenuated alpha-rhythm modulation. These properties are faithfully modeled by a phenomenological Langevin equation interpreted within a neural network context.
Configurational entropy of glueball states
Bernardini, Alex E.; Braga, Nelson R. F.; da Rocha, Roldão
2017-02-01
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.
Conditional entropy of glueball states
Bernardini, Alex E; da Rocha, Roldao
2016-01-01
The conditional 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 conditional entropy is studied as a function of the glueball spin and of the mass, providing information about the stability of the glueball states.
Evaluation of pedodiversity and land use diversity in terms of the Shannon Entropy
Yabuki, Tetsuo; Nakatani, Yoko
2009-01-01
Recently, the Shannon entropy, which was introduced originally as a measure of information amount, has been widely used as a useful index of various diversities such as biodiversity and geodiversity. In this work we have evaluated the diversity of soil and land use, in both composition distributions and spatial distributions, in terms of the Shanonn entropy. Moreover we have also proposed how to estimate the connection between the diversity of soil and land use in the spatial distribution using mutual entropy, and carried out the estimation of its connection.
A new Color Feature Extraction method Based on Dynamic Color Distribution Entropy of Neighbourhoods
Fatemeh Alamdar
2011-09-01
Full Text Available One of the important requirements in image retrieval, indexing, classification, clustering and etc. is extracting efficient features from images. The color feature is one of the most widely used visual features. Use of color histogram is the most common way for representing color feature. One of disadvantage of the color histogram is that it does not take the color spatial distribution into consideration. In this paper dynamic color distribution entropy of neighborhoods method based on color distribution entropy is presented, which effectively describes the spatial information of colors. The image retrieval results in compare to improved color distribution entropy show the acceptable efficiency of this approach.
Entropy in molecular association and folding: Theory and computation
Brady, Gerald Patrick, Jr.
1997-09-01
This thesis addresses two central questions regarding entropy changes in protein folding and molecular recognition: (1) Can the entropy of a system be decomposed into individual components arising from particular atomic groups or physical interactions? and (2) Can molecular association thermodynamics be reliably calculated using current computational methods? To address the first question, the statistical-mechanical justification for entropy decomposition is theoretically investigated via 'cumulant' and 'beta-derivative' expansions of the entropy. The cumulant expansion demonstrates that entropy components may indeed be meaningfully ascribed to particular groups or interactions, although these components are coupled both explicitly via cross-terms and implicitly through the Boltzmann factor. The beta-derivative expansion (βDE) is shown to yield a complete decomposition of entropy, in that, the total entropy is completely partitioned amongst the contributing groups or interactions, with no individually unattributable cross- terms remaining. The question of calculating molecular association thermodynamics is examined via computational analysis of binding and solvation in a model peptide system. In particular, the gas ←⇔ crystal ←⇔ solution phase equilibrium thermodynamics of cyclic di-glycine (cGG) and cyclic di- alanine (cAA) is computed using a variety of techniques, and the results are compared to experimental data. The calculated cGG gas-to-solution free energy and gas-to- crystal enthalpy agree very well with experimental values; however, the gas-to-crystal entropy is overestimated by 15 eu. Of particular note, a reliable value of 14 eu is obtained for the association entropy barrier to gas ⇒ crystal transfer, the unfavorable net result of exchanging translational and rotational freedom in the gas phase for vibrational motion in the crystal. A mean-field Einstein Model underestimates the vibrational entropy of the crystal by 15 eu and, thus, appears
Winter, Andreas
2016-10-01
We present a bouquet of continuity bounds for quantum entropies, falling broadly into two classes: first, a tight analysis of the Alicki-Fannes continuity bounds for the conditional von Neumann entropy, reaching almost the best possible form that depends only on the system dimension and the trace distance of the states. Almost the same proof can be used to derive similar continuity bounds for the relative entropy distance from a convex set of states or positive operators. As applications, we give new proofs, with tighter bounds, of the asymptotic continuity of the relative entropy of entanglement, E R , and its regularization {E_R^{∞}}, as well as of the entanglement of formation, E F . Using a novel "quantum coupling" of density operators, which may be of independent interest, we extend the latter to an asymptotic continuity bound for the regularized entanglement of formation, aka entanglement cost, {E_C=E_F^{∞}}. Second, we derive analogous continuity bounds for the von Neumann entropy and conditional entropy in infinite dimensional systems under an energy constraint, most importantly systems of multiple quantum harmonic oscillators. While without an energy bound the entropy is discontinuous, it is well-known to be continuous on states of bounded energy. However, a quantitative statement to that effect seems not to have been known. Here, under some regularity assumptions on the Hamiltonian, we find that, quite intuitively, the Gibbs entropy at the given energy roughly takes the role of the Hilbert space dimension in the finite-dimensional Fannes inequality.
A new parallel algorithm for image matching based on entropy
董开坤; 胡铭曾
2001-01-01
Presents a new parallel image matching algorithm based on the concept of entropy feature vector and suitable to SIMD computer, which, in comparison with other algorithms, has the following advantages: ( 1 ) The spatial information of an image is appropriately introduced into the definition of image entropy. (2) A large number of multiplication operations are eliminated, thus the algorithm is sped up. (3) The shortcoming of having to do global calculation in the first instance is overcome, and concludes the algorithm has very good locality and is suitable for parallel processing.
Thermodynamics, entropy and waterwheels
Bagnoli, Franco
2016-01-01
In textbooks, it is often repeated that Carnot arrived to the formulation of the second law of thermodynamics without knowing the first, using the caloric theory. In fact, in his book, R\\'eflexions sur la puissance motrice du feu, he often repeats that the "fall" of the caloric through a heat engine is equivalent to the fall of the water through a water wheel. Actually, one can play the analogy between thermal and hydraulic machines all the way down, and discover, with the help of the first principle and introducing the concept of the absolute height, what really "falls" through a waterwheel, i.e., the entropy. Adding a bit of relativity it is possible to extend the analogy to real machines and also to introduce the analogous of third law of thermodynamics.
Population entropies estimates of proteins
Low, Wai Yee
2017-05-01
The Shannon entropy equation provides a way to estimate variability of amino acids sequences in a multiple sequence alignment of proteins. Knowledge of protein variability is useful in many areas such as vaccine design, identification of antibody binding sites, and exploration of protein 3D structural properties. In cases where the population entropies of a protein are of interest but only a small sample size can be obtained, a method based on linear regression and random subsampling can be used to estimate the population entropy. This method is useful for comparisons of entropies where the actual sequence counts differ and thus, correction for alignment size bias is needed. In the current work, an R based package named EntropyCorrect that enables estimation of population entropy is presented and an empirical study on how well this new algorithm performs on simulated dataset of various combinations of population and sample sizes is discussed. The package is available at https://github.com/lloydlow/EntropyCorrect. This article, which was originally published online on 12 May 2017, contained an error in Eq. (1), where the summation sign was missing. The corrected equation appears in the Corrigendum attached to the pdf.
Development of a Refractory High Entropy Superalloy
Oleg N. Senkov
2016-03-01
Full Text Available Microstructure, phase composition and mechanical properties of a refractory high entropy superalloy, AlMo0.5NbTa0.5TiZr, are reported in this work. The alloy consists of a nano-scale mixture of two phases produced by the decomposition from a high temperature body-centered cubic (BCC phase. The first phase is present in the form of cuboidal-shaped nano-precipitates aligned in rows along <100>-type directions, has a disordered BCC crystal structure with the lattice parameter a1 = 326.9 ± 0.5 pm and is rich in Mo, Nb and Ta. The second phase is present in the form of channels between the cuboidal nano-precipitates, has an ordered B2 crystal structure with the lattice parameter a2 = 330.4 ± 0.5 pm and is rich in Al, Ti and Zr. Both phases are coherent and have the same crystallographic orientation within the former grains. The formation of this modulated nano-phase structure is discussed in the framework of nucleation-and-growth and spinodal decomposition mechanisms. The yield strength of this refractory high entropy superalloy is superior to the yield strength of Ni-based superalloys in the temperature range of 20 °C to 1200 °C.
Entanglement entropy converges to classical entropy around periodic orbits
Asplund, Curtis T., E-mail: ca2621@columbia.edu [Department of Physics, Columbia University, 538 West 120th Street, New York, NY 10027 (United States); Berenstein, David, E-mail: dberens@physics.ucsb.edu [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
2016-03-15
We consider oscillators evolving subject to a periodic driving force that dynamically entangles them, and argue that this gives the linearized evolution around periodic orbits in a general chaotic Hamiltonian dynamical system. We show that the entanglement entropy, after tracing over half of the oscillators, generically asymptotes to linear growth at a rate given by the sum of the positive Lyapunov exponents of the system. These exponents give a classical entropy growth rate, in the sense of Kolmogorov, Sinai and Pesin. We also calculate the dependence of this entropy on linear mixtures of the oscillator Hilbert-space factors, to investigate the dependence of the entanglement entropy on the choice of coarse graining. We find that for almost all choices the asymptotic growth rate is the same.
The concept of entropy. Relation between action and entropy
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.
Gravitational entropy of cosmic expansion
Sussman, Roberto A
2014-01-01
We apply a recent proposal to define "gravitational entropy" to the expansion of cosmic voids within the framework of non-perturbative General Relativity. By considering CDM void configurations compatible with basic observational constraints, we show that this entropy grows from post-inflationary conditions towards a final asymptotic value in a late time fully non-linear regime described by the Lemaitre-Tolman-Bondi (LTB) dust models. A qualitatively analogous behavior occurs if we assume a positive cosmological constant consistent with a $\\Lambda$-CDM background model. However, the $\\Lambda$ term introduces a significant suppression of entropy growth with the terminal equilibrium value reached at a much faster rate.
Ingo Klein
2016-07-01
Full Text Available A new kind of entropy will be introduced which generalizes both the differential entropy and the cumulative (residual entropy. The generalization is twofold. First, we simultaneously define the entropy for cumulative distribution functions (cdfs and survivor functions (sfs, instead of defining it separately for densities, cdfs, or sfs. Secondly, we consider a general “entropy generating function” φ, the same way Burbea et al. (IEEE Trans. Inf. Theory 1982, 28, 489–495 and Liese et al. (Convex Statistical Distances; Teubner-Verlag, 1987 did in the context of φ-divergences. Combining the ideas of φ-entropy and cumulative entropy leads to the new “cumulative paired φ-entropy” ( C P E φ . This new entropy has already been discussed in at least four scientific disciplines, be it with certain modifications or simplifications. In the fuzzy set theory, for example, cumulative paired φ-entropies were defined for membership functions, whereas in uncertainty and reliability theories some variations of C P E φ were recently considered as measures of information. With a single exception, the discussions in the scientific disciplines appear to be held independently of each other. We consider C P E φ for continuous cdfs and show that C P E φ is rather a measure of dispersion than a measure of information. In the first place, this will be demonstrated by deriving an upper bound which is determined by the standard deviation and by solving the maximum entropy problem under the restriction of a fixed variance. Next, this paper specifically shows that C P E φ satisfies the axioms of a dispersion measure. The corresponding dispersion functional can easily be estimated by an L-estimator, containing all its known asymptotic properties. C P E φ is the basis for several related concepts like mutual φ-information, φ-correlation, and φ-regression, which generalize Gini correlation and Gini regression. In addition, linear rank tests for scale that
Zero Modes and Entanglement Entropy
Yazdi, Yasaman K
2016-01-01
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.
Rindler Energy is Wald Entropy
Halyo, Edi
2014-01-01
We show that, in any theory of gravity, the entropy of any nonextreme black hole is given by $2 \\pi E_R$ where $E_R$ is the dimensionless Rindler energy. Separately, we show that $E_R$ is exactly Wald's Noether charge and therefore this entropy is identical to Wald entropy. However, it is off--shell and derived solely from the time evolution of the black hole. We examine Gauss--Bonnet black holes as an example and speculate on the degrees of freedom that $E_R$ counts.
Nonequilibrium stationary states and entropy.
Gallavotti, G; Cohen, E G D
2004-03-01
In transformations between nonequilibrium stationary states, entropy might not be a well defined concept. It might be analogous to the "heat content" in transformations in equilibrium which is not well defined either, if they are not isochoric (i.e., do involve mechanical work). Hence we conjecture that in a nonequilibrium stationary state the entropy is just a quantity that can be transferred or created, such as heat in equilibrium, but has no physical meaning as "entropy content" as a property of the system.
Relative Entropy and Torsion Coupling
Lin, Feng-Li
2016-01-01
We evaluate the relative entropy on a ball region near the UV fixed point of a holographic conformal field theory deformed by a fermionic operator of nonzero vacuum expectation value. The positivity of the relative entropy considered here is implied by the expected monotonicity of decrease of quantum entanglement under RG flow. The calculations are done in the perturbative framework of Einstein-Cartan gravity in four-dimensional asymptotically anti-de Sitter space with a postulated standard bilinear coupling between axial fermion current and torsion. Our results however imply that the positivity of the relative entropy disfavors such a coupling.
Osvaldo Guedes Filho
2010-02-01
Full Text Available Soil properties are closely related with crop production and spite of the measures implemented, spatial variation has been repeatedly observed and described. Identifying and describing spatial variations of soil properties and their effects on crop yield can be a powerful decision-making tool in specific land management systems. The objective of this research was to characterize the spatial and temporal variations in crop yield and chemical and physical properties of a Rhodic Hapludox soil under no-tillage. The studied area of 3.42 ha had been cultivated since 1985 under no-tillage crop rotation in summer and winter. Yield and soil property were sampled in a regular 10 x 10 m grid, with 302 sample points. Yields of several crops were analyzed (soybean, maize, triticale, hyacinth bean and castor bean as well as soil chemical (pH, Soil Organic Matter (SOM, P, Ca2+, Mg2+, H + Al, B, Fe, Mn, Zn, CEC, sum of bases (SB, and base saturation (V % and soil physical properties (saturated hydraulic conductivity, texture, density, total porosity, and mechanical penetration resistance. Data were analyzed using geostatistical analysis procedures and maps based on interpolation by kriging. Great variation in crop yields was observed in the years evaluated. The yield values in the Northern region of the study area were high in some years. Crop yields and some physical and soil chemical properties were spatially correlated.Os atributos do solo condicionam a produção das culturas e, apesar das práticas adotadas, a variação espacial destes tem sido recorrentemente encontrada e descrita. A caracterização da variabilidade espacial dos atributos do solo e de seus efeitos sobre a produtividade das culturas pode ser utilizada como uma poderosa ferramenta para tomada de decisão em sistemas de manejo específico. O objetivo deste trabalho foi caracterizar a variabilidade espacial e temporal da produtividade de culturas e de atributos químicos e físicos de um
Short interval expansion of R\\'enyi entropy on torus
Chen, Bin; Zhang, Jia-ju
2016-01-01
We investigate the short interval expansion of the R\\'enyi entropy for two-dimensional conformal field theory (CFT) on a torus. We require the length of the interval $\\ell$ 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 R\\'enyi entropy at any temperature. In particular, we pay special attention to the large $c$ CFTs dual to the AdS$_3$ gravity and its cousins. At both low and high temperature limits, we read the R\\'enyi entropies to order $\\ell^6$, 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.
Time Evolution of Entanglement Entropy from Black Hole Interiors
Hartman, Thomas
2013-01-01
We compute the time-dependent entanglement entropy of a CFT which starts in relatively simple initial states. The initial states are the thermofield double for thermal states, dual to eternal black holes, and a particular pure state, dual to a black hole formed by gravitational collapse. The entanglement entropy grows linearly in time. This linear growth is directly related to the growth of the black hole interior measured along "nice" spatial slices. These nice slices probe the spacelike direction in the interior, at a fixed special value of the interior time. In the case of a two-dimensional CFT, we match the bulk and boundary computations of the entanglement entropy. We briefly discuss the long time behavior of various correlators, computed via classical geodesics or surfaces, and point out that their exponential decay comes about for similar reasons. We also present the time evolution of the wavefunction in the tensor network description.
Time evolution of entanglement entropy from black hole interiors
Hartman, Thomas; Maldacena, Juan
2013-05-01
We compute the time-dependent entanglement entropy of a CFT which starts in relatively simple initial states. The initial states are the thermofield double for thermal states, dual to eternal black holes, and a particular pure state, dual to a black hole formed by gravitational collapse. The entanglement entropy grows linearly in time. This linear growth is directly related to the growth of the black hole interior measured along "nice" spatial slices. These nice slices probe the spacelike direction in the interior, at a fixed special value of the interior time. In the case of a two-dimensional CFT, we match the bulk and boundary computations of the entanglement entropy. We briefly discuss the long time behavior of various correlators, computed via classical geodesics or surfaces, and point out that their exponential decay comes about for similar reasons. We also present the time evolution of the wavefunction in the tensor network description.
Rodrigues da Silva, Vicente de P; Belo Filho, Adelgcio F; Rodrigues Almeida, Rafaela S; de Holanda, Romildo Morant; da Cunha Campos, João Hugo Baracuy
2016-02-15
The principle of maximum entropy can provide consistent basis to analyze water resources and geophysical processes in general. In this paper, we propose to assess the space-time variability of rainfall and streamflow in northeastern region of Brazil using the Shannon entropy. Mean values of marginal and relative entropies were computed for a 10-year period from 189 stations in the study area and entropy maps were then constructed for delineating annual and seasonal characteristics of rainfall and streamflow. The Mann-Kendall test was used to evaluate the long-term trend in marginal entropy as well as relative entropy for two sample stations. High degree of similarity was found between rainfall and streamflow, particularly during dry season. Both rainfall and streamflow variability can satisfactorily be obtained in terms of marginal entropy as a comprehensive measure of the regional uncertainty of these hydrological events. The Shannon entropy produced spatial patterns which led to a better understanding of rainfall and streamflow characteristics throughout the northeastern region of Brazil. The total relative entropy indicated that rainfall and streamflow carried the same information content at annual and rainy season time scales.
Entropy counting for microscopic black holes in LQG
Corichi, A; Fernandez-Borja, E; Corichi, Alejandro; Diaz-Polo, Jacobo; Fernandez-Borja, Enrique
2007-01-01
Quantum black holes within the loop quantum gravity (LQG) framework are considered. The number of microscopic states that are consistent with a black hole of a given horizon area $A_0$ are computed and the statistical entropy, as a function of the area, is obtained for $A_0$ up to $550 l^2_P$. The results are consistent with an asymptotic linear relation and a logarithmic correction with a coefficient equal to -1/2. The Barbero-Immirzi parameter that yields the asymptotic linear relation compatible with the Bekenstein-Hawking entropy is shown to coincide with a value close to $\\gamma=0.274$, which has been previously obtained analytically. However, a new and unexpected functional form for the entropy is found for small, Planck size, black holes that calls for a physical interpretation.
Feature selection with neighborhood entropy-based cooperative game theory.
