Electric Current Fluctuations, Entropy and Ionic Conductivity
Zhang, Yong-Jun
2016-01-01
This paper reports a relation between ionic conductivity and electric current fluctuations. The relation was derived using statistical analysis and entropy approach. The relation can be used to calculate ionic conductivity.
Generalized entropy production fluctuation theorems for quantum ...
Indian Academy of Sciences (India)
Based on trajectory-dependent path probability formalism in state space, we derive generalized entropy production fluctuation relations for a quantum system in the presence of measurement and ... Proceedings of the International Workshop/Conference on Computational Condensed Matter Physics and Materials Science
Fluctuation of Information Entropy Measures in Cell Image
Directory of Open Access Journals (Sweden)
Ishay Wohl
2017-10-01
Full Text Available A simple, label-free cytometry technique is introduced. It is based on the analysis of the fluctuation of image Gray Level Information Entropy (GLIE which is shown to reflect intracellular biophysical properties like generalized entropy. In this study, the analytical relations between cellular thermodynamic generalized entropy and diffusivity and GLIE fluctuation measures are explored for the first time. The standard deviation (SD of GLIE is shown by experiments, simulation and theoretical analysis to be indifferent to microscope system “noise”. Then, the ability of GLIE fluctuation measures to reflect basic cellular entropy conditions of early death and malignancy is demonstrated in a cell model of human, healthy-donor lymphocytes, malignant Jurkat cells, as well as dead lymphocytes and Jurkat cells. Utilization of GLIE-based fluctuation measures seems to have the advantage of displaying biophysical characterization of the tested cells, like diffusivity and entropy, in a novel, unique, simple and illustrative way.
Inflationary fluctuations, entropy generation and baryogenesis in a cold universe
International Nuclear Information System (INIS)
Ellis, J.; Enqvist, K.; Nanopoulos, D.V.; Olive, K.A.
1987-01-01
We study the implications of a generic inflationary model for scenarios of baryogenesis based on the decays of coherent oscillations of squark and slepton fields. We consider the effects of de Sitter fluctuations on the magnitudes of the coherent oscillations of squarks and sleptons. We see that the largest contribution to the entropy density is due to inflation decays which together with the value of the oscillation amplitude determined by the de Sitter fluctuations leads to a baryon to entropy ratio O(10 -10 ). The isothermal density fluctuations produced by the coherent oscillations are found to be negligible compared with the adiabatic fluctuations produced during inflation. (orig.)
Statistical properties of entropy production derived from fluctuation theorems
International Nuclear Information System (INIS)
Merhav, Neri; Kafri, Yariv
2010-01-01
Several implications of well-known fluctuation theorems, on the statistical properties of entropy production, are studied using various approaches. We begin by deriving a tight lower bound on the variance of the entropy production for a given mean of this random variable. It is shown that the Evans–Searles fluctuation theorem alone imposes a significant lower bound on the variance only when the mean entropy production is very small. It is then nonetheless demonstrated that upon incorporating additional information concerning the entropy production, this lower bound can be significantly improved, so as to capture extensivity properties. Another important aspect of the fluctuation properties of the entropy production is the relationship between the mean and the variance, on the one hand, and the probability of the event where the entropy production is negative, on the other hand. Accordingly, we derive upper and lower bounds on this probability in terms of the mean and the variance. These bounds are tighter than previous bounds that can be found in the literature. Moreover, they are tight in the sense that there exist probability distributions, satisfying the Evans–Searles fluctuation theorem, that achieve them with equality. Finally, we present a general method for generating a wide class of inequalities that must be satisfied by the entropy production. We use this method to derive several new inequalities that go beyond the standard derivation of the second law
Work fluctuation and total entropy production in nonequilibrium processes.
Funo, Ken; Shitara, Tomohiro; Ueda, Masahito
2016-12-01
Work fluctuation and total entropy production play crucial roles in small thermodynamic systems subject to large thermal fluctuations. We investigate a trade-off relation between them in a nonequilibrium situation in which a system starts from an arbitrary nonequilibrium state. We apply a variational method to study this problem and find a stationary solution against variations over protocols that describe the time dependence of the Hamiltonian of the system. Using the stationary solution, we find the minimum of the total entropy production for a given amount of work fluctuation. An explicit protocol that achieves this is constructed from an adiabatic process followed by a quasistatic process. The obtained results suggest how one can control the nonequilibrium dynamics of the system while suppressing its work fluctuation and total entropy production.
Permutation entropy analysis of density fluctuations in the torsatron TJ-K
Energy Technology Data Exchange (ETDEWEB)
Wang, Dong; Ramisch, Mirko [Institut fuer Grenzflaechenverfahrenstechnik und Plasmatechnologie, Universitaet Stuttgart (Germany)
2014-07-01
In order to explore the nature of density fluctuations in the edge of magnetically confined fusion plasmas, the technique of permutation entropy and statistical complexity is used. The location of fluctuations on the entropy versus complexity plane classifies the dynamical behaviour of the system. The behaviour can be differentiated between stochastic and chaotic. The latter is supposed to be connected to a specific temporal form of intermittent density events, i.e. blobs, in the scrape-off layer (SOL). In this contribution, density fluctuations measured with a Langmuir probe in the torsatron TJ-K are analyzed with respect to the dynamical nature. Radial scans are performed across the separatrix to distinguish the dynamics in the inner edge and the SOL. Comparisons with well known test systems indeed point to a qualitative change in the dynamics across the separatrix. In the region of maximum density gradient, the fluctuations are characterized by minimum entropy. The results will be discussed on separated scales.
Minimum entropy production principle from a dynamical fluctuation law
Czech Academy of Sciences Publication Activity Database
Maes, C.; Netočný, Karel
2007-01-01
Roč. 48, č. 5 (2007), 053306/1-053306/12 ISSN 0022-2488 R&D Projects: GA ČR GA202/07/0404 Institutional research plan: CEZ:AV0Z10100520 Keywords : dynamical fluctuations * entropy production Subject RIV: BE - Theoretical Physics Impact factor: 1.137, year: 2007
Heat Flux and Entropy Produced by Thermal Fluctuations
DEFF Research Database (Denmark)
Ciliberto, S.; Imparato, Alberto; Naert, A.
2013-01-01
, and a conservation law for the fluctuating entropy, which we justify theoretically. The system is ruled by the same equations as two Brownian particles kept at different temperatures and coupled by an elastic force. Our results set strong constraints on the energy exchanged between coupled nanosystems held...
Entropy Production and Fluctuation Theorems for Active Matter
Mandal, Dibyendu; Klymko, Katherine; DeWeese, Michael R.
2017-12-01
Active biological systems reside far from equilibrium, dissipating heat even in their steady state, thus requiring an extension of conventional equilibrium thermodynamics and statistical mechanics. In this Letter, we have extended the emerging framework of stochastic thermodynamics to active matter. In particular, for the active Ornstein-Uhlenbeck model, we have provided consistent definitions of thermodynamic quantities such as work, energy, heat, entropy, and entropy production at the level of single, stochastic trajectories and derived related fluctuation relations. We have developed a generalization of the Clausius inequality, which is valid even in the presence of the non-Hamiltonian dynamics underlying active matter systems. We have illustrated our results with explicit numerical studies.
Generalized entropy production fluctuation theorems for quantum ...
Indian Academy of Sciences (India)
The inequality of second law of thermodynamics gets modified in the presence of informa- tion. These FTs are robust ... Nonequlibrium processes are common in nature, but a general framework to understand them is lacking as ... possibility of transient violations of second law for individual realization [9]. These theo-.
Energy, entropy, and the flow of nature
Sherman, Thomas F
2018-01-01
A fresh and unified exploration of the laws that govern natural change, examining the historical roots and meaning of the concepts of energy and entropy. All natural processes--mechanical, thermal, chemical, electrical, and biological--are viewed as a flow across free energy gradients that interact with one another.
Fluctuation theorem for entropy production during effusion of a relativistic ideal gas.
Cleuren, B; Willaert, K; Engel, A; Van den Broeck, C
2008-02-01
The probability distribution of the entropy production for the effusion of a relativistic ideal gas is calculated explicitly. This result is then extended to include particle and antiparticle pair production and annihilation. In both cases, the fluctuation theorem is verified.
Time-evolution of the entropy of fluctuations in some biological systems as investigated by NMR
International Nuclear Information System (INIS)
Lenk, R.
1979-01-01
A simple expression for the entropy of fluctuations has been developed, using the tunnelling-effect model. This gives the possibility to estimate the changes and evolution of entropy in non-crystalline and biological samples by NMR investigations. On the other hand, the oscillatory character of the time-evolution of some properties, experimentally found in the investigated samples of plants, is interpreted in terms of the generalized master equation with an exponential memory function. (Auth.)
Detrended fluctuation analysis and Kolmogorov–Sinai entropy of electroencephalogram signals
International Nuclear Information System (INIS)
Lim, Jung Ho; Khang, Eun Joo; Lee, Tae Hyun; Kim, In Hye; Maeng, Seong Eun; Lee, Jae Woo
2013-01-01
We measured the electroencephalogram (EEG) of young students in the relaxed state and in the state of the mathematical activities. We applied the detrended fluctuation analysis and Kolmogorov–Sinai entropy (KSE) in the EEG signals. We found that the detrended fluctuation functions follow a power law with Hurst exponents larger than 1/2. The Hurst exponents enhanced at all EEG channels in the state of mathematical activities. The KSE in the relaxed state is larger than those in the state of the mathematical activities. These indicate that the entropy is enhanced in the disorder state of the brain.
Entropy in the Tangled Nature Model of evolution
DEFF Research Database (Denmark)
Roach, Ty N.F.; Nulton, James; Sibani, Paolo
2017-01-01
Applications of entropy principles to evolution and ecology are of tantamount importance given the central role spatiotemporal structuring plays in both evolution and ecological succession. We obtain here a qualitative interpretation of the role of entropy in evolving ecological systems. Our...... interpretation is supported by mathematical arguments using simulation data generated by the Tangled Nature Model (TNM), a stochastic model of evolving ecologies. We define two types of configurational entropy and study their empirical time dependence obtained from the data. Both entropy measures increase...... logarithmically with time, while the entropy per individual decreases in time, in parallel with the growth of emergent structures visible from other aspects of the simulation. We discuss the biological relevance of these entropies to describe niche space and functional space of ecosystems, as well as their use...
Entropy in bimolecular simulations: A comprehensive review of atomic fluctuations-based methods.
Kassem, Summer; Ahmed, Marawan; El-Sheikh, Salah; Barakat, Khaled H
2015-11-01
Entropy of binding constitutes a major, and in many cases a detrimental, component of the binding affinity in biomolecular interactions. While the enthalpic part of the binding free energy is easier to calculate, estimating the entropy of binding is further more complicated. A precise evaluation of entropy requires a comprehensive exploration of the complete phase space of the interacting entities. As this task is extremely hard to accomplish in the context of conventional molecular simulations, calculating entropy has involved many approximations. Most of these golden standard methods focused on developing a reliable estimation of the conformational part of the entropy. Here, we review these methods with a particular emphasis on the different techniques that extract entropy from atomic fluctuations. The theoretical formalisms behind each method is explained highlighting its strengths as well as its limitations, followed by a description of a number of case studies for each method. We hope that this brief, yet comprehensive, review provides a useful tool to understand these methods and realize the practical issues that may arise in such calculations. Copyright © 2015 Elsevier Inc. All rights reserved.
Fluctuation theorem for entropy production during effusion of an ideal gas with momentum transfer.
Wood, Kevin; Van den Broeck, C; Kawai, R; Lindenberg, Katja
2007-06-01
We derive an exact expression for entropy production during effusion of an ideal gas driven by momentum transfer in addition to energy and particle flux. Following the treatment in Cleuren [Phys. Rev. E 74, 021117 (2006)], we construct a master equation formulation of the process and explicitly verify the thermodynamic fluctuation theorem, thereby directly exhibiting its extended applicability to particle flows and hence to hydrodynamic systems.
Entropy in the Tangled Nature Model of Evolution
Directory of Open Access Journals (Sweden)
Ty N. F. Roach
2017-04-01
Full Text Available Applications of entropy principles to evolution and ecology are of tantamount importance given the central role spatiotemporal structuring plays in both evolution and ecological succession. We obtain here a qualitative interpretation of the role of entropy in evolving ecological systems. Our interpretation is supported by mathematical arguments using simulation data generated by the Tangled Nature Model (TNM, a stochastic model of evolving ecologies. We define two types of configurational entropy and study their empirical time dependence obtained from the data. Both entropy measures increase logarithmically with time, while the entropy per individual decreases in time, in parallel with the growth of emergent structures visible from other aspects of the simulation. We discuss the biological relevance of these entropies to describe niche space and functional space of ecosystems, as well as their use in characterizing the number of taxonomic configurations compatible with different niche partitioning and functionality. The TNM serves as an illustrative example of how to calculate and interpret these entropies, which are, however, also relevant to real ecosystems, where they can be used to calculate the number of functional and taxonomic configurations that an ecosystem can realize.
Natural extensions and entropy of α-continued fractions
International Nuclear Information System (INIS)
Kraaikamp, Cor; Schmidt, Thomas A; Steiner, Wolfgang
2012-01-01
We construct a natural extension for each of Nakada's α-continued fraction transformations and show the continuity as a function of α of both the entropy and the measure of the natural extension domain with respect to the density function (1 + xy) −2 . For 0 2 /6. We show that the interval (3-√5)/2≤α≤(1+√5)/2 is a maximal interval upon which the entropy is constant. As a key step for all this, we give the explicit relationship between the α-expansion of α − 1 and of α. (paper)
Enhancing Entropy and Enthalpy Fluctuations to Drive Crystallization in Atomistic Simulations.
Piaggi, Pablo M; Valsson, Omar; Parrinello, Michele
2017-07-07
Crystallization is a process of great practical relevance in which rare but crucial fluctuations lead to the formation of a solid phase starting from the liquid. As in all first order first transitions, there is an interplay between enthalpy and entropy. Based on this idea, in order to drive crystallization in molecular simulations, we introduce two collective variables, one enthalpic and the other entropic. Defined in this way, these collective variables do not prejudge the structure into which the system is going to crystallize. We show the usefulness of this approach by studying the cases of sodium and aluminum that crystallize in the bcc and fcc crystalline structures, respectively. Using these two generic collective variables, we perform variationally enhanced sampling and well tempered metadynamics simulations and find that the systems transform spontaneously and reversibly between the liquid and the solid phases.