Zeng, Kai; She, Kun; Niu, Xinzheng
2014-01-01
Feature selection plays an important role in machine learning and data mining. In recent years, various feature measurements have been proposed to select significant features from high-dimensional datasets. However, most traditional feature selection methods will ignore some features which have strong classification ability as a group but are weak as individuals. To deal with this problem, we redefine the redundancy, interdependence, and independence of features by using neighborhood entropy. Then the neighborhood entropy-based feature contribution is proposed under the framework of cooperative game. The evaluative criteria of features can be formalized as the product of contribution and other classical feature measures. Finally, the proposed method is tested on several UCI datasets. The results show that neighborhood entropy-based cooperative game theory model (NECGT) yield better performance than classical ones.
A novel averaging technique for discrete entropy-stable dissipation operators for ideal MHD
Derigs, Dominik; Winters, Andrew R.; Gassner, Gregor J.; Walch, Stefanie
2017-02-01
Entropy stable schemes can be constructed with a specific choice of the numerical flux function. First, an entropy conserving flux is constructed. Secondly, an entropy stable dissipation term is added to this flux to guarantee dissipation of the discrete entropy. Present works in the field of entropy stable numerical schemes are concerned with thorough derivations of entropy conservative fluxes for ideal MHD. However, as we show in this work, if the dissipation operator is not constructed in a very specific way, it cannot lead to a generally stable numerical scheme. The two main findings presented in this paper are that the entropy conserving flux of Ismail & Roe can easily break down for certain initial conditions commonly found in astrophysical simulations, and that special care must be taken in the derivation of a discrete dissipation matrix for an entropy stable numerical scheme to be robust. We present a convenient novel averaging procedure to evaluate the entropy Jacobians of the ideal MHD and the compressible Euler equations that yields a discretization with favorable robustness properties.
A Note on Burg’s Modified Entropy in Statistical Mechanics
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.
Entropy exchange for infinite-dimensional systems
Duan, Zhoubo; Hou, Jinchuan
2017-01-01
In this paper the entropy exchange for channels and states in infinite-dimensional systems are defined and studied. It is shown that, this entropy exchange depends only on the given channel and the state. An explicit expression of the entropy exchange in terms of the state and the channel is proposed. The generalized Klein’s inequality, the subadditivity and the triangle inequality about the entropy including infinite entropy for the infinite-dimensional systems are established, and then, applied to compare the entropy exchange with the entropy change. PMID:28164995
An adaptable binary entropy coder
Kiely, A.; Klimesh, M.
2001-01-01
We present a novel entropy coding technique which is based on recursive interleaving of variable-to-variable length binary source codes. We discuss code design and performance estimation methods, as well as practical encoding and decoding algorithms.
Entropy of Quantum States: Ambiguities
Balachandran, A P; Vaidya, S
2012-01-01
The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. As pointed out to us by Sorkin, this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy. This non-unique entropy can occur at zero temperature. We will argue elsewhere in detail that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies. Finally, we establish the analogue of an H-theorem for this entropy by showing that its evolution is Markovian, determined by a stochastic matrix.
Entropy of Open Lattice Systems
Derrida, B.; Lebowitz, J. L.; Speer, E. R.
2007-03-01
We investigate the behavior of the Gibbs-Shannon entropy of the stationary nonequilibrium measure describing a one-dimensional lattice gas, of L sites, with symmetric exclusion dynamics and in contact with particle reservoirs at different densities. In the hydrodynamic scaling limit, L → ∞, the leading order ( O( L)) behavior of this entropy has been shown by Bahadoran to be that of a product measure corresponding to strict local equilibrium; we compute the first correction, which is O(1). The computation uses a formal expansion of the entropy in terms of truncated correlation functions; for this system the k th such correlation is shown to be O( L - k+1). This entropy correction depends only on the scaled truncated pair correlation, which describes the covariance of the density field. It coincides, in the large L limit, with the corresponding correction obtained from a Gaussian measure with the same covariance.
Renyi entropy and conformal defects
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.
Quantum entropy and special relativity.
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.
Wang, W. H.
2014-10-01
The high-entropy alloys are defined as solid-solution alloys containing five or more than five principal elements in equal or near-equal atomic percent. The concept of high mixing entropy introduces a new way for developing advanced metallic materials with unique physical and mechanical properties that cannot be achieved by the conventional microalloying approach based on only a single base element. The metallic glass (MG) is the metallic alloy rapidly quenched from the liquid state, and at room temperature it still shows an amorphous liquid-like structure. Bulk MGs represent a particular class of amorphous alloys usually with three or more than three components but based on a single principal element such as Zr, Cu, Ce, and Fe. These materials are very attractive for applications because of their excellent mechanical properties such as ultrahigh (near theoretical) strength, wear resistance, and hardness, and physical properties such as soft magnetic properties. In this article, we review the formation and properties of a series of high-mixing-entropy bulk MGs based on multiple major elements. It is found that the strategy and route for development of the high-entropy alloys can be applied to the development of the MGs with excellent glass-forming ability. The high-mixing-entropy bulk MGs are then loosely defined as metallic glassy alloys containing five or more than five elements in equal or near-equal atomic percent, which have relatively high mixing entropy compared with the conventional MGs based on a single principal element. The formation mechanism, especially the role of the mixing entropy in the formation of the high-entropy MGs, is discussed. The unique physical, mechanical, chemical, and biomedical properties of the high-entropy MGs in comparison with the conventional metallic alloys are introduced. We show that the high-mixing-entropy MGs, along the formation idea and strategy of the high-entropy alloys and based on multiple major elements, might provide
Entropy Production in a Lepton-Photon Universe
Husdal, Lars
2016-01-01
We look at the entropy production during the lepton era in the early Universe by using a model where we exclude all particles except the leptons and photons. We assume a temperature dependent viscosity as calculated recently by one of us (Husdal 2016) with use of relativistic kinetic theory. We consider only the bulk viscosity, the shear viscosity being omitted because of spatial isotropy. The rate of entropy production is highest just before the neutrinos decouple. Our results show that the increase in entropy during the lepton era is quite small, about 0.071\\% at a decoupling temperature of $T=10^{10}~\\mathrm{K}$. This result is slightly smaller than that obtained earlier by Caderni and Fabbri (1977). After the neutrino decoupling, when the Universe has entered the photon era, kinetic-theory arguments no longer support the appearance of a bulk viscosity. At high temperatures and a stable particle ratio, entropy production ($\\dv*{\\sigma}{T}$) goes as $T^{-8}$, with the total entropy ($\\Delta \\sigma$) increas...
Entropy production in a lepton-photon universe
Husdal, Lars; Brevik, Iver
2017-02-01
We look at the entropy production during the lepton era in the early universe by using a model where we exclude all particles except the leptons and photons. We assume a temperature dependent viscosity as calculated recently by one of us (Husdal in Astrophys. Space Sci. 361(8):1, 2016b) with the use of relativistic kinetic theory. We consider only the bulk viscosity, the shear viscosity being omitted because of spatial isotropy. The rate of entropy production is highest just before the neutrinos decouple. Our results show that the increase in entropy during the lepton era is quite small, about 0.071 % at a decoupling temperature of T=10^{10} K. This result is slightly smaller than that obtained earlier by Caderni and Fabbri (Phys. Lett. B 69:508, 1977). After the neutrino decoupling, when the Universe has entered the photon era, kinetic theory arguments no longer support the appearance of a bulk viscosity. At high temperatures and a stable particle ratio, entropy production (d{σ }/d{T}) goes as T^{-8}, with the total entropy (Δ σ) increasing as T^{-7}. These rates go slightly down just before the neutrinos decouple, where Δσ∝ T^{-6.2}.
Crack status analysis for concrete dams based on measured entropy
WU BangBin; WU ZhongRu; CHEN Bo; SU HuaiZhi; BAO TengFei; WANG ShaoWei
2016-01-01
The integrity and safety of concrete dams are seriously affected by the existing cracks in dam bodies,and some serious cracks may cause dam failure or disaster.The propagation of cracks in concrete dams is accompanied by changes in energy distribution,which can be represented by changes in the structure's system entropy.Therefore,the entropy theory can be used in analyzing the behavior of dam cracks.Due to the randomness and locality of crack propagation,it is difficult to predict the location of cracks by traditional monitoring methods.To solve this problem,the influence of spatial positions of monitoring points on inspection zones is represented by a weight index,and the weight index is determined by the distance measure method proposed in this paper.Through the weighted linear fusion method,the entropy of multiple monitoring points is obtained for analyzing the behavior of dam cracks in the selected zones.Meanwhile,the catastrophe theory is used as the variation criterion of an entropy sequence in order to predict the instability time of dam cracks.Case studies are put forward on a high arch dam,and the fusion entropy is calculated according to the monitoring data from strain gauges.Results show that the proposed method can effectively predict the occurrence time and location of dam cracks regardless of the layout of monitoring instruments,and it is a new way to analyze the occurrence and propagation of dam cracks.
Good Use of a `Bad' Metaphor. Entropy as Disorder
Haglund, Jesper
2017-05-01
Entropy is often introduced to students through the use of the disorder metaphor. However, many weaknesses and limitations of this metaphor have been identified, and it has therefore been argued that it is more harmful than useful in teaching. For instance, under the influence of the disorder metaphor, students tend to focus on spatial configuration with regard to entropy but disregard the role of energy, which may lead their intuition astray in problem solving. Albeit so, a review of research of students' ideas about entropy in relation to the disorder metaphor shows that students can use the metaphor in developing a more nuanced, complex view of the concept, by connecting entropy as disorder to other concepts such as microstates and spreading. The disorder metaphor—in combination with other explanatory approaches—can be used as a resource for learning, in giving students an early flavour of what entropy means, so long as we acknowledge its limitations; we can put this "bad" metaphor to good use in teaching.
Boundary effects in entanglement entropy
Berthiere, Clément; Solodukhin, Sergey N.
2016-09-01
We present a number of explicit calculations of Renyi and entanglement entropies in situations where the entangling surface intersects the boundary of d-dimensional Minkowski spacetime. When the boundary is a single plane we compute the contribution to the entropy due to this intersection, first in the case of the Neumann and Dirichlet boundary conditions, and then in the case of a generic Robin type boundary condition. The flow in the boundary coupling between the Neumann and Dirichlet phases is analyzed in arbitrary dimension d and is shown to be monotonic, the peculiarity of d = 3 case is noted. We argue that the translational symmetry along the entangling surface is broken due the presence of the boundary which reveals that the entanglement is not homogeneous. In order to characterize this quantitatively, we introduce a density of entanglement entropy and compute it explicitly. This quantity clearly indicates that the entanglement is maximal near the boundary. We then consider the situation where the boundary is composed of two parallel planes at a finite separation and compute the entanglement entropy as well as its density in this case. The complete contribution to entanglement entropy due to the boundaries is shown not to depend on the distance between the planes and is simply twice the entropy in the case of single plane boundary. Additionally, we find how the area law, the part in the entropy proportional to the area of entire entangling surface, depends on the size of the separation between the two boundaries. The latter is shown to appear in the UV finite part of the entropy.
Holographic avatars of entanglement entropy
Barbon, J.L.F. [Instituto de Fisica Teorica IFT UAM/CSIC, Ciudad Universitaria de Cantoblanco 28049, Madrid (Spain)
2009-07-15
This is a rendering of the blackboard lectures at the 2008 Cargese summer school, discussing some elementary facts regarding the application of AdS/CFT techniques to the computation of entanglement entropy in strongly coupled systems. We emphasize the situations where extensivity of the entanglement entropy can be used as a crucial criterion to characterize either nontrivial dynamical phenomena at large length scales, or nonlocality in the short-distance realm.
On Entropy Bounds and Holography
Halyo, Edi
2009-01-01
We show that the holographic entropy bound for gravitational systems and the Bekenstein entropy bound for nongravitational systems are holographically related. Using the AdS/CFT correspondence, we find that the Bekenstein bound on the boundary is obtained from the holographic bound in the bulk by minimizing the boundary energy with respect the AdS radius or the cosmological constant. This relation may also ameliorate some problems associated with the Bekenstein bound.
Review on Image Segmentation Based on Entropy%图像分割的熵方法综述
曹建农
2012-01-01
The image segmentation based on entropy is analyzed and reviewed including one-dimensional maximum entropy, minimum cross entropy, maximum cross entropy and so on. The relations of Shannon entropy, Tsallis entropy and Renyi entropy are analyzed and commented, and the performance of two dimensional (high dimension) entropy and spatial entropy is also appraised. In conclusion, it points out the future research direction, such as the computational efficiency of the high-dimensional entropy model and one-dimensional entropy and other theories integrated.%对图像分割的熵方法进行较全面地分析和综述,其中包括一维最大熵、最小交叉熵、最大交叉熵图像分割方法等.对Shannon熵、Tsallis熵及Renyi熵之间的关系等进行分析与评述.对二维(高维)熵及空间熵等进行分析与评述.最后指出一维熵与其它理论的有机结合、高维熵模型的计算效率等未来研究方向.
Applications of Entropy in Finance: A Review
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.
Possible extended forms of thermodynamic entropy
Sasa, Shin-ichi
2013-01-01
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 therm...
Horizon entropy and higher curvature equations of state
Guedens, Raf; Sarkar, Sudipta
2011-01-01
The Clausius relation between entropy change and heat flux has previously been used to derive Einstein's field equations as an equation of state. In that derivation the entropy is proportional to the area of a local causal horizon, and the heat is the energy flux across the horizon, defined relative to an approximate boost Killing vector. We examine here whether a similar derivation can be given for extensions beyond Einstein gravity to include higher derivative and higher curvature terms. We review previous proposals which, in our opinion, are problematic or incomplete. Refining one of these, we assume that the horizon entropy depends on an approximate local Killing vector in a way that mimics the diffeomorphism Noether charge that yields the entropy of a stationary black hole. We show how this can be made to work if various restrictions are imposed on the nature of the horizon slices and the approximate Killing vector. Also, an integrability condition on the assumed horizon entropy density must hold. This c...
Entropy Production in Chemical Reactors
Kingston, Diego; Razzitte, Adrián C.
2017-06-01
We have analyzed entropy production in chemically reacting systems and extended previous results to the two limiting cases of ideal reactors, namely continuous stirred tank reactor (CSTR) and plug flow reactor (PFR). We have found upper and lower bounds for the entropy production in isothermal systems and given expressions for non-isothermal operation and analyzed the influence of pressure and temperature in entropy generation minimization in reactors with a fixed volume and production. We also give a graphical picture of entropy production in chemical reactions subject to constant volume, which allows us to easily assess different options. We show that by dividing a reactor into two smaller ones, operating at different temperatures, the entropy production is lowered, going as near as 48 % less in the case of a CSTR and PFR in series, and reaching 58 % with two CSTR. Finally, we study the optimal pressure and temperature for a single isothermal PFR, taking into account the irreversibility introduced by a compressor and a heat exchanger, decreasing the entropy generation by as much as 30 %.
Entropy stable wall boundary conditions for the compressible Navier-Stokes equations
Parsani, Matteo; 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...
Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations
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.
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.
Scaling of the asymptotic entropy jump in the superadiabatic layers of stellar atmospheres
Magic, Zazralt
2016-01-01
Stellar structure calculations are able to predict precisely the properties of stars during their evolution. However, convection is still modelled by the mixing length theory; therefore, the upper boundary conditions near the optical surface do not agree with asteroseismic observations. We want to improve how the outer boundary conditions are determined in stellar structure calculations. We study realistic 3D stellar atmosphere models to find alternative properties. We find that the asymptotic entropy run of the superadiabatic convective surface layers exhibit a distinct universal stratification when normalised by the entropy minimum and jump. The normalised entropy can be represented by a 5th order polynomial very accurately, and a 3rd order polynomial also yields accurate coefficients. This generic entropy stratification or the solar stratification, when scaled by the entropy jump and minimum, can be used to improve the modelling of superadiabatic surface layers in stellar structure calculations. Furthermor...
Mitigating Entropy Selfishness in Distributed Collaborative Spectrum Sensing
Li, Shuai; Gao, Zhaoyu; Guan, Xinping
2011-01-01
Collaborative spectrum sensing has been recognized as a promising approach to improve the sensing performance via exploiting the spatial diversity of the CR users. Such kind of cooperation, however, might be easily disrupted by the selfish users, especially for the distributed collaborative sensing. In this study, we identify a new kind of selfish behavior in collaborative sensing. Specifically, the selfish user could pretend to be an honest one by claiming a duplicated or slightly modified sensing report from others as a new one. This selfish behavior may significantly reduce the spatial diversity of the sensing reports and thus degrade the performance of collaborative spectrum sensing. We denote such a selfishness issue as Entropy Selfishness. Since it represents a challenge to decide whether a sensing report is a fresh one, entropy selfishness makes the existing incentive schemes designed for conventional wireless networks (e.g., mobile ad hoc networks) unsuitable for Cognitive Radio Networks (CRNs). To th...
Numerical Stability of Generalized Entropies
Steinbrecher, György
2016-01-01
In many applications, the probability density function is subject to experimental errors. In this work the continuos dependence of a class of generalized entropies on the experimental errors is studied. This class includes the C. Shannon, C. Tsallis, A. R\\'enyi and generalized R\\'enyi entropies. By using the connection between R\\'enyi or Tsallis entropies, and the "distance" in a family of metric functional spaces, family that includes the Lebesgue normed vector spaces, we introduce a further extensive generalizations of the R\\'enyi entropy. In this work we suppose that the experimental error is measured by some $L^{p}$ norm. In line with the methodology normally used for treating the so called "ill-posed problems", auxiliary stabilizing conditions are determined, such that small - in the sense of $L^{p}$ metric - experimental errors provoke small variations of the classical and generalized entropies. These stabilizing conditions are formulated in terms of $L^{p}$ metric in a class of generalized $L^{p}$ spac...
Mutual information challenges entropy bounds
Casini, H
2006-01-01
We consider some formulations of the entropy bounds at the semiclassical level. The entropy S(V) localized in a region V is divergent in quantum field theory (QFT). Instead of it we focus on the mutual information I(V,W)=S(V)+S(W)-S(V U W) between two different non-intersecting sets V and W. This is a low energy quantity, independent of the regularization scheme. In addition, the mutual information is bounded above by twice the entropy corresponding to the sets involved. Calculations of I(V,W) in QFT show that the entropy in empty space cannot be renormalized to zero, and must be actually very large. We find that this entropy due to the vacuum fluctuations violates the FMW bound in Minkowski space. The mutual information also gives a precise, cutoff independent meaning to the statement that the number of degrees of freedom increases with the volume in QFT. If the holographic bound holds, this points to the essential non locality of the physical cutoff. Violations of the Bousso bound would require conformal th...
A Model of Mechanothermodynamic Entropy in Tribology
Leonid A. Sosnovskiy
2017-03-01
Full Text Available A brief analysis of entropy concepts in continuum mechanics and thermodynamics is presented. The methods of accounting for friction, wear and fatigue processes in the calculation of the thermodynamic entropy are described. It is shown that these and other damage processes of solids are more adequately described by tribo-fatigue entropy. It was established that mechanothermodynamic entropy calculated as the sum of interacting thermodynamic and tribo-fatigue entropy components has the most general character. Examples of usage (application of tribo-fatigue and mechanothermodynamic entropies for practical analysis of wear and fatigue processes are given.
Information Entropy Production of Spatio-Temporal Maximum Entropy Distributions
Cofre, Rodrigo
2015-01-01
Spiking activity from populations of neurons display causal interactions and memory effects. Therefore, they are expected to show some degree of irreversibility in time. Motivated by the spike train statistics, in this paper we build a framework to quantify the degree of irreversibility of any maximum entropy distribution. Our approach is based on the transfer matrix technique, which enables us to find an homogeneous irreducible Markov chain that shares the same maximum entropy measure. We provide relevant examples in the context of spike train statistics
Bekenstein-Hawking Entropy as Topological Entanglement Entropy
McGough, Lauren; Verlinde, Herman
2013-01-01
Black holes in 2+1 dimensions enjoy long range topological interactions similar to those of non-abelian anyon excitations in a topologically ordered medium. Using this observation, we compute the topological entanglement entropy of BTZ black holes, via the established formula S_top = log(S^a_0), with S_b^a the modular S-matrix of the Virasoro characters chi_a(tau). We find a precise match with the Bekenstein-Hawking entropy. This result adds a new twist to the relationship between quantum ent...
Colossal dielectric constant in high entropy oxides
Berardan, David; Franger, Sylvain; Dragoe, Diana; Meena, Arun Kumar; Dragoe, Nita [ICMMO (UMR 8182 CNRS), Universite Paris-Sud, Universite Paris-Saclay, 91405, Orsay (France)
2016-04-15
Entropic contributions to the stability of solids are very well understood and the mixing entropy has been used for forming various solids, for instance such as inverse spinels, see Nawrotsky et al., J. Inorg. Nucl. Chem. 29, 2701 (1967) [1]. A particular development was related to high entropy alloys by Yeh et al., Adv. Eng. Mater. 6, 299 (2004) [2] and Cantor et al., Mater. Sci. Eng. A 375-377, 213 (2004) [3] (for recent reviews see Zhang et al., Prog. Mater. Sci. 61, 1 (2014) [4] and Tsai et al., Mater. Res. Lett. 2, 107 (2014) [5]) in which the configurational disorder is responsible for forming simple solid solutions and which are thoroughly studied for various applications especially due to their mechanical properties, e.g. Gludovatz et al., Science 345, 1153 (2014) [6] and Lu et al., Sci. Rep. 4, 6200 (2014) [7], but also electrical properties, Kozelj et al., Phys. Rev. Lett. 113, 107001 (2014) [8], hydrogen storage, Kao et al., Int. J. Hydrogen Energy 35, 9046 (2010) [9], magnetic properties, Zhang et al., Sci. Rep. 3, 1455 (2013) [10]. Many unexplored compositions and properties still remain for this class of materials due to their large phase space. In a recent report it has been shown that the configurational disorder can be used for stabilizing simple solid solutions of oxides, which should normally not form solid solutions, see Rost et al., Nature Commun. 6, 8485 (2015) [11] these new materials were called ''entropy-stabilized oxides''. In this pioneering report, it was shown that mixing five equimolar binary oxides yielded, after heating at high temperature and quenching, an unexpected rock salt structure compound with statistical distribution of the cations in a face centered cubic lattice. Following this seminal study, we show here that these high entropy oxides (named HEOx hereafter) can be substituted by aliovalent elements with a charge compensation mechanism. This possibility largely increases the potential development of new
Márcio William Roque
2008-10-01
variability of soil penetration resistance and crop yield based on geostatistics can indicate alternative management practices, not only to reduce the effects of soil variability on crop yield, but also to improve the estimated crop response under certain management practices. This study aimed to correlate soil penetration resistance (RP and spatial yield variability in irrigated no-till snapbean cultivation in two consecutive cycles. The experiment was carried out on a typical dystrophic Red Latosol (Oxisol, in an experimental field of the FEAGRI/UNICAMP, in Campinas-SP (lat 22 ° 48 ' 57 " S, long 47 ° 03 ' 33 " W, mean altitude of 640 m asl. The evaluations were performed in a regular sampling grid of 3 x 3 m, totaling 60 points per treatment. Spatial dependence was evaluated by geostatistical techniques as well as semivariogram parameters to generate isoline maps, by means of kriging interpolation, using program Surfer 8.0. The simple linear regression between maps (pixel-to-pixel detected an inverse correlation between RP and crop yield, whereas the bean yield was loosely correlated with soil penetration resistance under irrigated no-till system in the studied growing seasons.
Miguel Angel Uribe-Opazo
2009-07-01
Full Text Available The objective of this paper was to study the spatial variability influence of soil physical attributes in wheat yield. The geostatistics techniques used were semivariogram and contour maps produced by interpolation through usual kriging representing the spatial variability of the soil physical attributes: soil water content, soil total porosity, soil compaction degree and soil resistance to penetration.. Experimental data were at a Rhodic Ferralsol from the Agricultural Engineering Experimental Nucleus at UNIOESTE – Cascavel Campus. Soil physical attributes and wheat yield maps presented a variability standard regarding distribution in experimental area, showing low wheat yield where there was high soil compaction degree, low soil total porosity and low soil water content also presenting good wheat yield where low and medium soil resistance to penetration, medium and high soil water content and low soil compaction degree occurred. Among the studied soil physical attributes studied, soil resistance to penetration was the best attribute in correlation with wheat yield. The second best attribute was soil compaction degree. This paper enabled us to understand in a better way the spatial dependence structure of the studied attributes, as well as the concepts and geostatistics applications.Este trabalho teve como objetivo estudar a influência da variabilidade espacial dos atributos físicos do solo sobre a produtividade de trigo. Foram utilizadas técnicas de geoestatística como a construção de semivariogramas e confecção de mapas temáticos, produzidos por interpolação por krigagem de atributos físicos do solo, tais como: conteúdo gravimétrico de água no solo, porosidade total, grau de compactação e resistência do solo à penetração. Os dados experimentais foram obtidos em uma área de Latossolo Vermelho-Escuro, pertencente ao Núcleo Experimental de Engenharia Agrícola da Universidade Estadual do Oeste do Paraná – Campus de
Entropy of an extremal electrically charged thin shell and the extremal black hole
Lemos, José P S; Zaslavskii, Oleg B
2015-01-01
There is a debate as to what is the value of the the entropy $S$ of extremal black holes. There are approaches that yield zero entropy $S=0$, while there are others that yield the Bekenstein-Hawking entropy $S=A_+/4$, in Planck units. There are still other approaches that give that $S$ is proportional to $r_+$ or even that $S$ is a generic well-behaved function of $r_+$. Here $r_+$ is the black hole horizon radius and $A_+=4\\pi r_+^2$ is its horizon area. Using a thin matter shell with extremal electric charge, we find the entropy expression for the extremal thin shell spacetime. When the shell's radius approaches its own gravitational radius, and thus turns into an extremal black hole, we encounter that the entropy is $S=S(r_+)$, i.e., the entropy of an extremal black hole is a function of $r_+$ alone. We speculate that the range of values for the entropy of an extremal black hole is $0\\leq S(r_+) \\leq A_+/4$.
Feeding upon negative entropy in a thermal-equilibrium environment
Crosignani, B.; Di Porto, P.; Conti, C.
2003-01-01
The validity of the Second Law of thermodynamics, indisputable in the macroscopic world, is challenged at the mesoscopic level: a mesoscopic isolated system, possessing spatial dimensions of the order of a few microns, is capable, as shown by a straightforward kinetic analysis, to exhibit a perpetuum mobile behavior associated with large negative variations of the Clausius entropy of the system. This violation of the Second Law is expedient for devising a cyclic process through which an isola...
Entanglement Entropy for Singular Surfaces
Myers, Robert C
2012-01-01
We study entanglement entropy for regions with a singular boundary in higher dimensions using the AdS/CFT correspondence and find that various singularities make new universal contributions. When the boundary CFT has an even spacetime dimension, we find that the entanglement entropy of a conical surface contains a term quadratic in the logarithm of the UV cut-off. In four dimensions, the coefficient of this contribution is proportional to the central charge 'c'. A conical singularity in an odd number of spacetime dimensions contributes a term proportional to the logarithm of the UV cut-off. We also study the entanglement entropy for various boundary surfaces with extended singularities. In these cases, similar universal terms may appear depending on the dimension and curvature of the singular locus.
Boundary effects in entanglement entropy
Berthiere, Clement
2016-01-01
We present a number of explicit calculations of Renyi and entanglement entropies in situations where the entangling surface intersects the boundary in $d$-dimensional Minkowski spacetime. When the boundary is a single plane we compute the contribution to the entropy due to this intersection, first in the case of the Neumann and Dirichlet boundary conditions, and then in the case of a generic Robin type boundary condition. The flow in the boundary coupling between the Neumann and Dirichlet phases is analyzed in arbitrary dimension $d$ and is shown to be monotonic, the peculiarity of $d=3$ case is noted. We argue that the translational symmetry along the entangling surface is broken due the presence of the boundary which reveals that the entanglement is not homogeneous. In order to characterize this quantitatively, we introduce a density of entanglement entropy and compute it explicitly. This quantity clearly indicates that the entanglement is maximal near the boundary. We then consider the situation where the ...
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.
Quantum geometry and gravitational entropy
Simon, Joan; Balasubramanian, Vijay; Czech, Bart Iomiej; Larjo, Klaus; Marolf, Donald; Simon, Joan
2007-05-29
Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S5 universes. In this sector we devise a"coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.
Louis de Grange
2010-09-01
Full Text Available Maximum entropy models are often used to describe supply and demand behavior in urban transportation and land use systems. However, they have been criticized for not representing behavioral rules of system agents and because their parameters seems to adjust only to modeler-imposed constraints. In response, it is demonstrated that the solution to the entropy maximization problem with linear constraints is a multinomial logit model whose parameters solve the likelihood maximization problem of this probabilistic model. But this result neither provides a microeconomic interpretation of the entropy maximization problem nor explains the equivalence of these two optimization problems. This work demonstrates that an analysis of the dual of the entropy maximization problem yields two useful alternative explanations of its solution. The first shows that the maximum entropy estimators of the multinomial logit model parameters reproduce rational user behavior, while the second shows that the likelihood maximization problem for multinomial logit models is the dual of the entropy maximization problem.
Construction of microcanonical entropy on thermodynamic pillars.
Campisi, Michele
2015-05-01
A question that is currently highly debated is whether the microcanonical entropy should be expressed as the logarithm of the phase volume (volume entropy, also known as the Gibbs entropy) or as the logarithm of the density of states (surface entropy, also known as the Boltzmann entropy). Rather than postulating them and investigating the consequence of each definition, as is customary, here we adopt a bottom-up approach and construct the entropy expression within the microcanonical formalism upon two fundamental thermodynamic pillars: (i) The second law of thermodynamics as formulated for quasistatic processes: δQ/T is an exact differential, and (ii) the law of ideal gases: PV=k(B)NT. The first pillar implies that entropy must be some function of the phase volume Ω. The second pillar singles out the logarithmic function among all possible functions. Hence the construction leads uniquely to the expression S=k(B)lnΩ, that is, the volume entropy. As a consequence any entropy expression other than that of Gibbs, e.g., the Boltzmann entropy, can lead to inconsistencies with the two thermodynamic pillars. We illustrate this with the prototypical example of a macroscopic collection of noninteracting spins in a magnetic field, and show that the Boltzmann entropy severely fails to predict the magnetization, even in the thermodynamic limit. The uniqueness of the Gibbs entropy, as well as the demonstrated potential harm of the Boltzmann entropy, provide compelling reasons for discarding the latter at once.
An Entropy Formula for Higher Spin Black Holes via Conical Singularities
Kraus, Per
2013-01-01
We consider the entropy of higher spin black holes in 2+1 dimensions using the conical singularity approach. By introducing a conical singularity along a non contractible cycle and carefully evaluating its contribution to the Chern Simons action, we derive a simple expression for the entropy of a general stationary higher spin black hole. The resulting formula is shown to satisfy the first law of thermodynamics, and yields agreement with previous results based on integrating the first law.
Entropy Index as a Measure of Heartbeat Irregularity
Hwa, R C
1998-01-01
A method is proposed to analyze the heartbeat waveform that can yield a reliable characterization of the structure after only a few pulses. The measure suggested is entropy index that is related to the one found effective in describing chaotic behaviors in a wide variety of physical systems. When applied to the ECG data that include ventricular fibrillation, the index is shown to change drastically within a few pulses. Wavelet analysis is used to exhibit different scaling behaviors in different phases.
Entropy-Based Bounds On Redundancies Of Huffman Codes
Smyth, Padhraic J.
1992-01-01
Report presents extension of theory of redundancy of binary prefix code of Huffman type which includes derivation of variety of bounds expressed in terms of entropy of source and size of alphabet. Recent developments yielded bounds on redundancy of Huffman code in terms of probabilities of various components in source alphabet. In practice, redundancies of optimal prefix codes often closer to 0 than to 1.
Carlos A. Silva
2009-01-01
Full Text Available The first and second laws of thermodynamic were applied to statistical databases on nutrition and human growth in order to estimate the entropy generation over the human lifespan. The calculations were performed for the cases of variation in the diet composition and calorie restriction diets; and results were compared to a base case in which lifespan entropy generation was found to be 11 404 kJ/K per kg of body mass, predicting a lifespan of 73.78 and 81.61 years for the average male and female individuals respectively. From the analysis of the results, it was found that changes of diet % of fat and carbohydrates do not have a significant impact on predicted lifespan, while the diet % of proteins has an important effect. Reduction of diet protein % to the minimum recommended in nutrition literature yields an average increase of 3.3 years on the predicted lifespan. Changes in the calorie content of the diet also have an important effect, yielding a % increase in lifespan equal or higher than the % reduction in the diet caloric content. This correlates well experimental data on small mammal and insects, in which lifespan has been increased by diet restriction.
Grammar Specialization through Entropy Thresholds
Samuelsson, C
1994-01-01
Explanation-based generalization is used to extract a specialized grammar from the original one using a training corpus of parse trees. This allows very much faster parsing and gives a lower error rate, at the price of a small loss in coverage. Previously, it has been necessary to specify the tree-cutting criteria (or operationality criteria) manually; here they are derived automatically from the training set and the desired coverage of the specialized grammar. This is done by assigning an entropy value to each node in the parse trees and cutting in the nodes with sufficiently high entropy values.
Entanglement entropy of round spheres
Solodukhin, Sergey N., E-mail: Sergey.Solodukhin@lmpt.univ-tours.f [Laboratoire de Mathematiques et Physique Theorique, Universite Francois-Rabelais Tours Federation Denis Poisson - CNRS, Parc de Grandmont, 37200 Tours (France)
2010-10-18
We propose that the logarithmic term in the entanglement entropy computed in a conformal field theory for a (d-2)-dimensional round sphere in Minkowski spacetime is identical to the logarithmic term in the entanglement entropy of extreme black hole. The near horizon geometry of the latter is H{sub 2}xS{sub d-2}. For a scalar field this proposal is checked by direct calculation. We comment on relation of this and earlier calculations to the 'brick wall' model of 't Hooft. The case of generic 4d conformal field theory is discussed.
Barrañon, A; Roa, J E
2005-01-01
Distinct entropy definitions have been used to obtain an inverse correlation between the residual size and entropy for Heavy Ion Collisions. This explains the existence of several temperatures for different residual size bins, as reported elsewhere (Natowitz et. al., 2002). HIC collisions were simulated using binary interaction LATINO model where Pandharipande potential replicates internucleonic interaction. System temperature is defined as the temperature obtained when Kinetic Gas Theory is applied to the nucleons in the participant region. Fragments are detected with an Early Cluster Recognition Algorithm that optimizes the partitions in energy space.
Duality of Maximum Entropy and Minimum Divergence
Shinto Eguchi
2014-06-01
Full Text Available We discuss a special class of generalized divergence measures by the use of generator functions. Any divergence measure in the class is separated into the difference between cross and diagonal entropy. The diagonal entropy measure in the class associates with a model of maximum entropy distributions; the divergence measure leads to statistical estimation via minimization, for arbitrarily giving a statistical model. The dualistic relationship between the maximum entropy model and the minimum divergence estimation is explored in the framework of information geometry. The model of maximum entropy distributions is characterized to be totally geodesic with respect to the linear connection associated with the divergence. A natural extension for the classical theory for the maximum likelihood method under the maximum entropy model in terms of the Boltzmann-Gibbs-Shannon entropy is given. We discuss the duality in detail for Tsallis entropy as a typical example.
The entropy principle thermodynamics for the unsatisfied
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.
Using entropy measures to characterize human locomotion.
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.
On thermodynamic limits of entropy densities
Moriya, H; Van Enter, A
1998-01-01
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.
Determination of potential management zones from soil electrical conductivity, yield and crop data
Yan LI; Zhou SHI; Ci-fang WU; Hong-yi LI; Feng LI
2008-01-01
One approach to apply precision agriculture to optimize crop production and environmental quality is identifying management zones. In this paper, the variables of soil electrical conductivity (EC) data, cotton yield data and normalized difference vegetation index (NDVI) data in an about 15 ha field in a coastal saline land were selected as data resources, and their spatial variabilities were firstly analyzed and spatial distribution maps constructed with geostatistics technique. Then fuzzy c-means clustering algorithm was used to define management zones, fuzzy performance index (FPI) and normalized classification entropy (NCE) were used to determine the optimal cluster numbers. Finally one-way variance analysis was performed on 224 georeferenced soil and yield sampling points to assess how well the defined management zones reflected the soil properties and productivity level. The results reveal that the optimal number of management zones for the present study area was 3 and the defined management zones provided a better description of soil properties and yield variation. Statistical analyses indicate significant differences between the chemical properties of soil samples and crop yield in each management zone, and management zone 3 presented the highest nutrient level and potential crop productivity, whereas management zone 1 the lowest. Based on these findings, we conclude that fuzzy c-means clustering approach can be used to delineate management zones by using the given three variables in the coastal saline soils, and the defined management zones form an objective basis for targeting soil samples for nutrient analysis and development of site-specific application strategies.
Remainder terms for some quantum entropy inequalities
Carlen, Eric A.; Lieb, Elliott H. [Department of Mathematics, Hill Center, Rutgers University, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019 (United States); Departments of Mathematics and Physics, Jadwin Hall, Princeton University, Washington Road, Princeton, New Jersey 08544-0001 (United States)
2014-04-15
We consider three von Neumann entropy inequalities: subadditivity; Pinsker's inequality for relative entropy; and the monotonicity of relative entropy. For these we state conditions for equality, and we prove some new error bounds away from equality, including an improved version of Pinsker's inequality.