Enhancing Entropy and Enthalpy Fluctuations to Drive Crystallization in Atomistic Simulations
Piaggi, Pablo M.; Valsson, Omar; Parrinello, Michele
2017-07-01
Crystallization is a process of great practical relevance in which rare but crucial fluctuations lead to the formation of a solid phase starting from the liquid. As in all first order first transitions, there is an interplay between enthalpy and entropy. Based on this idea, in order to drive crystallization in molecular simulations, we introduce two collective variables, one enthalpic and the other entropic. Defined in this way, these collective variables do not prejudge the structure into which the system is going to crystallize. We show the usefulness of this approach by studying the cases of sodium and aluminum that crystallize in the bcc and fcc crystalline structures, respectively. Using these two generic collective variables, we perform variationally enhanced sampling and well tempered metadynamics simulations and find that the systems transform spontaneously and reversibly between the liquid and the solid phases.
Entropy transport in high-Tc superconductors in the fluctuation regime
International Nuclear Information System (INIS)
Maki, K.
1991-01-01
Making use of the expression for the heat current associated with the space-time-dependent order parameter for the s-wave superconductor, we calculate, in the clean limit, the heat current induced by an electric field. In the absence of a magnetic field we find an extra Peltier coefficient associated with the fluctuations, which diverges logarithmically as the temperature T approaches the transition temperature T c . In the presence of a magnetic field perpendicular to the ab plane, the fluctuation gives rise to the Ettingshausen effect. In a small magnetic field, the corresponding entropy transported by magnetic flux is calculated: left-angle S φ right-angle f =[2π 3 τT/21ζ(3)d](h/var-epsilon)(1 +2α) -1/2 where τ and d are the transport lifetime and the interlayer spacing, ζ(3)=1.202. . ., h=2eξ a 2 B, var-epsilon=ln(T/T c ), and α=2(ξ c /d) 2 var-epsilon -1 . The result is compared with a recent observation of the Ettinghausen effect in a single crystal of YBa 2 Cu 3 O 7
Entropy Generation for Natural Convection in a Darcy – Brinkman Porous Cavity
Ali Mchirgui; Nejib Hidouri; Mourad Magherbi; Ammar Ben Brahim
2013-01-01
The paper provides a numerical investigation of the entropy generation analysis due to natural convection in an inclined square porous cavity. The coupled equations of mass, momentum, energy and species conservation are solved using the Control Volume Finite-Element Method. Effect of medium permeability and inclination angle on entropy generation is analysed. It was found that according to the Darcy number and the porous thermal Raleigh number values, the entropy generati...
Nonsymmetric entropy and maximum nonsymmetric entropy principle
International Nuclear Information System (INIS)
Liu Chengshi
2009-01-01
Under the frame of a statistical model, the concept of nonsymmetric entropy which generalizes the concepts of Boltzmann's entropy and Shannon's entropy, is defined. Maximum nonsymmetric entropy principle is proved. Some important distribution laws such as power law, can be derived from this principle naturally. Especially, nonsymmetric entropy is more convenient than other entropy such as Tsallis's entropy in deriving power laws.
The Elusive Nature of Entropy and Its Physical Meaning
Directory of Open Access Journals (Sweden)
Milivoje M. Kostic
2014-02-01
Full Text Available Entropy is the most used and often abused concept in science, but also in philosophy and society. Further confusions are produced by some attempts to generalize entropy with similar but not the same concepts in other disciplines. The physical meaning of phenomenological, thermodynamic entropy is reasoned and elaborated by generalizing Clausius definition with inclusion of generated heat, since it is irrelevant if entropy is changed due to reversible heat transfer or irreversible heat generation. Irreversible, caloric heat transfer is introduced as complementing reversible heat transfer. It is also reasoned and thus proven why entropy cannot be destroyed but is always generated (and thus over-all increased locally and globally, at every space and time scales, without any exception. It is concluded that entropy is a thermal displacement (dynamic thermal-volume of thermal energy due to absolute temperature as a thermal potential (dQ = TdS, and thus associated with thermal heat and absolute temperature, i.e., distribution of thermal energy within thermal micro-particles in space. Entropy is an integral measure of (random thermal energy redistribution (due to heat transfer and/or irreversible heat generation within a material system structure in space, per absolute temperature level: dS = dQSys/T = mCSysdT/T, thus logarithmic integral function, with J/K unit. It may be also expressed as a measure of “thermal disorder”, being related to logarithm of number of all thermal, dynamic microstates W (their position and momenta, S = kBlnW, or to the sum of their logarithmic probabilities S = −kB∑pilnpi, that correspond to, or are consistent with the given thermodynamic macro-state. The number of thermal microstates W, is correlated with macro-properties temperature T and volume V for ideal gases. A system form and/or functional order or disorder are not (thermal energy order/disorder and the former is not related to Thermodynamic entropy. Expanding
Improving performance of two-phase natural circulation loops by reducing of entropy generation
International Nuclear Information System (INIS)
Goudarzi, N.; Talebi, S.
2015-01-01
This paper aims to investigate the effects of various parameters on stability behavior and entropy generation through a two-phase natural circulation loop. Two-phase natural circulation systems have low driving head and, consequently, low heat removal capability. To have a higher thermodynamic efficiency, in addition to the stability analysis, minimization of entropy generation by loop should be taken into account in the design of these systems. In the present study, to investigate the stability behavior, the non-linear method (known as the direct solution method or time domain method) which is able to simulate the uniform and non-uniform diameter loops, was applied. To best calculate entropy generation rates, the governing equations of the entropy generation were solved analytically. The effects of various parameters such as operating conditions and geometrical dimensions on the stability behavior and the entropy generation in the two-phase natural circulation loop were then analyzed. - Highlights: • Effects of all important parameters on entropy generation of a loop are studied. • The governing equations of the entropy generation are solved analytically. • Effects of all important parameters on stability of a loop are investigated. • Improvement of two-phase natural circulation loop is investigated.
Relative Entropy, Interaction Energy and the Nature of Dissipation
Directory of Open Access Journals (Sweden)
Bernard Gaveau
2014-06-01
Full Text Available Many thermodynamic relations involve inequalities, with equality if a process does not involve dissipation. In this article we provide equalities in which the dissipative contribution is shown to involve the relative entropy (a.k.a. Kullback-Leibler divergence. The processes considered are general time evolutions both in classical and quantum mechanics, and the initial state is sometimes thermal, sometimes partially so. By calculating a transport coefficient we show that indeed—at least in this case—the source of dissipation in that coefficient is the relative entropy.