Abbe Mowshowitz
2015-03-01
Full Text Available This paper demonstrates properties of Hosoya entropy, a quantitative measure of graph complexity based on a decomposition of the vertices linked to partial Hosoya polynomials. Connections between the information content of a graph and Hosoya entropy are established, and the special case of Hosoya entropy of trees is investigated.
Entropy and temperatures of Nariai black hole
Eune, Myungseok; Kim, Wontae
2013-06-01
The statistical entropy of the Nariai black hole in a thermal equilibrium is calculated by using the brick-wall method. Even if the temperature depends on the choice of the timelike Killing vector, the entropy can be written by the ordinary area law which agrees with the Wald entropy. We discuss some physical consequences of this result and the properties of the temperatures.
Tachyon condensation and black hole entropy.
Dabholkar, Atish
2002-03-04
String propagation on a cone with deficit angle 2pi(1-1 / N) is considered for the purpose of computing the entropy of a large mass black hole. The entropy computed using the recent results on condensation of twisted-sector tachyons in this theory is found to be in precise agreement with the Bekenstein-Hawking entropy.
Logical entropy of quantum dynamical systems
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.
The Entropy of Morbidity Trauma and Mortality
Neal-Sturgess, Clive
2010-01-01
In this paper it is shown that statistical mechanics in the form of thermodynamic entropy can be used as a measure of the severity of individual injuries (AIS), and that the correct way to account for multiple injuries is to sum the entropies. It is further shown that summing entropies according to the Planck-Boltzmann (P-B) definition of entropy is formally the same as ISS, which is why ISS works. Approximate values of the probabilities of fatality are used to calculate the Gibb's entropy, which is more accurate than the P-B entropy far from equilibrium, and are shown to be again proportional to ISS. For the categorisation of injury using entropies it is necessary to consider the underlying entropy of the individuals morbidity to which is added the entropy of trauma, which then may result in death. Adding in the underlying entropy and summing entropies of all AIS3+ values gives a more extended scale than ISS, and so entropy is considered the preferred measure. A small scale trial is conducted of these concep...
Entropy production by simple electrical circuits
Miranda, E N
2012-01-01
The entropy production by simple electrical circuits (R, RC, RL) is analyzed. It comes out that the entropy production is minimal, in agreement with a well known theorem due to Prigogine. In this way, it is wrong a recent result by Zupanovic, Juretic and Botric (Physica Review E 70, 056198) who claimed that the entropy production in simple electrical circuits is a maximum
The entropy of dense non-commutative fermion gases
Kriel, Johannes N
2011-01-01
We investigate the properties of two- and three-dimensional non-commutative fermion gases with fixed total z-component of angular momentum, J_z, and at high density for the simplest form of non-commutativity involving constant spatial commutators. Analytic expressions for the entropy and pressure are found. The entropy exhibits non-extensive behaviour while the pressure reveals the presence of incompressibility in two, but not in three dimensions. Remarkably, for two-dimensional systems close to the incompressible density, the entropy is proportional to the square root of the system size, i.e., for such systems the number of microscopic degrees of freedom is determined by the circumference, rather than the area (size) of the system. The absence of incompressibility in three dimensions, and subsequently also the absence of a scaling law for the entropy analogous to the one found in two dimensions, is attributed to the form of the non-commutativity used here, the breaking of the rotational symmetry it implies a...
Homero Bergamaschi
2007-05-01
Full Text Available This study aimed to establish relationships between maize yield and rainfall on different temporal and spatial scales, in order to provide a basis for crop monitoring and modelling. A 16-year series of maize yield and daily rainfall from 11 municipalities and micro-regions of Rio Grande do Sul State was used. Correlation and regression analyses were used to determine associations between crop yield and rainfall for the entire crop cycle, from tasseling to 30 days after, and from 5 days before tasseling to 40 days after. Close relationships between maize yield and rainfall were found, particularly during the reproductive period (45-day period comprising the flowering and grain filling. Relationships were closer on a regional scale than at smaller scales. Implications of the crop-rainfall relationships for crop modelling are discussed.Este trabalho teve como objetivo estabelecer relações entre rendimentos de milho e totais de chuva em diferentes escalas temporais e espaciais, com a finalidade de fornecer bases para modelagem e monitoramento de safras. Utilizou-se uma série de 16 anos de rendimento de milho e dados diários de chuva de 11 municípios e microrregiões do Estado do Rio Grande do Sul. Análises de correlação e regressão foram utilizadas para determinar associações entre rendimento e total de chuva no ciclo do milho, do pendoamento até 30 dias depois, e de 5 dias antes a 40 dias após o pendoamento. Altas relações foram encontradas entre rendimento de milho e chuvas do período reprodutivo, em particular dos 45 dias que englobam florescimento e enchimento de grãos. Essas relações foram mais elevadas em escala regional do que em nível de município. São discutidas implicações das relações clima-chuva para modelagem de cultivos.
A Note on Entropy Relations of Black Hole Horizons
Meng, Xin-He; Xu, Wei; Wang, Jia
2014-01-01
We focus on the entropy relations of black holes in three, four and higher dimensions. These entropy relations include entropy product, "part" entropy product and entropy sum. We also discuss their differences and similarities, in order to make a further study on understanding the origin of black hole entropy at the microscopic level.
Probability representation entropy for spin-state tomogram
Man'ko, O. V.; Man'ko, V. I.
2004-01-01
Probability representation entropy (tomographic entropy) of arbitrary quantum state is introduced. Using the properties of spin tomogram to be standard probability distribution function the tomographic entropy notion is discussed. Relation of the tomographic entropy to Shannon entropy and von Neumann entropy is elucidated.
Alternative Multiview Maximum Entropy Discrimination.
Chao, Guoqing; Sun, Shiliang
2016-07-01
Maximum entropy discrimination (MED) is a general framework for discriminative estimation based on maximum entropy and maximum margin principles, and can produce hard-margin support vector machines under some assumptions. Recently, the multiview version of MED multiview MED (MVMED) was proposed. In this paper, we try to explore a more natural MVMED framework by assuming two separate distributions p1( Θ1) over the first-view classifier parameter Θ1 and p2( Θ2) over the second-view classifier parameter Θ2 . We name the new MVMED framework as alternative MVMED (AMVMED), which enforces the posteriors of two view margins to be equal. The proposed AMVMED is more flexible than the existing MVMED, because compared with MVMED, which optimizes one relative entropy, AMVMED assigns one relative entropy term to each of the two views, thus incorporating a tradeoff between the two views. We give the detailed solving procedure, which can be divided into two steps. The first step is solving our optimization problem without considering the equal margin posteriors from two views, and then, in the second step, we consider the equal posteriors. Experimental results on multiple real-world data sets verify the effectiveness of the AMVMED, and comparisons with MVMED are also reported.
Holographic Entropy and Calabi's Diastasis
D'Hoker, Eric
2014-01-01
The entanglement entropy for interfaces and junctions of two-dimensional CFTs is evaluated on holographically dual half-BPS solutions to six-dimensional Type 4b supergravity with m anti-symmetric tensor supermultiplets. It is shown that the moduli space for an N-junction solution projects to N points in the Kaehler manifold SO(2,m)/( SO(2) x SO(m)). For N=2 the interface entropy is expressed in terms of the central charge and Calabi's diastasis function on SO(2,m)/(SO(2) x SO(m)), thereby lending support from holography to a proposal of Bachas, Brunner, Douglas, and Rastelli. For N=3, the entanglement entropy for a 3-junction decomposes into a sum of diastasis functions between pairs, weighed by combinations of the three central charges, provided the flux charges are all parallel to one another or, more generally, provided the space of flux charges is orthogonal to the space of unattracted scalars. Under similar assumptions for N>3, the entanglement entropy for the N-junction solves a variational problem whos...
Entropy of Quantum Black Holes
Romesh K. Kaul
2012-02-01
Full Text Available In the Loop Quantum Gravity, black holes (or even more general Isolated Horizons are described by a SU(2 Chern-Simons theory. There is an equivalent formulation of the horizon degrees of freedom in terms of a U(1 gauge theory which is just a gauged fixed version of the SU(2 theory. These developments will be surveyed here. Quantum theory based on either formulation can be used to count the horizon micro-states associated with quantum geometry fluctuations and from this the micro-canonical entropy can be obtained. We shall review the computation in SU(2 formulation. Leading term in the entropy is proportional to horizon area with a coefficient depending on the Barbero-Immirzi parameter which is fixed by matching this result with the Bekenstein-Hawking formula. Remarkably there are corrections beyond the area term, the leading one is logarithm of the horizon area with a definite coefficient −3/2, a result which is more than a decade old now. How the same results are obtained in the equivalent U(1 framework will also be indicated. Over years, this entropy formula has also been arrived at from a variety of other perspectives. In particular, entropy of BTZ black holes in three dimensional gravity exhibits the same logarithmic correction. Even in the String Theory, many black hole models are known to possess such properties. This suggests a possible universal nature of this logarithmic correction.
Mushotzky, R.
2008-01-01
I will discuss how one can determine the origin of the 'extra entropy' in groups and clusters and the feedback needed in models of galaxy formation. I will stress the use of x-ray spectroscopy and imaging and the critical value that Con-X has in this regard.
Exponential convergence rate in entropy
Mu-Fa Chen
2007-01-01
The exponential convergence rate in entropy is studied for symmetric forms, with a specia! attention to the Markov chain with a state space having two points only. Some upper and lower bounds of the rate are obtained and five examples with precise or qualitatively exact estimates are presented.
Biosemiotic Entropy: Concluding the Series
John W. Oller
2014-07-01
Full Text Available This article concludes the special issue on Biosemiotic Entropy looking toward the future on the basis of current and prior results. It highlights certain aspects of the series, concerning factors that damage and degenerate biosignaling systems. As in ordinary linguistic discourse, well-formedness (coherence in biological signaling systems depends on valid representations correctly construed: a series of proofs are presented and generalized to all meaningful sign systems. The proofs show why infants must (as empirical evidence shows they do proceed through a strict sequence of formal steps in acquiring any language. Classical and contemporary conceptions of entropy and information are deployed showing why factors that interfere with coherence in biological signaling systems are necessary and sufficient causes of disorders, diseases, and mortality. Known sources of such formal degeneracy in living organisms (here termed, biosemiotic entropy include: (a toxicants, (b pathogens; (c excessive exposures to radiant energy and/or sufficiently powerful electromagnetic fields; (d traumatic injuries; and (e interactions between the foregoing factors. Just as Jaynes proved that irreversible changes invariably increase entropy, the theory of true narrative representations (TNR theory demonstrates that factors disrupting the well-formedness (coherence of valid representations, all else being held equal, must increase biosemiotic entropy—the kind impacting biosignaling systems.
Entropy, semantic relatedness and proximity.
Hahn, Lance W; Sivley, Robert M
2011-09-01
Although word co-occurrences within a document have been demonstrated to be semantically useful, word interactions over a local range have been largely neglected by psychologists due to practical challenges. Shannon's (Bell Systems Technical Journal, 27, 379-423, 623-665, 1948) conceptualization of information theory suggests that these interactions should be useful for understanding communication. Computational advances make an examination of local word-word interactions possible for a large text corpus. We used Brants and Franz's (2006) dataset to generate conditional probabilities for 62,474 word pairs and entropy calculations for 9,917 words in Nelson, McEvoy, and Schreiber's (Behavior Research Methods, Instruments, & Computers, 36, 402-407, 2004) free association norms. Semantic associativity correlated moderately with the probabilities and was stronger when the two words were not adjacent. The number of semantic associates for a word and the entropy of a word were also correlated. Finally, language entropy decreases from 11 bits for single words to 6 bits per word for four-word sequences. The probabilities and entropies discussed here are included in the supplemental materials for the article.
Entanglement entropy of non-unitary integrable quantum field theory
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 ceff3logℓ 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.
Relation Entropy and Transferable Entropy Think of Aggregation on Group Decision Making
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.
杨晓晨; 明博; 陶洪斌; 王璞
2015-01-01
Global warming has caused strong increase in temperature in China and this especially evident in Northeast China. As a consequence, drought stress has been more frequent, severe and over larger areas in this region. The severe drought stress has increased the risk of spring maize production in this major maize cultivation area of China. Thus understanding the spatial distribution of drought in relation to spring maize growth and yield formation was critical for in depth understanding of policy and decision making to deter yield reduction in Northeast China. Daily meteorological data for the period 1961-2012 were collected at 69 meteorological stations to analyze the effects of global warming on drought stress and yield of maize in Northeast China. Also spring maize growth and yield data were collected for the same period in the study area. The Penman-Monteit method was used to calculate potential evapotranspiration (PET). Based on the PET, the Standardized Precipitation Evapotranspiration Index (SPEI) was calculated (SPEIPM), which was used to classify drought grade of the study area. The drought hazard index in each meteorological station was calculated then with weight and occurrence rating score of every drought grade. The trend in SPEI was calculated for five growth stages using the Mann-Kendall test and the relationship between SPEIPM and climate-driven maize yield determined using regression analysis. The results showed West Jilin Province and West Liaoning Province were high drought risk areas during maize growing season, while East Jilin Province and East Liaoning Province were low drought risk areas. Drought risk also increased with maize growth in East Heilongjiang Province. Moreover, drought intensity and drought-affected area decreased at maize seedling stage but increased at later growth stages of maize for the 52-year study period. High correlations were observed between SPEIPM3-7 (SPEIPM from May to July) and climate-driven maize yield in West
Entropy-based portfolio models: Practical issues
Shirazi, Yasaman Izadparast; Sabiruzzaman, Md.; Hamzah, Nor Aishah
2015-10-01
Entropy is a nonparametric alternative of variance and has been used as a measure of risk in portfolio analysis. In this paper, the computation of entropy risk for a given set of data is discussed with illustration. A comparison between entropy-based portfolio models is made. We propose a natural extension of the mean entropy portfolio to make it more general and diversified. In terms of performance, this new model is similar to the mean-entropy portfolio when applied to real and simulated data, and offers higher return if no constraint is set for the desired return; also it is found to be the most diversified portfolio model.
Tsallis Entropy Composition and the Heisenberg Group
Kalogeropoulos, Nikos
2013-03-01
We present an embedding of the Tsallis entropy into the three-dimensional Heisenberg group, in order to understand the meaning of generalized independence as encoded in the Tsallis entropy composition property. We infer that the Tsallis entropy composition induces fractal properties on the underlying Euclidean space. Using a theorem of Milnor/Wolf/Tits/Gromov, we justify why the underlying configuration/phase space of systems described by the Tsallis entropy has polynomial growth for both discrete and Riemannian cases. We provide a geometric framework that elucidates Abe's formula for the Tsallis entropy, in terms the Pansu derivative of a map between sub-Riemannian spaces.
Towards information inequalities for generalized graph entropies.
Lavanya Sivakumar
Full Text Available In this article, we discuss the problem of establishing relations between information measures for network structures. Two types of entropy based measures namely, the Shannon entropy and its generalization, the Rényi entropy have been considered for this study. Our main results involve establishing formal relationships, by means of inequalities, between these two kinds of measures. Further, we also state and prove inequalities connecting the classical partition-based graph entropies and partition-independent entropy measures. In addition, several explicit inequalities are derived for special classes of graphs.
Receiver function estimated by maximum entropy deconvolution
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.
Enthalpy-entropy compensation in protein unfolding
无
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.
Negative temperatures and the definition of entropy
Swendsen, Robert H.; Wang, Jian-Sheng
2016-07-01
The concept of negative temperature has recently received renewed interest in the context of debates about the correct definition of the thermodynamic entropy in statistical mechanics. Several researchers have identified the thermodynamic entropy exclusively with the "volume entropy" suggested by Gibbs, and have further concluded that by this definition, negative temperatures violate the principles of thermodynamics. We disagree with these conclusions. We demonstrate that volume entropy is inconsistent with the postulates of thermodynamics for systems with non-monotonic energy densities, while a definition of entropy based on the probability distributions of macroscopic variables does satisfy the postulates of thermodynamics. Our results confirm that negative temperature is a valid extension of thermodynamics.
A violation of the covariant entropy bound?
Masoumi, Ali
2014-01-01
Several arguments suggest that the entropy density at high energy density $\\rho$ should be given by the expression $s=K\\sqrt{\\rho/G}$, where $K$ is a constant of order unity. On the other hand the covariant entropy bound requires that the entropy on a light sheet be bounded by $A/4G$, where $A$ is the area of the boundary of the sheet. We find that in a suitably chosen cosmological geometry, the above expression for $s$ violates the covariant entropy bound. We consider different possible explanations for this fact; in particular the possibility that entropy bounds should be defined in terms of volumes of regions rather than areas of surfaces.
Generalized gravitational entropy from total derivative action
Dong, Xi; Miao, Rong-Xin
2015-12-01
We investigate the generalized gravitational entropy from total derivative terms in the gravitational action. Following the method of Lewkowycz and Maldacena, we find that the generalized gravitational entropy from total derivatives vanishes. We compare our results with the work of Astaneh, Patrushev, and Solodukhin. We find that if total derivatives produced nonzero entropy, the holographic and the field-theoretic universal terms of entanglement entropy would not match. Furthermore, the second law of thermodynamics could be violated if the entropy of total derivatives did not vanish.
Generalized Gravitational Entropy from Total Derivative Action
Dong, Xi
2015-01-01
We investigate the generalized gravitational entropy from total derivative terms in the gravitational action. Following the method of Lewkowycz and Maldacena, we find that the generalized gravitational entropy from total derivatives vanishes. We compare our results with the work of Astaneh, Patrushev, and Solodukhin. We find that if total derivatives produced nonzero entropy, the holographic and the field-theoretic universal terms of entanglement entropy would not match. Furthermore, the second law of thermodynamics could be violated if the entropy of total derivatives did not vanish.
陈秧分; 李先德
2013-01-01
Despite high attention to the stability and increase of grain production and market supply by Chinese government, grain yield in China has been undergoing a great fluctuation during the past decades, which could be a big challenge to national food security. This paper thus analyzes the spatial-temporal characteristics and influence factors of grain yield change in China since 1990 from the aspect of evolution stages and main types. Statistical indicators and spatial econometric models for panel data are introduced, which are supported by Geodata, ArcGIS, and Matlab software. It shows that the growing process of Chinese grain yield has three stages, namely stage 1990-1998, 1998-2003, and 2003-2011 respectively. Meanwhile, provinces in China can be categorized into three sets according to different supply-demand relationships, which are provinces with surplus grain (PGSG), provinces with balanced grain supply and demand (PBGSD), and provinces with insufficient grain supply (PIGS). The three separate types vary every year, with different provinces included each other. Roughly speaking, the grain production status of eastern provinces, central provinces, western provinces, and northeastern provinces is decreased, weakened, enhanced and strengthened respectively. In 2011, the PGSG, the PBGSD, and the PIGS distribute mainly at North, Middle, and South China respectively. Among all the factors that influence grain yield, the land factor has a significant positive impact, changing from strong to weak. It indicates grain production in China is increasingly dependent upon factors that contribute to per unit yield, such as technical progress, capital investment, etc. The labor factor brings an effect from positive significant to insignificant then negative significant, reflecting the change of agricultural surplus labor, rural labor structure, etc. The impact of different types of capital input varies as follows. Definitely, agricultural infrastructure investment, represented
Entropy of space-time outcome in a movement speed-accuracy task.
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.
Entropy-based financial asset pricing.
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.
Entropy-based financial asset pricing.
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.
Entropy Generation Across Earth's Bow Shock
Parks, George K.; McCarthy, Michael; Fu, Suiyan; Lee E. s; Cao, Jinbin; Goldstein, Melvyn L.; Canu, Patrick; Dandouras, Iannis S.; Reme, Henri; Fazakerley, Andrew; Lin, Naiguo; Wilber, Mark
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.
Thermodynamic law from the entanglement entropy bound
Park, Chanyong
2015-01-01
From black hole thermodynamics, the Bekenstein bound has been proposed as a universal thermal entropy bound. It has been further generalized to an entanglement entropy bound which is valid even in a quantum system. In a quantumly entangled system, the non-negativity of the relative entropy leads to the entanglement entropy bound. When the entanglement entropy bound is saturated, a quantum system satisfies the thermodynamics-like law with an appropriately defined entanglement temperature. We show that the saturation of the entanglement entropy bound accounts for a universal feature of the entanglement temperature proportional to the inverse of the system size. In addition, we also find that a global quench unlike the excitation does not preserve the entanglement entropy bound.
Thermodynamic law from the entanglement entropy bound
Park, Chanyong
2016-04-01
From black hole thermodynamics, the Bekenstein bound has been proposed as a universal thermal entropy bound. It has been further generalized to an entanglement entropy bound which is valid even in a quantum system. In a quantumly entangled system, the non-negativity of the relative entropy leads to the entanglement entropy bound. When the entanglement entropy bound is saturated, a quantum system satisfies the thermodynamicslike law with an appropriately defined entanglement temperature. We show that the saturation of the entanglement entropy bound accounts for a universal feature of the entanglement temperature proportional to the inverse of the system size. In addition, we show that the deformed modular Hamiltonian under a global quench also satisfies the generalized entanglement entropy boundary after introducing a new quantity called the entanglement chemical potential.
How objective is black hole entropy?
Lau, Y K
1994-01-01
The objectivity of black hole entropy is discussed in the particular case of a Schwarzchild black hole. Using Jaynes' maximum entropy formalism and Euclidean path integral evaluation of partition function, it is argued that in the semiclassical limit when the fluctutation of metric is neglected, the black hole entropy of a Schwarzchild black hole is equal to the maximal information entropy of an observer whose sole knowledge of the black hole is its mass. Black hole entropy becomes a measure of number of its internal mass eigenstates in accordance with the Boltzmann principle only in the limit of negligible relative mass fluctutation. {}From the information theoretic perspective, the example of a Schwarzchild black hole seems to suggest that black hole entropy is no different from ordinary thermodynamic entropy. It is a property of the experimental data of a black hole, rather than being an intrinsic physical property of a black hole itself independent of any observer. However, it is still weakly objective in...
Small-window parametric imaging based on information entropy for ultrasound tissue characterization
Tsui, Po-Hsiang; Chen, Chin-Kuo; Kuo, Wen-Hung; Chang, King-Jen; Fang, Jui; Ma, Hsiang-Yang; Chou, Dean
2017-01-01
Constructing ultrasound statistical parametric images by using a sliding window is a widely adopted strategy for characterizing tissues. Deficiency in spatial resolution, the appearance of boundary artifacts, and the prerequisite data distribution limit the practicability of statistical parametric imaging. In this study, small-window entropy parametric imaging was proposed to overcome the above problems. Simulations and measurements of phantoms were executed to acquire backscattered radiofrequency (RF) signals, which were processed to explore the feasibility of small-window entropy imaging in detecting scatterer properties. To validate the ability of entropy imaging in tissue characterization, measurements of benign and malignant breast tumors were conducted (n = 63) to compare performances of conventional statistical parametric (based on Nakagami distribution) and entropy imaging by the receiver operating characteristic (ROC) curve analysis. The simulation and phantom results revealed that entropy images constructed using a small sliding window (side length = 1 pulse length) adequately describe changes in scatterer properties. The area under the ROC for using small-window entropy imaging to classify tumors was 0.89, which was higher than 0.79 obtained using statistical parametric imaging. In particular, boundary artifacts were largely suppressed in the proposed imaging technique. Entropy enables using a small window for implementing ultrasound parametric imaging. PMID:28106118
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.
Entropy of an extremal electrically charged thin shell and the extremal black hole
José P.S. Lemos
2015-11-01
Full Text Available There is a debate as to what is the value of the entropy S of extremal black holes. There are approaches that yield zero entropy S=0, while there are others that yield the Bekenstein–Hawking entropy S=A+/4, in Planck units. There are still other approaches that give that S is proportional to r+ or even that S is a generic well-behaved function of r+. Here r+ is the black hole horizon radius and A+=4πr+2 is its horizon area. Using a spherically symmetric thin matter shell with extremal electric charge, we find the entropy expression for the extremal thin shell spacetime. When the shell's radius approaches its own gravitational radius, and thus turns into an extremal black hole, we encounter that the entropy is S=S(r+, i.e., the entropy of an extremal black hole is a function of r+ alone. We speculate that the range of values for an extremal black hole is 0≤S(r+≤A+/4.
Thermodynamic Model of Spatial Memory
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.
Cosmological evolution of the gravitational entropy of the large-scale structure
Marozzi, Giovanni; Umeh, Obinna; Clarkson, Chris
2015-01-01
This article derives the entropy associated with the large-scale structure of the Universe in the linear regime, where the Universe can be described by a perturbed Friedmann-Lema\\^{\\i}tre spacetime. In particular, it compares two different definitions proposed in the literature for the entropy using a spatial averaging prescription. For one definition, the entropy of the large-scale structure and for a given comoving volume always grows with time, both for a CDM and a $\\Lambda$CDM model. In particular, while it diverges for a CDM model, it saturates to a constant value in the presence of a cosmological constant. The use of a light-cone averaging prescription in the context of the evaluation of the entropy is also discussed.
Entanglement Entropy and Wilson Loop in St\\"{u}ckelberg Holographic Insulator/Superconductor Model
Cai, Rong-Gen; Li, Li; Li, Li-Fang
2012-01-01
We study the behaviors of entanglement entropy and vacuum expectation value of Wilson loop in the St\\"{u}ckelberg holographic insulator/superconductor model. This model has rich phase structures depending on model parameters. Both the entanglement entropy for a strip geometry and the heavy quark potential from the Wilson loop show that there exists a "confinement/deconfinement" phase transition. In addition, we find that the non-monotonic behavior of the entanglement entropy with respect to chemical potential is universal in this model. The pseudo potential from the spatial Wilson loop also has a similar non-monotonic behavior. It turns out that the entanglement entropy and Wilson loop are good probes to study the properties of the holographic superconductor phase transition.
Preparation of Low Entropy Correlated Many-body States via Conformal Cooling Quenches
Zaletel, Michael P; Yao, Norman Y
2016-01-01
We analyze a method for preparing low-entropy many-body states in isolated quantum optical systems of atoms, ions and molecules. Our approach is based upon shifting entropy between different regions of a system by spatially modulating the magnitude of the effective Hamiltonian. We conduct two case studies, on a topological spin chain and the spinful fermionic Hubbard model, focusing on the key question: can a "conformal cooling quench" remove sufficient entropy within experimentally accessible timescales? Finite temperature, time-dependent matrix product state calculations reveal that even moderately sized "bath" regions can remove enough energy and entropy density to expose coherent low temperature physics. The protocol is particularly natural in systems with long-range interactions such lattice-trapped polar molecules and Rydberg dressed atoms where the magnitude of the Hamiltonian scales directly with the density. To this end, we propose a simple implementation of conformal cooling quenches in a dilutely-f...
Measuring entanglement entropy in a quantum many-body system
Rispoli, Matthew; Preiss, Philipp; Tai, Eric; Lukin, Alex; Schittko, Robert; Kaufman, Adam; Ma, Ruichao; Islam, Rajibul; Greiner, Markus
2016-05-01
The presence of large-scale entanglement is a defining characteristic of exotic quantum phases of matter. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. However, measuring entanglement remains a challenge. This is especially true in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. We demonstrate a novel approach to the measurement of entanglement entropy of any bosonic system, using a quantum gas microscope with tailored potential landscapes. This protocol enables us to directly measure quantum purity, Rényi entanglement entropy, and mutual information. In general, these experiments exemplify a method enabling the measurement and characterization of quantum phase transitions and in particular would be apt for studying systems such as magnetic ordering within the quantum Ising model.
Entanglement Entropy in Two-Dimensional String Theory.
Hartnoll, Sean A; Mazenc, Edward A
2015-09-18
To understand an emergent spacetime is to understand the emergence of locality. Entanglement entropy is a powerful diagnostic of locality, because locality leads to a large amount of short distance entanglement. Two-dimensional string theory is among the very simplest instances of an emergent spatial dimension. We compute the entanglement entropy in the large-N matrix quantum mechanics dual to two-dimensional string theory in the semiclassical limit of weak string coupling. We isolate a logarithmically large, but finite, contribution that corresponds to the short distance entanglement of the tachyon field in the emergent spacetime. From the spacetime point of view, the entanglement is regulated by a nonperturbative "graininess" of space.
Preserved entropy and fragile magnetism.
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.
Entropy of Isolated Horizons revisited
Basu, Rudranil; Majumdar, Parthasarathi
2009-01-01
The decade-old formulation of the isolated horizon classically and within loop quantum gravity, and the extraction of the microcanonical entropy of such a horizon from this formulation, is reviewed, in view of recent renewed interest. There are two main approaches to this problem: one employs an SU(2) Chern-Simons theory describing the isolated horizon degrees of freedom, while the other uses a reduced U(1) Chern-Simons theory obtained from the SU(2) theory, with appropriate constraints imposed on the spectrum of boundary states `living' on the horizon. It is shown that both these ways lead to the same infinite series asymptotic in horizon area for the microcanonical entropy of an isolated horizon. The leading area term is followed by an unambiguous correction term logarithmic in area with a coefficient $-\\frac32$, with subleading corrections dropping off as inverse powers of the area.
Entropy: The Markov Ordering Approach
Alexander N. Gorban
2010-05-01
Full Text Available The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant “additivity” properties: (i existence of a monotonic transformation which makes the functional additive with respect to the joining of independent systems and (ii existence of a monotonic transformation which makes the functional additive with respect to the partitioning of the space of states. All Lyapunov functionals for Markov chains which have properties (i and (ii are derived. We describe the most general ordering of the distribution space, with respect to which all continuous-time Markov processes are monotonic (the Markov order. The solution differs significantly from the ordering given by the inequality of entropy growth. For inference, this approach results in a convex compact set of conditionally “most random” distributions.
Entanglement Entropy of Two Spheres
Shiba, Noburo
2012-01-01
We study the entanglement entropy S_{AB} of a massless free scalar field on two spheres A and B whose radii are R_1 and R_2, respectively, and the distance between them is r. The state of the massless free scalar field is the vacuum state. We obtain the result that the mutual information S_{A;B}:=S_A+S_B-S_{AB} is independent of the ultraviolet cutoff and proportional to the product of the areas of the two spheres when r>>R_1,R_2, where S_A and S_B are the entanglement entropy on the inside region of A and B, respectively. We discuss possible connections of this result with the physics of black holes.
Dark energy from entanglement entropy
Capozziello, Salvatore
2013-01-01
We show that quantum decoherence, in the context of observational cosmology, can be connected to the cosmic dark energy. The decoherence signature could be characterized by the existence of quantum entanglement between cosmological eras. As a consequence, the Von Neumann entropy related to the entanglement process, can be compared to the thermodynamical entropy in a homogeneous and isotropic universe. The corresponding cosmological models are compatible with the current observational bounds being able to reproduce viable equations of state without introducing {\\it a priori} any cosmological constant. In doing so, we investigate two cases, corresponding to two suitable cosmic volumes, $V\\propto a^3$ and $V\\propto H^{-3}$, and find two models which fairly well approximate the current cosmic speed up. The existence of dark energy can be therefore reinterpreted as a quantum signature of entanglement, showing that the cosmological constant represents a limiting case of a more complicated model derived from the qua...
Multicomponent and High Entropy Alloys
Brian Cantor
2014-08-01
Full Text Available This paper describes some underlying principles of multicomponent and high entropy alloys, and gives some examples of these materials. Different types of multicomponent alloy and different methods of accessing multicomponent phase space are discussed. The alloys were manufactured by conventional and high speed solidification techniques, and their macroscopic, microscopic and nanoscale structures were studied by optical, X-ray and electron microscope methods. They exhibit a variety of amorphous, quasicrystalline, dendritic and eutectic structures.
Multivariate Generalized Multiscale Entropy Analysis
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.
Entropy estimation and Fibonacci numbers
Timofeev, Evgeniy A.; Kaltchenko, Alexei
2013-05-01
We introduce a new metric on a space of right-sided infinite sequences drawn from a finite alphabet. Emerging from a problem of entropy estimation of a discrete stationary ergodic process, the metric is important on its own part and exhibits some interesting properties. Notably, the number of distinct metric values for a set of sequences of length m is equal to Fm+3 - 1, where Fm is a Fibonacci number.
Entropy-based benchmarking methods
2012-01-01
We argue that benchmarking sign-volatile series should be based on the principle of movement and sign preservation, which states that a bench-marked series should reproduce the movement and signs in the original series. We show that the widely used variants of Denton (1971) method and the growth preservation method of Causey and Trager (1981) may violate this principle, while its requirements are explicitly taken into account in the pro-posed entropy-based benchmarking methods. Our illustrati...
Entropy Bounds in Spherical Space
Brevik, I; Odintsov, S D; Brevik, Iver; Milton, Kimball A.; Odintsov, Sergei D.
2002-01-01
Exact calculations are given for the Casimir energy for various fields in $R\\times S^3$ geometry. The Green's function method naturally gives a result in a form convenient in the high-temperature limit, while the statistical mechanical approach gives a form appropriate for low temperatures. The equivalence of these two representations is demonstrated. Some discrepancies with previous work are noted. In no case, even for ${\\cal N}=4$ SUSY, is the ratio of entropy to energy found to be bounded.
Normalized Minimum Error Entropy Algorithm with Recursive Power Estimation
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.
SLEAS: Supervised Learning using Entropy as Attribute Selection Measure
Kishor Kumar Reddy C
2014-10-01
Full Text Available There is embryonic importance in scaling up the broadly used decision tree learning algorithms to huge datasets. Even though abundant diverse methodologies have been proposed, a fast tree growing algorithm without substantial decrease in accuracy and substantial increase in space complexity is essential to a greater extent. This paper aims at improving the performance of the SLIQ (Supervised Learning in Quest decision tree algorithm for classification in data mining. In the present research, we adopted entropy as attribute selection measure, which overcomes the problems facing with Gini Index. Classification accuracy of the proposed supervised learning using entropy as attribute selection measure (SLEAS algorithm is compared with the existing SLIQ algorithm using twelve datasets taken from UCI Machine Learning Repository, and the results yields that the SLEAS outperforms when compared with SLIQ decision tree. Further, error rate is also computed and the results clearly show that the SLEAS algorithm is giving less error rate when compared with SLIQ decision tree.
Area evolution, bulk viscosity and entropy principles for dynamical horizons
Gourgoulhon, E; Gourgoulhon, Eric; Jaramillo, Jose Luis
2006-01-01
We derive from Einstein equation an evolution law for the area of a trapping or dynamical horizon. The solutions to this differential equation show a causal behavior. Moreover, in a viscous fluid analogy, the equation can be interpreted as an energy balance law, yielding to a positive bulk viscosity. These two features contrast with the event horizon case, where the non-causal evolution of the area and the negative bulk viscosity require teleological boundary conditions. This reflects the local character of trapping horizons as opposed to event horizons. Interpreting the area as the entropy, we propose to use an area/entropy evolution principle to select a unique dynamical horizon and time slicing in the Cauchy evolution of an initial marginally trapped surface.
The Homological Nature of Entropy
Pierre Baudot
2015-05-01
Full Text Available We propose that entropy is a universal co-homological class in a theory associated to a family of observable quantities and a family of probability distributions. Three cases are presented: (1 classical probabilities and random variables; (2 quantum probabilities and observable operators; (3 dynamic probabilities and observation trees. This gives rise to a new kind of topology for information processes, that accounts for the main information functions: entropy, mutual-informations at all orders, and Kullback–Leibler divergence and generalizes them in several ways. The article is divided into two parts, that can be read independently. In the first part, the introduction, we provide an overview of the results, some open questions, future results and lines of research, and discuss briefly the application to complex data. In the second part we give the complete definitions and proofs of the theorems A, C and E in the introduction, which show why entropy is the first homological invariant of a structure of information in four contexts: static classical or quantum probability, dynamics of classical or quantum strategies of observation of a finite system.
Economics and Maximum Entropy Production
Lorenz, R. D.
2003-04-01
Price differentials, sales volume and profit can be seen as analogues of temperature difference, heat flow and work or entropy production in the climate system. One aspect in which economic systems exhibit more clarity than the climate is that the empirical and/or statistical mechanical tendency for systems to seek a maximum in production is very evident in economics, in that the profit motive is very clear. Noting the common link between 1/f noise, power laws and Self-Organized Criticality with Maximum Entropy Production, the power law fluctuations in security and commodity prices is not inconsistent with the analogy. There is an additional thermodynamic analogy, in that scarcity is valued. A commodity concentrated among a few traders is valued highly by the many who do not have it. The market therefore encourages via prices the spreading of those goods among a wider group, just as heat tends to diffuse, increasing entropy. I explore some empirical price-volume relationships of metals and meteorites in this context.
Linearity of Holographic Entanglement Entropy
Almheiri, Ahmed; Swingle, Brian
2016-01-01
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 genera...
On Thermodynamic Interpretation of Transfer Entropy
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.