Distinct nature of orbital-selective Mott phases dominated by low-energy local spin fluctuations
Song, Ze-Yi; Jiang, Xiu-Cai; Lin, Hai-Qing; Zhang, Yu-Zhong
2017-12-01
Quantum orbital-selective Mott (OSM) transitions are investigated within dynamical mean-field theory based on a two-orbital Hubbard model with different bandwidth at half filling. We find two distinct OSM phases both showing coexistence of itinerant electrons and localized spins, dependent on whether the Hund's coupling is full or of Ising type. The critical values and the nature of the OSM transitions are efficiently determined by entanglement entropy. We reveal that vanishing of the Kondo energy scale evidenced by absence of local spin fluctuations at low frequency in local dynamical spin susceptibility is responsible for the appearance of non-Fermi-liquid OSM phase in Ising Hund's coupling case. We argue that this scenario can also be applied to account for emergent quantum non-Fermi liquid in the one-band Hubbard model when short-range antiferromagnetic order is considered.
Modeling the Mass Action Dynamics of Metabolism with Fluctuation Theorems and Maximum Entropy
Cannon, William; Thomas, Dennis; Baxter, Douglas; Zucker, Jeremy; Goh, Garrett
The laws of thermodynamics dictate the behavior of biotic and abiotic systems. Simulation methods based on statistical thermodynamics can provide a fundamental understanding of how biological systems function and are coupled to their environment. While mass action kinetic simulations are based on solving ordinary differential equations using rate parameters, analogous thermodynamic simulations of mass action dynamics are based on modeling states using chemical potentials. The latter have the advantage that standard free energies of formation/reaction and metabolite levels are much easier to determine than rate parameters, allowing one to model across a large range of scales. Bridging theory and experiment, statistical thermodynamics simulations allow us to both predict activities of metabolites and enzymes and use experimental measurements of metabolites and proteins as input data. Even if metabolite levels are not available experimentally, it is shown that a maximum entropy assumption is quite reasonable and in many cases results in both the most energetically efficient process and the highest material flux.
Munakata, T; Rosinberg, M L
2014-05-09
Continuous feedback control of Langevin processes may be non-Markovian due to a time lag between the measurement and the control action. We show that this requires one to modify the basic relation between dissipation and time reversal and to include a contribution arising from the noncausal character of the reverse process. We then propose a new definition of the quantity measuring the irreversibility of a path in a nonequilibrium stationary state, which can also be regarded as the trajectory-dependent total entropy production. This leads to an extension of the second law, which takes a simple form in the long-time limit. As an illustration, we apply the general approach to linear systems that are both analytically tractable and experimentally relevant.
International Nuclear Information System (INIS)
Li, Rui; Wang, Jun
2016-01-01
A financial price model is developed based on the voter interacting system in this work. The Lempel–Ziv complexity is introduced to analyze the complex behaviors of the stock market. Some stock market stylized facts including fat tails, absence of autocorrelation and volatility clustering are investigated for the proposed price model firstly. Then the complexity of fluctuation behaviors of the real stock markets and the proposed price model are mainly explored by Lempel–Ziv complexity (LZC) analysis and multi-scale weighted-permutation entropy (MWPE) analysis. A series of LZC analyses of the returns and the absolute returns of daily closing prices and moving average prices are performed. Moreover, the complexity of the returns, the absolute returns and their corresponding intrinsic mode functions (IMFs) derived from the empirical mode decomposition (EMD) with MWPE is also investigated. The numerical empirical study shows similar statistical and complex behaviors between the proposed price model and the real stock markets, which exhibits that the proposed model is feasible to some extent. - Highlights: • A financial price dynamical model is developed based on the voter interacting system. • Lempel–Ziv complexity is the firstly applied to investigate the stock market dynamics system. • MWPE is employed to explore the complexity fluctuation behaviors of the stock market. • Empirical results show the feasibility of the proposed financial model.
Energy Technology Data Exchange (ETDEWEB)
Chen, Yong, E-mail: 83229994@qq.com [School of Mathematics and Computing Science, Hunan University of Science and Technology, Xiangtan 411201, Hunan (China); Ge, Hao, E-mail: haoge@pku.edu.cn [Beijing International Center for Mathematical Research and Biodynamic Optical Imaging Center, Peking University, Beijing 100871 (China); Xiong, Jie, E-mail: jiexiong@umac.mo [Department of Mathematics, Faculty of Science and Technology, University of Macau, Av. Padre Tomás Pereira, Taipa Macau (China); Xu, Lihu, E-mail: lihuxu@umac.mo [Department of Mathematics, Faculty of Science and Technology, University of Macau, Av. Padre Tomás Pereira, Taipa Macau (China); UMacau Zhuhai Research Institute, Zhuhai, 519080, Canton province (China)
2016-07-15
Fluctuation theorem is one of the major achievements in the field of nonequilibrium statistical mechanics during the past two decades. There exist very few results for steady-state fluctuation theorem of sample entropy production rate in terms of large deviation principle for diffusion processes due to the technical difficulties. Here we give a proof for the steady-state fluctuation theorem of a diffusion process in magnetic fields, with explicit expressions of the free energy function and rate function. The proof is based on the Karhunen-Loève expansion of complex-valued Ornstein-Uhlenbeck process.
International Nuclear Information System (INIS)
Alvarez R, J.T.
1998-01-01
This thesis presents a microscopic model for the non-linear fluctuating hydrodynamic of superfluid helium ( 4 He), model developed by means of the Maximum Entropy Method (Maxent). In the chapter 1, it is demonstrated the necessity to developing a microscopic model for the fluctuating hydrodynamic of the superfluid helium, starting from to show a brief overview of the theories and experiments developed in order to explain the behavior of the superfluid helium. On the other hand, it is presented the Morozov heuristic method for the construction of the non-linear hydrodynamic fluctuating of simple fluid. Method that will be generalized for the construction of the non-linear fluctuating hydrodynamic of the superfluid helium. Besides, it is presented a brief summary of the content of the thesis. In the chapter 2, it is reproduced the construction of a Generalized Fokker-Planck equation, (GFP), for a distribution function associated with the coarse grained variables. Function defined with aid of a nonequilibrium statistical operator ρhut FP that is evaluated as Wigneris function through ρ CG obtained by Maxent. Later this equation of GFP is reduced to a non-linear local FP equation from considering a slow and Markov process in the coarse grained variables. In this equation appears a matrix D mn defined with a nonequilibrium coarse grained statistical operator ρhut CG , matrix elements are used in the construction of the non-linear fluctuating hydrodynamics equations of the superfluid helium. In the chapter 3, the Lagrange multipliers are evaluated for to determine ρhut CG by means of the local equilibrium statistical operator ρhut l -tilde with the hypothesis that the system presents small fluctuations. Also are determined the currents associated with the coarse grained variables and furthermore are evaluated the matrix elements D mn but with aid of a quasi equilibrium statistical operator ρhut qe instead of the local equilibrium operator ρhut l -tilde. Matrix
Effect of an External Oriented Magnetic Field on Entropy Generation in Natural Convection
Directory of Open Access Journals (Sweden)
Atef El Jery
2010-05-01
Full Text Available The influence of an external oriented magnetic field on entropy generation in natural convection for air and liquid gallium is numerically studied in steady-unsteady states by solving the mass, the momentum and the energy conservation equations. Entropy generation depends on five parameters which are: the Prandtl number, the irreversibility coefficients, the inclination angle of the magnetic field, the thermal Grashof and the Hartmann numbers. Effects of these parameters on total and local irreversibilities as well as on heat transfer and fluid flow are studied. It was found that the magnetic field tends to decrease the convection currents, the heat transfer and entropy generation inside the enclosure. Influence of inclination angle of the magnetic field on local irreversibility is then studied.