Local entropy of a nonequilibrium fermion system
Stafford, Charles A.; Shastry, Abhay
2017-03-01
The local entropy of a nonequilibrium system of independent fermions is investigated and analyzed in the context of the laws of thermodynamics. It is shown that the local temperature and chemical potential can only be expressed in terms of derivatives of the local entropy for linear deviations from local equilibrium. The first law of thermodynamics is shown to lead to an inequality, not equality, for the change in the local entropy as the nonequilibrium state of the system is changed. The maximum entropy principle (second law of thermodynamics) is proven: a nonequilibrium distribution has a local entropy less than or equal to a local equilibrium distribution satisfying the same constraints. It is shown that the local entropy of the system tends to zero when the local temperature tends to zero, consistent with the third law of thermodynamics.
Large Field Inflation and Gravitational Entropy
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....
Paracrystalline property of high-entropy alloys
Shaoqing Wang
2013-10-01
Full Text Available Atomic structure models of six-component high-entropy alloys with body-centered cubic structure are successfully built according to the principle of maximum entropy for the first time. The lattice distortion parameters g of seven typical high-entropy alloys are calculated. From the optimized lattice configuration of high-entropy alloys, we show that these alloys are ideal three-dimensional paracrystals. The formation mechanism, structural feature, mechanical property, and application prospect of high-entropy alloys are discussed in comparison with the traditional alloys. The novel properties of body-centered cubic high-entropy alloys are attributed to the failure of dislocation deformation mechanism and the difficulty of directed particle diffusion.
Relative entropy and the RG flow
Casini, Horacio; Torroba, Gonzalo
2016-01-01
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 $\\Delta$ of the perturbation that triggers the RG flow.
Generalized Gravitational Entropy from Fermion Fields
Huang, Wung-Hong
2016-01-01
The generalized gravitational entropy proposed in recent by Lewkowycz and Maldacena [1] is extended to the system of Fermion fields. We first find the regular wave solution of Fermion field which has arbitrary frequency and mode number on the BTZ spacetime, and then use it to calculate the exact gravitational entropy. The results show that there is a threshold frequency below which the Fermion fields could not contribute the generalized gravitational entropy. Also, the static and zero-mode solutions have not entropy, contrast to that in scalar field. We also found that the entropy of the static scalar fields and non-static fermions is an increasing function of mode number and, after arriving the maximum entropy it becomes a deceasing function and is derived to the asymptotic value.
Ground target detection based on discrete cosine transform and Rényi entropy for imaging ladar
Xu, Yuannan; Chen, Weili; Li, Junwei; Dong, Yanbing
2016-01-01
The discrete cosine transform (DCT) due to its excellent properties that the images can be represented in spatial/spatial-frequency domains, has been applied in sequence data analysis and image fusion. For intensity and range images of ladar, through the DCT using one dimension window, the statistical property of Rényi entropy for images is studied. We also analyzed the change of Rényi entropy's statistical property in the ladar intensity and range images when the man-made objects appear. From this foundation, a novel method for generating saliency map based on DCT and Rényi entropy is proposed. After that, ground target detection is completed when the saliency map is segmented using a simple and convenient threshold method. For the ladar intensity and range images, experimental results show the proposed method can effectively detect the military vehicles from complex earth background with low false alarm.
de Sitter entropy from conformal field theory
Kabat, D; Kabat, Daniel; Lifschytz, Gilad
2002-01-01
We propose that the entropy of de Sitter space can be identified with the mutual entropy of a dual conformal field theory. We argue that unitary time evolution in de Sitter space restricts the total number of excited degrees of freedom to be bounded by the de Sitter entropy, and we give a CFT interpretation of this restriction. We also clarify issues arising from the fact that both de Sitter and anti de Sitter have dual descriptions in terms of conformal field theory.
Generalized Gravitational Entropy from Various Matter Fields
Huang, Wung-Hong
2016-01-01
The generalized gravitational entropy proposed in recent by Lewkowycz and Maldacena [1] is extended to the systems of Boson fields, Fermion fields and Maxwell fields which have arbitrary frequency and mode numbers on the BTZ spacetime. We find the associated regular wave solution in each case and use it to calculate the exact gravitational entropy. The results show that there is a threshold frequency below which the Fermion fields could not contribute the generalized gravitational entropy. Al...
Entropy computing via integration over fractal measures.
Słomczynski, Wojciech; Kwapien, Jarosław; Zyczkowski, Karol
2000-03-01
We discuss the properties of invariant measures corresponding to iterated function systems (IFSs) with place-dependent probabilities and compute their Renyi entropies, generalized dimensions, and multifractal spectra. It is shown that with certain dynamical systems, one can associate the corresponding IFSs in such a way that their generalized entropies are equal. This provides a new method of computing entropy for some classical and quantum dynamical systems. Numerical techniques are based on integration over the fractal measures. (c) 2000 American Institute of Physics.
Quantitative Entropy Study of Language Complexity
Xie, R R; Wang, D J; Csernai, L P
2016-01-01
We study the entropy of Chinese and English texts, based on characters in case of Chinese texts and based on words for both languages. Significant differences are found between the languages and between different personal styles of debating partners. The entropy analysis points in the direction of lower entropy, that is of higher complexity. Such a text analysis would be applied for individuals of different styles, a single individual at different age, as well as different groups of the population.
New Definition and Properties of Fuzzy Entropy
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.
Gravity Quanta, Entropy and Black Holes
Alfonso-Faus, A
1999-01-01
We propose the use of a gravitational uncertainty principle for gravitation.We define the corresponding gravitational Planck's constant and thegravitational quantum of mass. We define entropy in terms of the quantum ofgravity with the property of having an extensive quality. The equivalent 2ndlaw of thermodynamics is derived, the entropy increasing linearly withcosmological time. These concepts are applied to the case of black holes,finding their entropy and discussing their radiation.
Entropy and temperatures of Nariai black hole
Eune, Myungseok; Kim, Wontae
2012-01-01
The statistical entropy of the Nariai black hole in a thermal equilibrium is calculated by using the brick-wall method. Even if the temperature depends on the choice of the time-like Killing vector, the entropy can be written by the ordinary area law which agrees with the Wald entropy. We discuss some physical consequences of this result and the properties of the temperatures.
On Gravitational Entropy of de Sitter Universe
Ulhoa, S C
2013-01-01
The paper deals with the calculation of the gravitational entropy in the context of teleparallel gravity for de Sitter space-time. In such a theory it is possible to define gravitational energy and pressure, thus we use those expressions to construct the gravitational entropy. We interpret the cosmological constant as the temperature and write the first law of thermodynamics. In the limit $\\Lambda\\ll 1$ we find that the entropy is proportional to volume and $\\Delta S\\geq 0$.
Quantum aspects of black hole entropy
Parthasarathi Majumdar
2000-10-01
This survey intends to cover recent approaches to black hole entropy which attempt to go beyond the standard semiclassical perspective. 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 holes in string-based = 2 supergravity are also discussed, albeit more brieﬂy.
Study on the Spatial Variance and Types of Scientific and Technical Yields%我国科技产出的空间变异及类型识别研究
王成丽; 刘锐金
2013-01-01
This paper analyzes the province level spatial distribution of scientific and technical yields which contains patents, scientific papers, technology market, and high - tech industry in " Eleventh Five - Year" period, and the type i-dentification is also done. The results show that; the output polarization is serious; granted patents of design are more unbalanced than invention or utility mode; scientific papers taken by SCI tend to equilibrium distribution; most of provinces technology markets are unable to meet the needs; the capability of developing new products is generally weak. The outputs of province level are divided into 6 categories, which need to be considered when the governments make policies for scientific and technical development of regions.%以“十一五”期间省级区域科技产出为研究对象,从专利、论文、技术市场、高技术产业四个方面分析科技产出的区域分布及类型识别.研究结果表明:科技产出两极化严重,科技产出的外观设计专利的不均衡程度高于发明和实用新型专利；SCI收录论文数量分布趋于均衡；大部分省区的技术市场无法满足本地区的技术需求；新产品研发能力整体偏弱.省级区域科技产出划分为6类,应当根据产出类型的不同对各地区科技发展予以不同的支持政策.
Metric Entropy of Nonautonomous Dynamical Systems
Kawan Christoph
2014-01-01
Full Text Available We introduce the notion of metric entropy for a nonautonomous dynamical system given by a sequence (Xn; μn of probability spaces and a sequence of measurable maps fn : Xn → Xn+1 with fnμn = μn+1. This notion generalizes the classical concept of metric entropy established by Kolmogorov and Sinai, and is related via a variational inequality to the topological entropy of nonautonomous systems as defined by Kolyada, Misiurewicz, and Snoha. Moreover, it shares several properties with the classical notion of metric entropy. In particular, invariance with respect to appropriately defined isomorphisms, a power rule, and a Rokhlin-type inequality are proved
Link prediction based on path entropy
Xu, Zhongqi; Yang, Jian
2015-01-01
Information theory has been taken as a prospective tool for quantifying the complexity of complex networks. In this paper, we first study the information entropy or uncertainty of a path using the information theory. Then we apply the path entropy to the link prediction problem in real-world networks. Specifically, we propose a new similarity index, namely Path Entropy (PE) index, which considers the information entropies of shortest paths between node pairs with penalization to long paths. Empirical experiments demonstrate that PE index outperforms the mainstream link predictors.
Can Holographic Entanglement Entropy Distinguish Relaxation Timescales?
Rahimi, M; Lezgi, M
2016-01-01
We use gauge-gravity duality to compute entanglement entropy in a non-conformal background with an energy scale $\\Lambda$. At zero temperature, we observe that entanglement entropy decreases by raising $\\Lambda$. However, at finite temperature, we realize that both $\\frac{\\Lambda}{T}$ and entanglement entropy rise together. Comparing entanglement entropy of the non-conformal theory, $S_{A(N)}$, and of its conformal theory at the $UV$ limit, $ S_{A(C)}$, rereals that $S_{A(N)}$ can be larger or smaller than $S_{A(C)}$, depending on the value of $\\frac{\\Lambda}{T}$
Limitations on Dimensional Regularization in Renyi Entropy
Bao, Ning
2016-01-01
Dimensional regularization is a common method used to regulate the UV divergence of field theoretic quantities. When it is used in the context of Renyi entropy, however, it is important to consider whether such a procedure eliminates the statistical interpretation thereof as a measure of entanglement of states living on a Hilbert space. We therefore examine the dimensionally regularized Renyi entropy of a 4d unitary CFT and show that it admits no underlying Hilbert space in the state-counting sense. This gives a concrete proof that dimensionally regularized Renyi entropy cannot always be obtained as a limit of the Renyi entropy of some finite-dimensional quantum system.
Quantification Of Leakage In Microvessels Using Entropy
Desoky, Ahmed H.; O'Connor, Carol; Harris, Patrick D.; Hall, Steven
1989-05-01
This paper describes the use of entropy to quantify leakage of large molecules in a microvascular system. This measure can be used as a global parameter to characterize leakage. A software package for analysis of a sequence of images comprising leakage in rat cremaster tissue has been developed. The analysis is based on the statistics of both gray level components and frequency components of the images. Results show that entropy provides a better measure of leakage because it does not depend on variation in illumination or translation and rotation of image objects. Moreover entropy based on frequency components provides a more sensitive leakage measure than entropy based on gray level components.
On the relationship between entropy and information
Shafiee, A; Karimi, Majid; Shafiee, Afshin
2006-01-01
In this paper, we analyze the relationship between entropy and information in the context of the mixing process of two identical ideal gases. We will argue that entropy has an information-based feature that is enfolded in the statistical entropy, but the second law does not include it directly. Therefore, in some given processes in thermodynamics where there is no matter and energy interaction between the system and the environment, the state of the system may goes towards a situation of lower probability to increase observer's information in the environment. This is a kind of an information-based interaction in which the total entropy is not constrained by the second law.
Cyclic Entropy: An Alternative to Inflationary Cosmology
Frampton, Paul Howard
2015-01-01
We address how to construct an infinitely cyclic universe model. A major consideration is to make the entropy cyclic which requires the entropy to be reset to zero in each cycle expansion to turnaround, to contraction, to bounce, etc. Here we reset entropy at the turnaround by selecting the visible universe from the multiverse which is generated by the accelerated expansion. In the model, the observed homogeneity is explained by the low entropy at the bounce, The observed flatness arises from the contraction together with the reduction in size between the expanding and contracting universe. The present flatness is predicted to be very precise.
Dynamical entropy for systems with stochastic perturbation
Ostruszka, A; Slomczynski, W; Zyczkowski, K; Ostruszka, Andrzej; Pakonski, Prot; Slomczynski, Wojciech; Zyczkowski, Karol
1999-01-01
Dynamics of deterministic systems perturbed by random additive noise is characterized quantitatively. Since for such systems the KS-entropy diverges we analyse the difference between the total entropy of a noisy system and the entropy of the noise itself. We show that this quantity is non negative and in the weak noise limit is conjectured to tend to the KS-entropy of the deterministic system. In particular, we consider one-dimensional systems with noise described by a finite-dimensional kernel, for which the Frobenius-Perron operator can be represented by a finite matrix.
Time Dependence of Hawking Radiation Entropy
Page, Don N
2013-01-01
If a black hole starts in a pure quantum state and evaporates completely by a unitary process, the von Neumann entropy of the Hawking radiation initially increases and then decreases back to zero when the black hole has disappeared. Here numerical results are given for an approximation to the time dependence of the radiation entropy under an assumption of fast scrambling, for large nonrotating black holes that emit essentially only photons and gravitons. The maximum of the von Neumann entropy then occurs after about 53.81% of the evaporation time, when the black hole has lost about 40.25% of its original Bekenstein-Hawking (BH) entropy (an upper bound for its von Neumann entropy) and then has a BH entropy that equals the entropy in the radiation, which is about 59.75% of the original BH entropy 4 pi M_0^2, or about 7.509 M_0^2 \\approx 6.268\\times 10^{76}(M_0/M_\\odot)^2, using my 1976 calculations that the photon and graviton emission process into empty space gives about 1.4847 times the BH entropy loss of the...
ENTROPY AND NEGENTROPY SIGNS IN LANGUAGE SYSTEM
Ирина Михайловна Некипелова
2013-12-01
Full Text Available The article is devoted to research of entropy in language. Complexity of the description of entropy is connected with that it is not a material factor of development of language, because language is not real, but the imaginable category, existing only in humans thinking. For this reason the modern researches devoted to studying and calculating of entropy are concentrated on the speech and text material. For understanding of the idea of entropy of language (not of its speech expression it is necessary to investigate the entropy of structure of objective language, not sets of subjective languages, i.e. language as model. The research has showed that in system of a natural language signs of entropy are such language phenomena as synonimy, polysemanticism, language redundancy, variability of forms, loyalty and flexibility of rules, existence of styles. These signs are detected in comparison with signs of absolutely systematized language system, acting as a hypothesis. Entropy of such system is reduced to zero. The negentropy as negative entropy is opposed to entropy. Negentropy markers are homonymy, absence of a synonimy, invariancy, strict rules of language, monostyle. DOI: http://dx.doi.org/10.12731/2218-7405-2013-9-58
Spatial Variation of Scale Effects of Sediment Yield in the Yangtze River Basin%长江流域侵蚀产沙尺度效应的区域分异
闫云霞; 许炯心; Marwan Hasson; 廖建华
2011-01-01
以长江流域水文站点的观测数据为依据,基于一定的分区原则,将整个长江流域分成了8个区域,对所有分区产沙模数的尺度效应进行了深入分析.研究表明,所有分区产沙模数的尺度效应可以概括为三类:产沙模数随流域面积的增大而减小,或先减小后基本保持不变的,主要包括长江中下游干流沿岸区域,岷江主体区域,洞庭湖流域和鄱阳湖流域;产沙模数随流域面积的增大基本保持不变的,包括嘉陵江主体区域和汉江流域;产沙模数随流域面积增大而增大,或先增大后基本保持不变的,包括长江上游干流沿岸的非泥石流区域和乌江流域.不同流域尺度效应的差异主要与流域土地利用方式有关.基于各分区校正方程,将所有站点进行了标准面积为100 km2,1 000 km2,10 000 km2的尺度校正,结果表明,当校正面积为100 km2,侵蚀最强烈的区域主要是岷江流域,其次是鄱阳湖和洞庭湖流域,校正面积为1 000 km2和10 000 km2,产沙模数图变化不显著,但明显区别于校正面积为100km2下的产沙模数图.侵蚀最强烈的区域主要是嘉陵江流域,其次是长江上游干流沿岸的部分区域和汉江流域的部分区域.不同校正面积下产沙模数图的变化,显示了不同流域侵蚀来源的差异.%Spatial variation of sediment yield of Yangtze river basin is studied in this paper. The basin is divided into eight homogenous subbasins. 326 stations with drainage area less than 30 000 km2 were used to study the scale effect of sediment yield for the whole study area. As a river basin which suffers intensive human activities, scale effect of each sub region is heavily influenced by land use and cover. All of 8 subbasins are classified as 3 types,Ⅰ, soil erosion mainly comes from deforestation and sleep slope cultivation, Ys increases as a increases; Ⅱ, soil erosion mainly occurs in middle-lower mountains and lower mountains and hilly areas
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
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.
Mechanically Alloyed High Entropy Composite
Popescu, G.; Adrian, M. M.; Csaki, I.; Popescu, C. A.; Mitrică, D.; Vasile, S.; Carcea, I.
2016-08-01
In the last years high entropy alloys have been investigated due to their high hardness, high temperature stability and unusual properties that make these alloys to have significant interest. In comparison with traditional alloys that are based on two or three major elements, this new generation alloys consists at least of 5 principal elements, with the concentration between 5 and 35 at.%. The present paper reports synthesis of high entropy alloys (HEA) and high entropy composites (HEC) synthesized by mechanical alloying (MA). The equiatomic AlCrFeNiMn matrix was used for creating the HEA matrix, starting from elemental powders and as reinforcing material for composites was used pure graphite. The mechanical alloying process was carried out at different duration, in a high energy planetary ball mill, under argon atmosphere. The elemental powders alloying began after '5 hours of milling and was complete after 40 hours. The mechanical alloyed matrix and composite was pressed and heat treated under argon protection. The elemental powers were investigated for physical - technological properties, and by X-ray diffraction and scanning electron microscopy. Phase pressing operation was realized with a hydraulic press and the applied pressure was progressive. The sintering process was carried out at 850°C for 2 h. The X-ray diffraction revealed that the MA process resulted in solid solutions formation and also revealed body- centred cubic (BCC) and face-centred cubic (FCC) structures with average grain size around 40 nm. In addition, nanoscale particles were highlighted by scanning electron microscopy, as well as the homogeneity of the chemical composition of the matrix and composite that was confirmed by EDX microanalysis. It was noted that HEA matrix and HEA composites were processed with a high degree of compaction and with a quite large capacity of mixed powder densification (around 70%).
BAYESIAN ENTROPY FOR SPATIAL SAMPLING DESIGN OF ENVIRONMENTAL DATA
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...