Entropy: A Unifying Path for Understanding Complexity in Natural, Artificial and Social Systems
2011-07-01
us now address complex systems which include a substantial social component. We may start with economics and theory of finance. Given the long memory ...Entropy: A Unifying Path for Understanding Complexity in Natural, Artificial and Social Systems * Constantino Tsallis Centro Brasileiro de...Path for Understanding Complexity in Natural, Artificial and Social Systems 5a. CONTRACT NUMBER FA23861114006 5b. GRANT NUMBER 5c. PROGRAM ELEMENT
International Nuclear Information System (INIS)
Sheikhzadeh, G. A.; Nikfar, M.
2013-01-01
In the present study, aspect ratio (AR) effects of a centered adiabatic rectangular obstacle numerically investigated on natural convection and entropy generation in a differentially heated enclosure filled with either water or nanofluid (Cu-water). The governing equations are solved numerically with finite volume method using the SIMPLER algorithm. The study has been done for Rayleigh numbers between 10 3 and 10 6 , the aspect ratio of 1/3, 1/2, 1, 2 and 3 and for base fluid as well as nanofluid. It is found that, using the nanofluid leads to increase the flow strength, average Nusselt number and entropy generation and decrease the Bejan number especially at high Rayleigh numbers. At low Rayleigh numbers entropy generation is very low. By increasing Rayleigh number, entropy generation and Bejan number increases. It is observed that the viscose entropy generation is more considerable than the thermal entropy generation and has dominant role in total entropy generation. The maximum entropy generation occurs at AR = 1/3 and 3 and the minimum entropy generation occurs at AR = 1 and 1/2. It is observed that the effect of AR on Nusselt number, entropy generation and Bejan number depends on Rayleigh number.
Misuse of thermodynamic entropy in economics
International Nuclear Information System (INIS)
Kovalev, Andrey V.
2016-01-01
The direct relationship between thermodynamic entropy and economic scarcity is only valid for a thermodynamically isolated economy. References to the second law of thermodynamics in economics within the context of scarcity ignore the fact that the earth is not an isolated system. The earth interacts with external sources and sinks of entropy and the resulting total entropy fluctuates around a constant. Even if the mankind finally proves unable to recycle industrial waste and close the technological cycle, the economic disruption caused by the depletion of natural resources may happen while the total thermodynamic entropy of the ecosystem remains essentially at the present level, because the transfer of chemically refined products may not increase significantly the total entropy, but it may decrease their recyclability. The inutility of industrial waste is not connected with its entropy, which may be exemplified with the case of alumina production. The case also demonstrates that industrially generated entropy is discharged into surroundings without being accumulated in ‘thermodynamically unavailable matter’. Material entropy, as a measure of complexity and economic dispersal of resources, can be a recyclability metric, but it is not a thermodynamic parameter, and its growth is not equivalent to the growth of thermodynamic entropy. - Highlights: • Entropy cannot be used as a measure of economic scarcity. • There is no anthropogenic entropy separate from the entropy produced naturally. • Inutility of industrial waste is not connected with its thermodynamic entropy. • Industrially generated entropy may or may not be accumulated in industrial waste. • Recyclability is more important than thermodynamic entropy of a product.
Origin and nature of spontaneous shape fluctuations in "small" nanoparticles.
Yang, Ying; Zhang, Hao; Douglas, Jack F
2014-07-22
Normally chemically inert materials such as Au have been found to be catalytically active in the form of particles whose size is about 1 nm. Direct and indirect observations of various types of metal nanoparticles (NPs) in this size range, under catalytically relevant conditions for fuel-cell operation and catalysis, have indicated that such "small" particles can exhibit large spontaneous shape fluctuations and significant changes in shape and chemical activity in response to alterations in environmental conditions. NPs also normally exhibit facile coalescence when in proximity, impacting their stability and reactivity in applications. We perform molecular dynamics simulations on Ni nanoparticles, a commonly used NP in catalytic applications and carbon nanotube growth, in the ≈1 nm size regime where large-scale shape fluctuations have been observed experimentally. An analysis of the large-scale shape fluctuations observed in our simulations of these "small" NPs indicates that they are accompanied by collective motion of Ni atoms through the NP center, and we quantify these dynamic structures and their impact on NP shape. In contrast, stringlike collective atomic motion is confined to the NP interfacial region of NPs having a diameter greater than a few nanometers, and correspondingly, the overall NP shape remains roughly spherical, a case studied in our prior Ni NP simulations. Evidently, the large spontaneous NP shape fluctuations reflect a change in character of the collective atomic dynamics when the NPs become critically small in size.
Entropy of the Bose-Einstein-condensate ground state: Correlation versus ground-state entropy
Kim, Moochan B.; Svidzinsky, Anatoly; Agarwal, Girish S.; Scully, Marlan O.
2018-01-01
Calculation of the entropy of an ideal Bose-Einstein condensate (BEC) in a three-dimensional trap reveals unusual, previously unrecognized, features of the canonical ensemble. It is found that, for any temperature, the entropy of the Bose gas is equal to the entropy of the excited particles although the entropy of the particles in the ground state is nonzero. We explain this by considering the correlations between the ground-state particles and particles in the excited states. These correlations lead to a correlation entropy which is exactly equal to the contribution from the ground state. The correlations themselves arise from the fact that we have a fixed number of particles obeying quantum statistics. We present results for correlation functions between the ground and excited states in a Bose gas, so as to clarify the role of fluctuations in the system. We also report the sub-Poissonian nature of the ground-state fluctuations.
Directory of Open Access Journals (Sweden)
Ahmed Kadhim Hussein
2016-06-01
Full Text Available Numerical computation of unsteady laminar three-dimensional natural convection and entropy generation in an inclined cubical trapezoidal air-filled cavity is performed for the first time in this work. The vertical right and left sidewalls of the cavity are maintained at constant cold temperatures. The lower wall is subjected to a constant hot temperature, while the upper one is considered insulated. Computations are performed for Rayleigh numbers varied as 103 ⩽ Ra ⩽ 105, while the trapezoidal cavity inclination angle is varied as 0° ⩽ Φ ⩽ 180°. Prandtl number is considered constant at Pr = 0.71. Second law of thermodynamics is applied to obtain thermodynamic losses inside the cavity due to both heat transfer and fluid friction irreversibilities. The variation of local and average Nusselt numbers is presented and discussed, while, streamlines, isotherms and entropy contours are presented in both two and three-dimensional pattern. The results show that when the Rayleigh number increases, the flow patterns are changed especially in three-dimensional results and the flow circulation increases. Also, the inclination angle effect on the total entropy generation becomes insignificant when the Rayleigh number is low. Moreover, when the Rayleigh number increases the average Nusselt number increases.
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.
Dewar, R
2003-01-01
Jaynes' information theory formalism of statistical mechanics is applied to the stationary states of open, non-equilibrium systems. First, it is shown that the probability distribution p subGAMMA of the underlying microscopic phase space trajectories GAMMA over a time interval of length tau satisfies p subGAMMA propor to exp(tau sigma subGAMMA/2k sub B) where sigma subGAMMA is the time-averaged rate of entropy production of GAMMA. Three consequences of this result are then derived: (1) the fluctuation theorem, which describes the exponentially declining probability of deviations from the second law of thermodynamics as tau -> infinity; (2) the selection principle of maximum entropy production for non-equilibrium stationary states, empirical support for which has been found in studies of phenomena as diverse as the Earth's climate and crystal growth morphology; and (3) the emergence of self-organized criticality for flux-driven systems in the slowly-driven limit. The explanation of these results on general inf...
Kim, Y.; Johnson, M. S.
2017-12-01
Spectral entropy (Hs) is an index which can be used to measure the structural complexity of time series data. When a time series is made up of one periodic function, the Hs value becomes smaller, while Hs becomes larger when a time series is composed of several periodic functions. We hypothesized that this characteristic of the Hs could be used to quantify the water stress history of vegetation. For the ideal condition for which sufficient water is supplied to an agricultural crop or natural vegetation, there should be a single distinct phenological cycle represented in a vegetation index time series (e.g., NDVI and EVI). However, time series data for a vegetation area that repeatedly experiences water stress may include several fluctuations that can be observed in addition to the predominant phenological cycle. This is because the process of experiencing water stress and recovering from it generates small fluctuations in phenological characteristics. Consequently, the value of Hs increases when vegetation experiences several water shortages. Therefore, the Hs could be used as an indicator for water stress history. To test this hypothesis, we analyzed Moderate Resolution Imaging Spectroradiometer (MODIS) Normalized Difference Vegetation Index (NDVI) data for a natural area in comparison to a nearby sugarcane area in seasonally-dry western Costa Rica. In this presentation we will illustrate the use of spectral entropy to evaluate the vegetative responses of natural vegetation (dry tropical forest) and sugarcane under three different irrigation techniques (center pivot irrigation, drip irrigation and flood irrigation). Through this comparative analysis, the utility of Hs as an indicator will be tested. Furthermore, crop response to the different irrigation methods will be discussed in terms of Hs, NDVI and yield.
Entropy Generation Due to Natural Convection in a Partially Heated Cavity by Local RBF-DQ Method
DEFF Research Database (Denmark)
Soleimani, S.; Qajarjazi, A.; Bararnia, H.
2011-01-01
The Local Radial Basis Function-Differential Quadrature (RBF-DQ) method is applied to twodimensional incompressible Navier-Stokes equations in primitive form. Numerical results of heatlines and entropy generation due to heat transfer and fluid friction have been obtained for laminar natural...
Information and entropy theory for the sustainability of coupled human and natural systems
Directory of Open Access Journals (Sweden)
Audrey L. Mayer
2014-09-01
Full Text Available For coupled human and natural systems (CHANS, sustainability can be defined operationally as a feasible, desirable set of flows (material, currency, information, energy, individuals, etc. that can be maintained despite internal changes and changes in the environment. Sustainable development can be defined as the process by which CHANS can be moved toward sustainability. Specific indicators that give insight into the structure and behavior of feedbacks in CHANS are of particular interest because they would aid in the sustainable management of these systems through an understanding of the structures that govern system behavior. However, the use of specific feedbacks as monitoring tools is rare, possibly because of uncertainties regarding the nature of their dynamics and the diversity of types of feedbacks encountered in these systems. An information theory perspective may help to rectify this situation, as evidenced by recent research in sustainability science that supports the use of unit-free measures such as Shannon entropy and Fisher information to aggregate disparate indicators. These measures have been used for spatial and temporal datasets to monitor progress toward sustainability targets. Here, we provide a review of information theory and a theoretical framework for studying the dynamics of feedbacks in CHANS. We propose a combination of information-based indices that might productively inform our sustainability goals, particularly when related to key feedbacks in CHANS.
Tsallis non-additive entropy and natural time analysis of seismicity
Sarlis, N. V.; Skordas, E. S.; Varotsos, P.
2017-12-01
Within the context of Tsallis non-additive entropy [1] statistical mechanics -in the frame of which kappa distributions arise [2,3]- a derivation of the Gutenberg-Richter (GR) law of seismicity has been proposed [4,5]. Such an analysis leads to a generalized GR law [6,7] which is applied here to the earthquakes in Japan and California. These seismic data are also studied in natural time [6] revealing that although some properties of seismicity may be recovered by the non-additive entropy approach, temporal correlations between successive earthquake magnitudes should be also taken into account [6,8]. The importance of such correlations is strengthened by the observation of periods of long range correlated earthquake magnitude time series [9] a few months before all earthquakes of magnitude 7.6 or larger in the entire Japanese area from 1 January 1984 to 11 March 2011 (the day of the magnitude 9.0 Tohoku-Oki earthquake) almost simultaneously with characteristic order parameter variations of seismicity [10]. These variations appear approximately when low frequency abnormal changes of the electric and magnetic field of the Earth (less than around 1Hz) are recorded [11] before strong earthquakes as the magnitude 9.0 Tohoku-Oki earthquake in Japan in 2011 [12]. 1. C Tsallis, J Stat Phys 52 (1988) 479 2. G Livadiotis, and D J McComas, J Geophys Res 114 (2009) A11105 3. G Livadiotis, Kappa Distributions. (Elsevier, Amsterdam) 2017. doi: 10.1016/B978-0-12-804638-8.01001-9 4. O Sotolongo-Costa, A Posadas, Phys Rev Lett 92 (2004) 048501 5. R Silva, G França, C Vilar, J Alcaniz, Phys Rev E 73 (2006) 026102 6. N Sarlis, E Skordas, P Varotsos, Phys Rev E 82 (2010) 021110 7. L Telesca, Bull Seismol Soc Am 102 (2012) 886-891 8. P Varotsos, N Sarlis, E Skordas, Natural Time Analysis: The new view of time. (Springer, Berlin) 2011. doi: 10.1007/978-3-642-16449-1 9. P Varotsos, N Sarlis, E Skordas, J Geophys Res Space Physics 119 (2014) 9192. 10. N Sarlis, E Skordas, P Varotsos, T
Directory of Open Access Journals (Sweden)
Tommaso Toffoli
2016-06-01
Full Text Available Here we deconstruct, and then in a reasoned way reconstruct, the concept of “entropy of a system”, paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a count associated with a description; this count (traditionally expressed in logarithmic form for a number of good reasons is in essence the number of possibilities—specific instances or “scenarios”—that match that description. Very natural (and virtually inescapable generalizations of the idea of description are the probability distribution and its quantum mechanical counterpart, the density operator. We track the process of dynamically updating entropy as a system evolves. Three factors may cause entropy to change: (1 the system’s internal dynamics; (2 unsolicited external influences on it; and (3 the approximations one has to make when one tries to predict the system’s future state. The latter task is usually hampered by hard-to-quantify aspects of the original description, limited data storage and processing resource, and possibly algorithmic inadequacy. Factors 2 and 3 introduce randomness—often huge amounts of it—into one’s predictions and accordingly degrade them. When forecasting, as long as the entropy bookkeping is conducted in an honest fashion, this degradation will always lead to an entropy increase. To clarify the above point we introduce the notion of honest entropy, which coalesces much of what is of course already done, often tacitly, in responsible entropy-bookkeping practice. This notion—we believe—will help to fill an expressivity gap in scientific discourse. With its help, we shall prove that any dynamical system—not just our physical universe—strictly obeys Clausius’s original formulation of the second law of thermodynamics if and only if it is invertible. Thus this law is a tautological property of invertible systems!