Entropy Analysis as an Electroencephalogram Feature Extraction Method
P. I. Sotnikov
2014-01-01
Full Text Available The aim of this study was to evaluate a possibility for using an entropy analysis as an electroencephalogram (EEG feature extraction method in brain-computer interfaces (BCI. The first section of the article describes the proposed algorithm based on the characteristic features calculation using the Shannon entropy analysis. The second section discusses issues of the classifier development for the EEG records. We use a support vector machine (SVM as a classifier. The third section describes the test data. Further, we estimate an efficiency of the considered feature extraction method to compare it with a number of other methods. These methods include: evaluation of signal variance; estimation of spectral power density (PSD; estimation of autoregression model parameters; signal analysis using the continuous wavelet transform; construction of common spatial pattern (CSP filter. As a measure of efficiency we use the probability value of correctly recognized types of imagery movements. At the last stage we evaluate the impact of EEG signal preprocessing methods on the final classification accuracy. Finally, it concludes that the entropy analysis has good prospects in BCI applications.
Entropy coders of the H.264/AVC standard
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
Use of Maximum Entropy Modeling in Wildlife Research
Roger A. Baldwin
2009-11-01
Full Text Available Maximum entropy (Maxent modeling has great potential for identifying distributions and habitat selection of wildlife given its reliance on only presence locations. Recent studies indicate Maxent is relatively insensitive to spatial errors associated with location data, requires few locations to construct useful models, and performs better than other presence-only modeling approaches. Further advances are needed to better define model thresholds, to test model significance, and to address model selection. Additionally, development of modeling approaches is needed when using repeated sampling of known individuals to assess habitat selection. These advancements would strengthen the utility of Maxent for wildlife research and management.
A Maximum Entropy Modelling of the Rain Drop Size Distribution
Francisco J. Tapiador
2011-01-01
Full Text Available This paper presents a maximum entropy approach to Rain Drop Size Distribution (RDSD modelling. It is shown that this approach allows (1 to use a physically consistent rationale to select a particular probability density function (pdf (2 to provide an alternative method for parameter estimation based on expectations of the population instead of sample moments and (3 to develop a progressive method of modelling by updating the pdf as new empirical information becomes available. The method is illustrated with both synthetic and real RDSD data, the latest coming from a laser disdrometer network specifically designed to measure the spatial variability of the RDSD.
't Hooft suppression and holographic entropy
Kelly, William R; Marolf, Donald
2015-01-01
Recent works have related the bulk first law of black hole mechanics to the first law of entanglement in a dual CFT. These are first order relations, and receive corrections for finite changes. In particular, the latter is naively expected to be accurate only for small changes in the quantum state. But when Newton's constant is small relative to the AdS scale, the former holds to good approximation even for classical perturbations that contain many quanta. This suggests that -- for appropriate states -- corrections to the first law of entanglement are suppressed by powers of $N$ in CFTs whose correlators satisfy 't Hooft large-$N$ power counting. We take first steps toward verifying that this is so by studying the large-$N$ structure of the entropy of spatial regions for a class of CFT states motivated by those created from the vacuum by acting with real-time single-trace sources. We show that $1/N$ counting matches bulk predictions, though we require the effect of the source on the modular hamiltonian to be ...
't Hooft suppression and holographic entropy
Kelly, William R.; Kuns, Kevin; Marolf, Donald
2015-10-01
Recent works have related the bulk first law of black hole mechanics to the first law of entanglement in a dual CFT. These are first order relations, and receive corrections for finite changes. In particular, the latter is naively expected to be accurate only for small changes in the quantum state. But when Newton's constant is small relative to the AdS scale, the former holds to good approximation even for classical perturbations that contain many quanta. This suggests that — for appropriate states — corrections to the first law of entanglement are suppressed by powers of N in CFTs whose correlators satisfy 't Hooft large- N power counting. We take first steps toward verifying that this is so by studying the large- N structure of the entropy of spatial regions for a class of CFT states motivate dby those created from the vacuum by acting with real-time single-trace sources. We show that 1 /N counting matches bulk predictions, though we require the effect of the source on the modular hamiltonian to be non-singular. The magnitude of our sources is ɛ N with ɛ fixed-but-small as N → ∞. Our results also provide a perturbative derivation — without relying on the replica trick — of the subleading Faulkner-Lewkowycz-Maldacena correction to the Ryu-Takayagi and Hubeny-Rangamani-Takayanagi conjectures at all orders in 1 /N.
Coherent entropy induced and acoustic noise separation in compact nozzles
Tao, Wenjie; Schuller, Thierry; Huet, Maxime; Richecoeur, Franck
2017-04-01
A method to separate entropy induced noise from an acoustic pressure wave in an harmonically perturbed flow through a nozzle is presented. It is tested on an original experimental setup generating simultaneously acoustic and temperature fluctuations in an air flow that is accelerated by a convergent nozzle. The setup mimics the direct and indirect noise contributions to the acoustic pressure field in a confined combustion chamber by producing synchronized acoustic and temperature fluctuations, without dealing with the complexity of the combustion process. It allows generating temperature fluctuations with amplitude up to 10 K in the frequency range from 10 to 100 Hz. The noise separation technique uses experiments with and without temperature fluctuations to determine the relative level of acoustic and entropy fluctuations in the system and to identify the nozzle response to these forcing waves. It requires multi-point measurements of acoustic pressure and temperature. The separation method is first validated with direct numerical simulations of the nonlinear Euler equations. These simulations are used to investigate the conditions for which the separation technique is valid and yield similar trends as the experiments for the investigated flow operating conditions. The separation method then gives successfully the acoustic reflection coefficient but does not recover the same entropy reflection coefficient as predicted by the compact nozzle theory due to the sensitivity of the method to signal noises in the explored experimental conditions. This methodology provides a framework for experimental investigation of direct and indirect combustion noises originating from synchronized perturbations.
Time dependence of Hawking radiation entropy
Page, Don N.
2013-09-01
If a black hole starts in a pure quantum state and evaporates completely by a unitary process, the von Neumann entropy of the Hawking radiation initially increases and then decreases back to zero when the black hole has disappeared. Here numerical results are given for an approximation to the time dependence of the radiation entropy under an assumption of fast scrambling, for large nonrotating black holes that emit essentially only photons and gravitons. The maximum of the von Neumann entropy then occurs after about 53.81% of the evaporation time, when the black hole has lost about 40.25% of its original Bekenstein-Hawking (BH) entropy (an upper bound for its von Neumann entropy) and then has a BH entropy that equals the entropy in the radiation, which is about 59.75% of the original BH entropy 4πM02, or about 7.509M02 ≈ 6.268 × 1076(M0/Msolar)2, using my 1976 calculations that the photon and graviton emission process into empty space gives about 1.4847 times the BH entropy loss of the black hole. Results are also given for black holes in initially impure states. If the black hole starts in a maximally mixed state, the von Neumann entropy of the Hawking radiation increases from zero up to a maximum of about 119.51% of the original BH entropy, or about 15.018M02 ≈ 1.254 × 1077(M0/Msolar)2, and then decreases back down to 4πM02 = 1.049 × 1077(M0/Msolar)2.
A bound on the entropy of supergravity?
de Boer, Jan; Messamah, Ilies; Bleeken, Dieter Van den
2009-01-01
We determine, in two independent ways, the number of BPS quantum states arising from supergravity degrees of freedom in a system with fixed total D4D0 charge. First, we count states generated by quantizing the spacetime degrees of freedom of 'entropyless' multicentered solutions consisting of anti-D0-branes bound to a D6-anti-D6 pair. Second, we determine the number of free supergravity excitations of the corresponding AdS_3 geometry with the same total charge. We find that, although these two approaches yield a priori different sets of states, the leading degeneracies in a large charge expansion are equal to each other and that, furthermore, the number of such states is parametrically smaller than that arising from the D4D0 black hole's entropy. This strongly suggests that supergravity alone is not sufficient to capture all degrees of freedom of large supersymmetric black holes. Comparing the free supergravity calculation to that of the D6-anti-D6-D0 system we find that the bound on the free spectrum imposed...
Feynman's Entropy and Decoherence Mechanism
Kim, Y S
2000-01-01
If we reduce coherence in a given quantum system, the result is an increase in entropy. Does this necessarily convert this quantum system into a classical system? The answer to this question is No. The decrease of coherence means more uncertainty. This does not seem to make the system closer to classical system where there are no uncertainties. We examine the problem using two coupled harmonic oscillators where we make observations on one of them while the other oscillator is assumed to be unobservable or to be in Feynman's rest of the universe. Our ignorance about the rest of the universe causes an increase in entropy. However, does the system act like a classical system? The answer is again No. When and how does this system appear like a classical system? It is shown that this paradox can be resolved only if measurements are taken along the normal coordinates. It is also shown that Feynman's parton picture is one concrete physical example of this decoherence mechanism.
Exact Probability Distribution versus Entropy
Kerstin Andersson
2014-10-01
Full Text Available The problem addressed concerns the determination of the average number of successive attempts of guessing a word of a certain length consisting of letters with given probabilities of occurrence. Both first- and second-order approximations to a natural language are considered. The guessing strategy used is guessing words in decreasing order of probability. When word and alphabet sizes are large, approximations are necessary in order to estimate the number of guesses. Several kinds of approximations are discussed demonstrating moderate requirements regarding both memory and central processing unit (CPU time. When considering realistic sizes of alphabets and words (100, the number of guesses can be estimated within minutes with reasonable accuracy (a few percent and may therefore constitute an alternative to, e.g., various entropy expressions. For many probability distributions, the density of the logarithm of probability products is close to a normal distribution. For those cases, it is possible to derive an analytical expression for the average number of guesses. The proportion of guesses needed on average compared to the total number decreases almost exponentially with the word length. The leading term in an asymptotic expansion can be used to estimate the number of guesses for large word lengths. Comparisons with analytical lower bounds and entropy expressions are also provided.
Entanglement entropy and algebraic holography
Kay, Bernard S
2016-01-01
In 2006, Ryu and Takayanagi (RT) pointed out that (with a suitable cutoff) the entanglement entropy between two complementary regions of an equal-time surface of a d+1-dimensional conformal field theory on the conformal boundary of AdS_{d+2} is, when the AdS radius is appropriately related to the parameters of the CFT, equal to 1/4G times the area of the d-dimensional minimal surface in the AdS bulk which has the junction of those complementary regions as its boundary, where G is the bulk Newton constant. We point out here that the RT-equality implies that, in the quantum theory on the bulk AdS background which is related to the boundary CFT according to Rehren's 1999 algebraic holography theorem, the entanglement entropy between two complementary bulk Rehren wedges is equal to 1/4G times the (suitably cut off) area of their shared ridge. (This follows because of the geometrical fact that, for complementary ball-shaped regions, the RT minimal surface is precisely the shared ridge of the complementary bulk Reh...
On the dissipation and dispersion of entropy waves in heat transferring channel flows
Fattahi, A.; Hosseinalipour, S. M.; Karimi, N.
2017-08-01
This paper investigates the hydrodynamic and heat transfer effects on the dissipation and dispersion of entropy waves in non-reactive flows. These waves, as advected density inhomogeneities downstream of unsteady flames, may decay partially or totally before reaching the exit nozzle, where they are converted into sound. Attenuation of entropy waves dominates the significance of the subsequent acoustic noise generation. Yet, the extent of this decay process is currently a matter of contention and the pertinent mechanisms are still largely unexplored. To resolve this issue, a numerical study is carried out by compressible large eddy simulation of the wave advection in a channel subject to convective and adiabatic thermal boundary conditions. The dispersion, dissipation, and spatial correlation of the wave are evaluated by post-processing of the numerical results. This includes application of the classical coherence function as well as development of nonlinear quantitative measures of wave dissipation and dispersion. The analyses reveal that the high frequency components of the entropy wave are always strongly damped. The survival of the low frequency components heavily depends on the turbulence intensity and thermal boundary conditions of the channel. In general, high turbulence intensities and particularly heat transfer intensify the decay and destruction of the spatial coherence of entropy waves. In some cases, they can even result in the complete annihilation of the wave. The current work can therefore resolve the controversies arising over the previous studies of entropy waves with different thermal boundary conditions.
J. J. Vallino
2011-01-01
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 with spatial dimensions, 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.
Information Entropy As a Basic Building Block of Complexity Theory
Jing Hu
2013-08-01
Full Text Available What is information? What role does information entropy play in this information exploding age, especially in understanding emergent behaviors of complex systems? To answer these questions, we discuss the origin of information entropy, the difference between information entropy and thermodynamic entropy, the role of information entropy in complexity theories, including chaos theory and fractal theory, and speculate new fields in which information entropy may play important roles.
Statistical modelling and deconvolution of yield meter data
Tøgersen, Frede Aakmann; Waagepetersen, Rasmus Plenge
2004-01-01
This paper considers the problem of mapping spatial variation of yield in a field using data from a yield monitoring system on a combine harvester. The unobserved yield is assumed to be a Gaussian random field and the yield monitoring system data is modelled as a convolution of the yield and an i...
Black hole entropy in loop quantum gravity
Agulló, Iván; Barbero G, J. Fernando; Borja, E. F.; Díaz-Polo, Jacobo; Villaseñor, Eduardo J. S.
2012-05-01
We discuss the recent progress on black hole entropy in loop quantum gravity, focusing in particular on the recently discovered discretization effect for microscopic black holes. Powerful analytical techniques have been developed to perform the exact computation of entropy. A statistical analysis of the structures responsible for this effect shows its progressive damping and eventual disappearance as one increases the considered horizon area.
Generalised maximum entropy and heterogeneous technologies
Oude Lansink, A.G.J.M.
1999-01-01
Generalised maximum entropy methods are used to estimate a dual model of production on panel data of Dutch cash crop farms over the period 1970-1992. The generalised maximum entropy approach allows a coherent system of input demand and output supply equations to be estimated for each farm in the sam
Entanglement Entropy in Warped Conformal Field Theories
Castro, A.; Hofman, D.M.; Iqbal, N.
We present a detailed discussion of entanglement entropy in (1+1)-dimensional Warped Conformal Field Theories (WCFTs). We implement the Rindler method to evaluate entanglement and Renyi entropies for a single interval and along the way we interpret our results in terms of twist field correlation
Progress in High-Entropy Alloys
Gao, Michael C
2013-12-01
Strictly speaking, high-entropy alloys (HEAs) refer to single-phase, solid-solution alloys with multiprincipal elements in an equal or a near-equal molar ratio whose configurational entropy is tremendously high. This special topic was organized to reflect the focus and diversity of HEA research topics in the community.
Entropy, Macroscopic Information, and Phase Transitions
Parrondo, Juan M. R.
1999-01-01
The relationship between entropy and information is reviewed, taking into account that information is stored in macroscopic degrees of freedom, such as the order parameter in a system exhibiting spontaneous symmetry breaking. It is shown that most problems of the relationship between entropy and information, embodied in a variety of Maxwell demons, are also present in any symmetry breaking transition.
Quantum Measurements, Information and Entropy Production
Srivastava, Y N; Widom, A
1999-01-01
In order to understand the Landau-Lifshitz conjecture on the relationship between quantum measurements and the thermodynamic second law, we discuss the notion of ``diabatic'' and ``adiabatic'' forces exerted by the quantum object on the classical measurement apparatus. The notion of heat and work in measurements is made manifest in this approach, and the relationship between information entropy and thermodynamic entropy is explored.
Campbell's Rule for Estimating Entropy Changes
Jensen, William B.
2004-01-01
Campbell's rule for estimating entropy changes is discussed in relation to an earlier article by Norman Craig, where it was proposed that the approximate value of the entropy of reaction was related to net moles of gas consumed or generated. It was seen that the average for Campbell's data set was lower than that for Craig's data set and…
Campbell's Rule for Estimating Entropy Changes
Jensen, William B.
2004-01-01
Campbell's rule for estimating entropy changes is discussed in relation to an earlier article by Norman Craig, where it was proposed that the approximate value of the entropy of reaction was related to net moles of gas consumed or generated. It was seen that the average for Campbell's data set was lower than that for Craig's data set and…
Entropy and Certainty in Lossless Data Compression
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…
Quantum Measurements, Information and Entropy Production
Srivastava, Y. N.; Vitiello, G; Widom, A.
1998-01-01
In order to understand the Landau-Lifshitz conjecture on the relationship between quantum measurements and the thermodynamic second law, we discuss the notion of ``diabatic'' and ``adiabatic'' forces exerted by the quantum object on the classical measurement apparatus. The notion of heat and work in measurements is made manifest in this approach, and the relationship between information entropy and thermodynamic entropy is explored.
Ehrenfest's Lottery--Time and Entropy Maximization
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…
Chemical Engineering Students' Ideas of Entropy
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…
Some relations between entropy and approximation numbers
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.
Entropy Generation in a Chemical Reaction
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…
Entropy and Certainty in Lossless Data Compression
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…
The improved relative entropy for face recognition
Zhang Qi Rong
2016-01-01
Full Text Available The relative entropy is least sensitive to noise. In this paper, we propose the improved relative entropy for face recognition (IRE. The IRE method of recognition rate is far higher than the LDA, LPP method, by experimental results on CMU PIE face database and YALE B face database.
Holographic entanglement entropy in Lovelock gravities
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 v
Nonlinear Inequalities and Entropy-Concurrence Plane
Bovino, F A
2006-01-01
Nonlinear inequalities based on the quadratic Renyi entropy for mixed two-qubit states are characterized on the Entropy-Concurrence plane. This class of inequalities is stronger than Clauser-Horne-Shimony-Holt (CHSH) inequalities and, in particular, are violated "in toto" by the set of Type I Maximally-Entangled-Mixture States (MEMS I).
Entropy and Information: A Multidisciplinary Overview.
Shaw, Debora; Davis, Charles H.
1983-01-01
Cites representative extensions of concept of entropy (measure of the amount of energy unavailable for useful work; from the second law of thermodynamics) noting basic relationships between entropy, order, information, and meaning in such disciplines as biology, economics, information science, the arts, and religion. Seventy-eight references are…
The Thermal Entropy Density of Spacetime
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.
Ehrenfest's Lottery--Time and Entropy Maximization
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…
Chemical Engineering Students' Ideas of Entropy
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…
The improvement of Clausius entropy and its application in entropy analysis
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.