Order parameter fluctuations in natural time and b-value variation before large earthquakes
Directory of Open Access Journals (Sweden)
E. S. Skordas
2012-11-01
Full Text Available Self-similarity may stem from two origins: the process increments infinite variance and/or process memory. The b-value of the Gutenberg-Richter law comes from the first origin. In the frame of natural time analysis of earthquake data, a fall of the b-value observed before large earthquakes reflects an increase of the order parameter fluctuations upon approaching the critical point (mainshock. The increase of these fluctuations, however, is also influenced from the second origin of self-similarity, i.e., temporal correlations between earthquake magnitudes. This is supported by observations and simulations of an earthquake model.
Directory of Open Access Journals (Sweden)
Abdullah A.A.A Al-Rashed
2017-09-01
Full Text Available Natural convection and entropy generation due to the heat transfer and fluid friction irreversibilities in a three-dimensional cubical cavity with partially heated and cooled vertical walls has been investigated numerically using the finite volume method. Four different arrangements of partially active vertical sidewalls of the cubical cavity are considered. Numerical calculations are carried out for Rayleigh numbers from (103 ≤ Ra ≤ 106, various locations of the partial heating and cooling vertical sidewalls, while the Prandtl number of air is considered constant as Pr=0.7 and the irreversibility coefficient is taken as (φ=10−4. The results explain that the total entropy generation rate increases when the Rayleigh number increases. While, the Bejan number decreases as the Rayleigh number increases. Also, it is found that the arrangements of heating and cooling regions have a significant effect on the fluid flow and heat transfer characteristics of natural convection and entropy generation in a cubical cavity. The Middle-Middle arrangement produces higher values of average Nusselt numbers.
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Rashidi Mohammad Mehdi
2015-01-01
Full Text Available The similar solution on the equations of the revised Cheng-Minkowycz problem for natural convective boundary layer flow of nanofluid through a porous medium gives (using an analytical method, a system of non-linear partial differential equations which are solved by optimal homotopy analysis method. Effects of various drastic parameters on the fluid and heat transfer characteristics have been analyzed. A very good agreement is observed between the obtained results and the numerical ones. The entropy generation has been derived and a comprehensive parametric analysis on that has been done. Each component of the entropy generation has been analyzed separately and the contribution of each one on the total value of entropy generation has been determined. It is found that the entropy generation as an important aspect of the industrial applications has been affected by various parameters which should be controlled to minimize the entropy generation.
Measurement Invariance, Entropy, and Probability
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D. Eric Smith
2010-02-01
Full Text Available We show that the natural scaling of measurement for a particular problem defines the most likely probability distribution of observations taken from that measurement scale. Our approach extends the method of maximum entropy to use measurement scale as a type of information constraint. We argue that a very common measurement scale is linear at small magnitudes grading into logarithmic at large magnitudes, leading to observations that often follow Student’s probability distribution which has a Gaussian shape for small fluctuations from the mean and a power law shape for large fluctuations from the mean. An inverse scaling often arises in which measures naturally grade from logarithmic to linear as one moves from small to large magnitudes, leading to observations that often follow a gamma probability distribution. A gamma distribution has a power law shape for small magnitudes and an exponential shape for large magnitudes. The two measurement scales are natural inverses connected by the Laplace integral transform. This inversion connects the two major scaling patterns commonly found in nature. We also show that superstatistics is a special case of an integral transform, and thus can be understood as a particular way in which to change the scale of measurement. Incorporating information about measurement scale into maximum entropy provides a general approach to the relations between measurement, information and probability.
International Nuclear Information System (INIS)
El-Maghlany, Wael M.; Saqr, Khalid M.; Teamah, Mohamed A.
2014-01-01
Highlights: • Entropy generation in laminar natural convection in square cavity numerically studied. • The cavity subjected to an isotropic heat field with different intensities. • Study ranges 10 3 ⩽ Ra ⩽ 10 5 , 0 ⩽ ϕ ⩽ 10 and Pr = 0.7. • Entropy generation drastically affected by the superposition of an isotropic heat field. • CFD based empirical were derived for entropy generation as a function of Ra and φ. - Abstract: Entropy generation associated with laminar natural convection in an infinite square cavity, subjected to an isotropic heat field with different intensities; was numerically investigated for different values of Rayleigh number. The numerical work was carried out using, an in-house CFD code written in FORTRAN, which discretizes non-dimensional forms of the governing equations using the finite volume method and solves the resulting system of equations using Gauss-Seidal method utilizing a TDMA algorithm. Proper code validation was undertaken in order to establish the entropy generation calculations. It was found that the increase in the isotropic heat field intensity resulted in a corresponding exponential increase of the entropy augmentation number, and promoted high values of Bejan number within the flow. The entropy generation due to heat transfer was approximately one order of magnitude higher than the entropy generation due to fluid friction. The spatial uniformity of the Bejan number was more sensitive to the change in Rayleigh number than to the heat field intensity. The thermodynamic penalty of the isotropic heat field is shown by means of global integrals of the entropy source terms over the entire flow domain
Schoepf, Verena; Stat, Michael; Falter, James L; McCulloch, Malcolm T
2015-12-02
Naturally extreme temperature environments can provide important insights into the processes underlying coral thermal tolerance. We determined the bleaching resistance of Acropora aspera and Dipsastraea sp. from both intertidal and subtidal environments of the naturally extreme Kimberley region in northwest Australia. Here tides of up to 10 m can cause aerial exposure of corals and temperatures as high as 37 °C that fluctuate daily by up to 7 °C. Control corals were maintained at ambient nearshore temperatures which varied diurnally by 4-5 °C, while treatment corals were exposed to similar diurnal variations and heat stress corresponding to ~20 degree heating days. All corals hosted Symbiodinium clade C independent of treatment or origin. Detailed physiological measurements showed that these corals were nevertheless highly sensitive to daily average temperatures exceeding their maximum monthly mean of ~31 °C by 1 °C for only a few days. Generally, Acropora was much more susceptible to bleaching than Dipsastraea and experienced up to 75% mortality, whereas all Dipsastraea survived. Furthermore, subtidal corals, which originated from a more thermally stable environment compared to intertidal corals, were more susceptible to bleaching. This demonstrates that while highly fluctuating temperatures enhance coral resilience to thermal stress, they do not provide immunity to extreme heat stress events.
Heat of combustion, sound speed and component fluctuations in natural gas
International Nuclear Information System (INIS)
Burstein, L.; Ingman, D.