Effect of density and planting pattern on yield and yield
alireza yadavi
2009-06-01
Full Text Available In order to evaluate competition ability of Grain maize (Zea mays L. against redroot pigweed (Amaranthus retroflexus L. a field experiment was conducted at Esfahan on 2003. In this research the effect of corn spatial arrangement on yield and yield components of corn (647 Three Way Cross hybrids under different levels of redroot pigweed infestation was investigated. Treatments were arranged in a factorial split experiment based on RCBD with three replications. Factorial arrangement of corn densities (74000 and 111000 plant ha-1 and planting patterns (single row, rectangular twin row and zigzag twin row formed the main plots. Split-plots referred to pigweed densities (0, 4, 8 and 12 plant m-1. Results showed that both grain and biological yield of corn increased as corn density rates increased but rows number per cob, number of grains per row of cob and 1000 grains weight decreased. The effects of planting arrangement on yield and yield components despite rows grain in cob, 1000 seeds weight and harvest index were statistically significant. Corn grain yield and yield components decreased significantly by increasing pigweed density. The effect of redroot pigweed density on corn grain and biological yield loss was predicted using Cousence hyperbolic yield equation. It showed that maximum grain yield loss and biological yield loss happened in single row arrangement and low corn density. Rows number per cob and grain numbers per row in higher corn density treatment showed lower reduction slopes under pigweed competition. In addition, grain rows numbers per cob and corn harvest index in twin arrangement treatments decreased lower than single row treatment under pigweed competition. The results of this research indicated that corn competition ability against redroot pigweed could be increased using dense population (1/5 fold of general density and zigzag twin row arrangement.
Hanel, Rudolf; Gell-Mann, Murray
2014-01-01
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 exists an ongoing controversy whether the notion of the maximum entropy principle can be extended in a meaningful way to non-extensive, non-ergodic, 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 non-ergodic and complex statistical systems if their relative entropy can be factored into a general...
What is the entropy of the universe?
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.
Kabat, D
1994-01-01
For an arbitrary quantum field in flat space with a planar boundary, an entropy of entanglement, associated with correlations across the boundary, is present when the field is in its vacuum state. The vacuum state of the same quantum field appears thermal in Rindler space, with an associated thermal entropy. We show that the density matrices describing the two situations are identical, and therefore that the two entropies are equal. We comment on the generality and significance of this result, and make use of it in analyzing the area and cutoff dependence of the entropy. The equivalence of the density matrices leads us to speculate that a planar boundary in Minkowski space has a classical entropy given by the Bekenstein--Hawking formula.
Compressive sensing and entropy in seismic signals
Marinho, Eberton S.; Rocha, Tiago C.; Corso, Gilberto; Lucena, Liacir S.
2017-09-01
This work analyzes the correlation between the seismic signal entropy and the Compressive Sensing (CS) recovery index. The recovery index measures the quality of a signal reconstructed by the CS method. We analyze the performance of two CS algorithms: the ℓ1-MAGIC and the Fast Bayesian Compressive Sensing (BCS). We have observed a negative correlation between the performance of CS and seismic signal entropy. Signals with low entropy have small recovery index in their reconstruction by CS. The rationale behind our finding is: a sparse signal is easy to recover by CS and, besides, a sparse signal has low entropy. In addition, ℓ1-MAGIC shows a more significant correlation between entropy and CS performance than Fast BCS.
Dynamical entropy for systems with stochastic perturbation
Ostruszka; Pakonski; Slomczynski; Zyczkowski
2000-08-01
Dynamics of deterministic systems perturbed by random additive noise is characterized quantitatively. Since for such systems the Kolmogorov-Sinai (KS) entropy diverges if the diameter of the partition tends to zero, we analyze the difference between the total entropy of a noisy system and the entropy of the noise itself. We show that this quantity is finite and non-negative and we call it the dynamical entropy of the noisy system. In the weak noise limit this quantity is conjectured to tend to the KS entropy of the deterministic system. In particular, we consider one-dimensional systems with noise described by a finite-dimensional kernel for which the Frobenius-Perron operator can be represented by a finite matrix.
Black hole entropy, curved space and monsters
Hsu, Stephen D.H. [Institute of Theoretical Science, University of Oregon, Eugene, OR 97403 (United States)], E-mail: hsu@uoregon.edu; Reeb, David [Institute of Theoretical Science, University of Oregon, Eugene, OR 97403 (United States)], E-mail: dreeb@uoregon.edu
2008-01-10
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 Sentropy 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.
The role of entropy in magnetotail dynamics
Birn, Joachim [Los Alamos National Laboratory; Zaharia, Sorin [Los Alamos National Laboratory; Hesse, Michael [NASA/GSFC; Schindler, K [INSTITUT FOR THEORETISCHE
2008-01-01
The role of entropy conservation and loss in magnetospheric dynamics, particularly in relation to substorm phases, is discussed on the basis of MHD theory and simulations, using comparisons with PIC simulations for validation. Entropy conservation appears to be a crucial element leading to the formation of thin embedded current sheets in the late substorm growth phase and the potential loss of equilibrium. Entropy loss (in the form of plasmoids) is essential in the earthward transport of flux tubes (bubbles, bursty bulk flows). Entropy loss also changes the tail stability properties and may render ballooning modes unstable and thus contribute to cross-tail variability. We illustrate these effects through results from theory and simulations. Entropy conservation also governs the accessibility of final states of evolution and the amount of energy that may be released.
Entanglement entropy in top-down models
Jones, Peter A. R.; Taylor, Marika
2016-08-01
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 entan-glement entropy thus computed agrees with the entanglement entropy computed using the Ryu-Takayanagi formula from the lower-dimensional Einstein metric obtained from reduc-tion 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.
Entanglement entropy in top-down models
Jones, Peter A R
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.
Gabriel A. E S. Ferraz
2012-02-01
tools are important to the coffee management. This study was conducted on the Brejão farm in Três Pontas, Minas Gerais, in 2007/2008, 2008/2009 e 2009/2010 crop. As data base were used chemical soil data obtained by sampling in a georreferenced location using a quadricycle with a sampler and a GPS, and the yield data was obtained from manual harvest on the georreferenced location. It was possible to characterize the spatial variability magnitude of the studied attributes, and they presented huge variation on time and space. Adjusts of the best semivariograms enable to produce more accurate maps that contribute to the geostatistics uses on coffee crop.
Axiomatic Relation between Thermodynamic and Information-Theoretic Entropies
Weilenmann, Mirjam; Kraemer, Lea; Faist, Philippe; Renner, Renato
2016-12-01
Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a measure of uncertainty. In this Letter, we connect these two notions of entropy, using an axiomatic framework for thermodynamics [E. H. Lieb and J. Yngvason Proc. R. Soc. 469, 20130408 (2013)]. In particular, we obtain a direct relation between the Clausius entropy and the Shannon entropy, or its generalization to quantum systems, the von Neumann entropy. More generally, we find that entropy measures relevant in nonequilibrium thermodynamics correspond to entropies used in one-shot information theory.
Applying Improved Multiscale Fuzzy Entropy for Feature Extraction of MI-EEG
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
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.
Tuncay, Caglar
2010-01-01
The electroencephalographic (EEG) data intracerebrally recorded from 20 epileptic humans with different brain origins of focal epilepsies or types of seizures, ages and sexes are investigated (nearly 700 million data). Multi channel univariate amplitude analyses are performed and it is shown that time dependent Shannon entropies can be used to predict focal epileptic seizure onsets in different epileptogenic brain zones of different patients. Formations or time evolutions of the synchronizations in the brain signals from epileptogenic or non epileptogenic areas of the patients in ictal interval or inter-ictal interval are further investigated employing spatial or temporal differences of the entropies.
Chemical library subset selection algorithms: a unified derivation using spatial statistics.
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.
Increasing entropy for colloidal stabilization
Mo, Songping; Shao, Xuefeng; Chen, Ying; Cheng, Zhengdong
2016-11-01
Stability is of paramount importance in colloidal applications. Attraction between colloidal particles is believed to lead to particle aggregation and phase separation; hence, stability improvement can be achieved through either increasing repulsion or reducing attraction by modifying the fluid medium or by using additives. Two traditional mechanisms for colloidal stability are electrostatic stabilization and steric stabilization. However, stability improvement by mixing attractive and unstable particles has rarely been considered. Here, we emphasize the function of mixing entropy in colloidal stabilization. Dispersion stability improvement is demonstrated by mixing suspensions of attractive nanosized titania spheres and platelets. A three-dimensional phase diagram is proposed to illustrate the collaborative effects of particle mixing and particle attraction on colloidal stability. This discovery provides a novel method for enhancing colloidal stability and opens a novel opportunity for engineering applications.
Entanglement entropy in particle decay
Lello, Louis; Holman, Richard
2013-01-01
The decay of a parent particle into two or more daughter particles results in an entangled quantum state, as a consequence of conservation laws in the decay process. We use the Wigner-Weisskopf formalism to construct an approximation to this state that evolves in time in a {\\em manifestly unitary} way. We then construct the entanglement entropy for one of the daughter particles by use of the reduced density matrix obtained by tracing out the unobserved states and follow its time evolution. We find that it grows over a time scale determined by the lifetime of the parent particle to a maximum, which when the width of the parent particle is narrow, describes the phase space distribution of maximally entangled Bell-like states.
Entanglement entropy of two spheres
Shiba, Noburo
2012-07-01
We study the entanglement entropy S AB of a massless free scalar field on two spheres A and B whose radii are R 1 and R 2, respectively, and the distance between the centers of them is r. The state of the massless free scalar field is the vacuum state. We obtain the result that the mutual information {S_{{A;B}}} equiv {S_A} + {S_B} - {S_{{AB}}} is independent of the ultraviolet cutoff and proportional to the product of the areas of the two spheres when r ≫ R 1 ,R 2,where S A and S B aretheentanglemententropyontheinsideregionof A and B, respectively. We discuss possible connections of this result with the physics of black holes.
Nonrepetitive Colouring via Entropy Compression
Dujmović, Vida; Wood, David R
2011-01-01
A vertex colouring of a graph is \\emph{nonrepetitive} if there is no path whose first half receives the same sequence of colours as the second half. A graph is nonrepetitively $k$-choosable if given lists of at least $k$ colours at each vertex, there is a nonrepetitive colouring such that each vertex is coloured from its own list. It is known that every graph with maximum degree $\\Delta$ is $c\\Delta^2$-choosable, for some constant $c$. We prove this result with $c=4$. We then prove that every subdivision of a graph with sufficiently many division vertices per edge is nonrepetitively 6-choosable. The proofs of both these results are based on the Moser-Tardos entropy-compression method, and a recent extension by Grytczuk, Kozik and Micek for the nonrepetitive choosability of paths. Finally, we prove that every graph with pathwidth $k$ is nonrepetitively ($2k^2+6k+1$)-colourable.
Area terms in entanglement entropy
Casini, Horacio; Lino, Eduardo Testé
2014-01-01
We discuss area terms in entanglement entropy and show that a recent formula by Rosenhaus and Smolkin is equivalent to the term involving a correlator of traces of the stress tensor in Adler-Zee formula for the renormalization of the Newton constant. We elaborate on how to fix the ambiguities in these formulas: Improving terms for the stress tensor of free fields, boundary terms in the modular Hamiltonian, and contact terms in the Euclidean correlation functions. We make computations for free fields and show how to apply these calculations to understand some results for interacting theories which have been studied in the literature. We also discuss an application to the F-theorem.
Christoforou, Cleopatra
2016-03-27
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.
A Mean-Variance Hybrid-Entropy Model for Portfolio Selection with Fuzzy Returns
Rongxi Zhou
2015-05-01
Full Text Available In this paper, we define the portfolio return as fuzzy average yield and risk as hybrid-entropy and variance to deal with the portfolio selection problem with both random uncertainty and fuzzy uncertainty, and propose a mean-variance hybrid-entropy model (MVHEM. A multi-objective genetic algorithm named Non-dominated Sorting Genetic Algorithm II (NSGA-II is introduced to solve the model. We make empirical comparisons by using the data from the Shanghai and Shenzhen stock exchanges in China. The results show that the MVHEM generally performs better than the traditional portfolio selection models.
The improvement of Clausius entropy and its application in entropy analysis
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.
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.
Nonextensive entropy approach to space plasma fluctuations and turbulence
Leubner, M P; Baumjohann, W
2006-01-01
Spatial intermittency in fully developed turbulence is an established feature of astrophysical plasma fluctuations and in particular apparent in the interplanetary medium by in situ observations. In this situation the classical Boltzmann-Gibbs extensive thermo-statistics, applicable when microscopic interactions and memory are short ranged, fails. Upon generalization of the entropy function to nonextensivity, accounting for long-range interactions and thus for correlations in the system, it is demonstrated that the corresponding probability distributions (PDFs) are members of a family of specific power-law distributions. In particular, the resulting theoretical bi-kappa functional reproduces accurately the observed global leptokurtic, non-Gaussian shape of the increment PDFs of characteristic solar wind variables on all scales. Gradual decoupling is obtained by enhancing the spatial separation scale corresponding to increasing kappa-values in case of slow solar wind conditions where a Gaussian is approached i...
On entropy, financial markets and minority games
Zapart, Christopher A.
2009-04-01
The paper builds upon an earlier statistical analysis of financial time series with Shannon information entropy, published in [L. Molgedey, W. Ebeling, Local order, entropy and predictability of financial time series, European Physical Journal B-Condensed Matter and Complex Systems 15/4 (2000) 733-737]. A novel generic procedure is proposed for making multistep-ahead predictions of time series by building a statistical model of entropy. The approach is first demonstrated on the chaotic Mackey-Glass time series and later applied to Japanese Yen/US dollar intraday currency data. The paper also reinterprets Minority Games [E. Moro, The minority game: An introductory guide, Advances in Condensed Matter and Statistical Physics (2004)] within the context of physical entropy, and uses models derived from minority game theory as a tool for measuring the entropy of a model in response to time series. This entropy conditional upon a model is subsequently used in place of information-theoretic entropy in the proposed multistep prediction algorithm.
Entropy Generation Analysis of Desalination Technologies
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.
Entanglement Entropy in Causal Set Theory
Sorkin, Rafael D
2016-01-01
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. Defining entropy in a causal set is not straightforward because the type of canonical hypersurface-data on which definitions of entanglement typically rely is not available in a causal set. Instead, we will appeal to a more global expression given in 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. Carrying this formula over to the causal set, one obtains an entanglement entropy which is both finite and of a Lorentz invariant nature. Herein we evaluate this entropy for causal sets of 1+1 dimensions, and specifically for order-intervals ("causal diamonds") within the causal set, finding in the first instance an entropy that obey...
Superhorizon entanglement entropy from particle decay in inflation
Lello, L.; Boyanovsky, D. [Department of Physics and Astronomy, University of Pittsburgh,3941 O’Hara St, Pittsburgh, PA 15260 (United States); Holman, R. [Department of Physics, Carnegie Mellon University,5000 Forbes Ave., Pittsburgh, PA 15260 (United States)
2014-04-08
In inflationary cosmology all particle states decay as a consequence of the lack of kinematic thresholds. The decay of an initial single particle state yields an entangled quantum state of the product particles. We generalize and extend a manifestly unitary field theoretical method to obtain the time evolution of the quantum state. We consider the decay of a light scalar field with mass M≪H with a cubic coupling in de Sitter space-time. Radiative corrections feature an infrared enhancement manifest as poles in Δ=M{sup 2}/3H{sup 2} and we obtain the quantum state in an expansion in Δ. To leading order the pure state density matrix describing the decay of a particle with sub-horizon wavevector is dominated by the emission of superhorizon quanta, describing entanglement between superhorizon and subhorizon fluctuations and correlations across the horizon. Tracing over the superhorizon degrees of freedom yields a mixed state density matrix from which we obtain the entanglement entropy. Asymptotically this entropy grows with the physical volume as a consequence of more modes of the decay products crossing the Hubble radius. A generalization to localized wave packets is provided. The cascade decay of single particle states into many particle states is discussed. We conjecture on possible impact of these results on non-gaussianity and on the “low multipole anomalies” of the CMB.
Tripartite entanglement and quantum relative entropy
Galvao, E.F. [Centre for Quantum Computation, Clarendon Laboratory, University of Oxford, Oxford (United Kingdom). E-mail: e.galvao@physics.ox.ac.uk; Plenio, M.B. [Optics Section, Blackett Laboratory, Imperial College, London (United Kingdom). E-mail: m.plenio@ic.ac.uk; Virmani, S. [Optics Section, Blackett Laboratory, Imperial College, London (United Kingdom). E-mail: s.virmani@ic.ac.uk
2000-12-08
We establish relations between tripartite pure state entanglement and additivity properties of the bipartite relative entropy of entanglement. Our results pertain to the asymptotic limit of local manipulations on a large number of copies of the state. We show that additivity of the relative entropy would imply that there are at least two inequivalent types of asymptotic tripartite entanglement. The methods used include the application of some useful lemmas that enable us to analytically calculate the relative entropy for some classes of bipartite states. (author)
Component analysis of the protein hydration entropy
Chong, Song-Ho; Ham, Sihyun
2012-05-01
We report the development of an atomic decomposition method of the protein solvation entropy in water, which allows us to understand global change in the solvation entropy in terms of local changes in protein conformation as well as in hydration structure. This method can be implemented via a combined approach based on molecular dynamics simulation and integral-equation theory of liquids. An illustrative application is made to 42-residue amyloid-beta protein in water. We demonstrate how this method enables one to elucidate the molecular origin for the hydration entropy change upon conformational transitions of protein.
Emission and Absorption Entropy Generation in Semiconductors
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...
Entropy viscosity method for nonlinear conservation laws
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.
Entropy and temperatures of Nariai black hole
Eune, Myungseok
2013-01-01
The statistical entropy of the Nariai black hole in a thermal equilibrium is calculated by using the brick wall method based on two different temperatures. The first form of the entropy is given by the unexpected form of the area for the Bousso-Hawking temperature, while the second form can be written by the ordinary area law for the Hawking temperature with the standard normalization. It turns out that the Wald entropy supports the case of the standard normalization of the Hawking temperature. We discuss some physical consequences of this result and the properties of the temperatures.
Boundary Fluctuations and A Reduction Entropy
Herzog, Christopher
2016-01-01
The boundary Weyl anomalies live on a codimension-1 boundary, $\\partial {\\cal M}$. The entanglement entropy originates from infinite correlations on both sides of a codimension-2 surface, $\\Sigma$. Motivated to have a further understanding of the boundary effects, we introduce a notion of reduction entropy, which, guided by thermodynamics, is a combination of the boundary effective action and the boundary stress tensor defined by allowing the metric on $\\partial {\\cal M}$ to fluctuate. We discuss how a reduction might be performed so that the reduction entropy reproduces the entanglement structure.
Permutation Entropy for Random Binary Sequences
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.
The entropy of a hole in spacetime
Balasubramanian, Vijay; Chowdhury, Borun D; de Boer, Jan
2013-01-01
We compute the gravitational entropy of 'spherical Rindler space', a time-dependent, spherically symmetric generalization of ordinary Rindler space, defined with reference to a family of observers traveling along non-parallel, accelerated trajectories. All these observers are causally disconnected from a spherical region H (a 'hole') located at the origin of Minkowski space. The entropy evaluates to S = A/4G, where A is the area of the spherical acceleration horizon, which coincides with the boundary of H. We propose that S is the entropy of entanglement between quantum gravitational degrees of freedom supporting the interior and the exterior of the sphere H.