1998-01-01
The heat of combustion and sound speed of natural gas were studied as a function of random fluctuation of the gas fractions. A method of sound speed determination was developed and used for over 50,000 possible variants of component concentrations in four- and five- component mixtures. A test on binary (methane-ethane) and multicomponent (Gulf Coast) gas mixtures under standard pressure and moderate temperatures shows satisfactory predictability of sound speed on the basis of the binary virial coefficients, sound speeds and heat capacities of the pure components. Uncertainty in the obtained values does not exceed that of the pure component data. The results of comparison between two natural gas mixtures - with and without nonflammable components - are reported
Inquiries into the Nature of Free Energy and Entropy in Respect to Biochemical Thermodynamics
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Clinton D. Stoner
2000-08-01
Full Text Available Free energy and entropy are examined in detail from the standpoint of classical thermodynamics. The approach is logically based on the fact that thermodynamic work is mediated by thermal energy through the tendency for nonthermal energy to convert spontaneously into thermal energy and for thermal energy to distribute spontaneously and uniformly within the accessible space. The fact that free energy is a Second-Law, expendable energy that makes it possible for thermodynamic work to be done at finite rates is emphasized. Entropy, as originally defined, is pointed out to be the capacity factor for thermal energy that is hidden with respect to temperature; it serves to evaluate the practical quality of thermal energy and to account for changes in the amounts of latent thermal energies in systems maintained at constant temperature. With entropy thus operationally defined, it is possible to see that TDSÃ‚Â° of the Gibbs standard free energy relation DGÃ‚Â°= DHÃ‚Â°-TDSÃ‚Â° serves to account for differences or changes in nonthermal energies that do not contribute to DGÃ‚Â° and that, since DHÃ‚Â° serves to account for differences or changes in total energy, complete enthalpy-entropy (DHÃ‚Â° - TDSÃ‚Â° compensation must invariably occur in isothermal processes for which TDSÃ‚Â° is finite. A major objective was to clarify the means by which free energy is transferred and conserved in sequences of biological reactions coupled by freely diffusible intermediates. In achieving this objective it was found necessary to distinguish between a 'characteristic free energy' possessed by all First-Law energies in amounts equivalent to the amounts of the energies themselves and a 'free energy of concentration' that is intrinsically mechanical and relatively elusive in that it can appear to be free of First-Law energy. The findings in this regard serve to clarify the fact that the transfer of chemical potential energy from one
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Aich Walid
2018-01-01
Full Text Available A computational analysis of the natural ventilation process and entropy generation in 3-D prismatic greenhouse was performed using CFD. The aim of the study is to investigate how buoyancy forces influence air-flow and temperature patterns inside the greenhouse having lower level opening in its right heated façade and also upper level opening near the roof top in the opposite cooled façade. The bot-tom and all other walls are assumed to be perfect thermal insulators. Rayleigh number is the main parameter which changes from 103 to 106 and Prandtl number is fixed at Pr = 0.71. Results are reported in terms of particles trajectories, iso-surfaces of temperature, mean Nusselt number, and entropy generation. It has been found that the flow structure is sensitive to the value of Rayleigh number and that heat transfer increases with increasing this parameter. Also, it have been noticed that, using asymmetric opening positions improve the natural ventilation and facilitate the occurrence of buoyancy induced upward cross air-flow (low-level supply and upper-level extraction inside the greenhouse.
Xie, Hong-Bo; Guo, Jing-Yi; Zheng, Yong-Ping
2010-04-01
In the present contribution, a complexity measure is proposed to assess surface electromyography (EMG) in the study of muscle fatigue during sustained, isometric muscle contractions. Approximate entropy (ApEn) is believed to provide quantitative information about the complexity of experimental data that is often corrupted with noise, short data length, and in many cases, has inherent dynamics that exhibit both deterministic and stochastic behaviors. We developed an improved ApEn measure, i.e., fuzzy approximate entropy (fApEn), which utilizes the fuzzy membership function to define the vectors' similarity. Tests were conducted on independent, identically distributed (i.i.d.) Gaussian and uniform noises, a chirp signal, MIX processes, Rossler equation, and Henon map. Compared with the standard ApEn, the fApEn showed better monotonicity, relative consistency, and more robustness to noise when characterizing signals with different complexities. Performance analysis on experimental EMG signals demonstrated that the fApEn significantly decreased during the development of muscle fatigue, which is a similar trend to that of the mean frequency (MNF) of the EMG signal, while the standard ApEn failed to detect this change. Moreover, fApEn of EMG demonstrated a better robustness to the length of the analysis window in comparison with the MNF of EMG. The results suggest that the fApEn of an EMG signal may potentially become a new reliable method for muscle fatigue assessment and be applicable to other short noisy physiological signal analysis.
Fluctuating interaction network and time-varying stability of a natural fish community
Ushio, Masayuki; Hsieh, Chih-Hao; Masuda, Reiji; Deyle, Ethan R.; Ye, Hao; Chang, Chun-Wei; Sugihara, George; Kondoh, Michio
2018-02-01
Ecological theory suggests that large-scale patterns such as community stability can be influenced by changes in interspecific interactions that arise from the behavioural and/or physiological responses of individual species varying over time. Although this theory has experimental support, evidence from natural ecosystems is lacking owing to the challenges of tracking rapid changes in interspecific interactions (known to occur on timescales much shorter than a generation time) and then identifying the effect of such changes on large-scale community dynamics. Here, using tools for analysing nonlinear time series and a 12-year-long dataset of fortnightly collected observations on a natural marine fish community in Maizuru Bay, Japan, we show that short-term changes in interaction networks influence overall community dynamics. Among the 15 dominant species, we identify 14 interspecific interactions to construct a dynamic interaction network. We show that the strengths, and even types, of interactions change with time; we also develop a time-varying stability measure based on local Lyapunov stability for attractor dynamics in non-equilibrium nonlinear systems. We use this dynamic stability measure to examine the link between the time-varying interaction network and community stability. We find seasonal patterns in dynamic stability for this fish community that broadly support expectations of current ecological theory. Specifically, the dominance of weak interactions and higher species diversity during summer months are associated with higher dynamic stability and smaller population fluctuations. We suggest that interspecific interactions, community network structure and community stability are dynamic properties, and that linking fluctuating interaction networks to community-level dynamic properties is key to understanding the maintenance of ecological communities in nature.
Survival of rapidly fluctuating natural low winter temperatures by High Arctic soil invertebrates.
Convey, Peter; Abbandonato, Holly; Bergan, Frode; Beumer, Larissa Teresa; Biersma, Elisabeth Machteld; Bråthen, Vegard Sandøy; D'Imperio, Ludovica; Jensen, Christina Kjellerup; Nilsen, Solveig; Paquin, Karolina; Stenkewitz, Ute; Svoen, Mildrid Elvik; Winkler, Judith; Müller, Eike; Coulson, Stephen James
2015-12-01
The extreme polar environment creates challenges for its resident invertebrate communities and the stress tolerance of some of these animals has been examined over many years. However, although it is well appreciated that standard air temperature records often fail to describe accurately conditions experienced at microhabitat level, few studies have explicitly set out to link field conditions experienced by natural multispecies communities with the more detailed laboratory ecophysiological studies of a small number of 'representative' species. This is particularly the case during winter, when snow cover may insulate terrestrial habitats from extreme air temperature fluctuations. Further, climate projections suggest large changes in precipitation will occur in the polar regions, with the greatest changes expected during the winter period and, hence, implications for the insulation of overwintering microhabitats. To assess survival of natural High Arctic soil invertebrate communities contained in soil and vegetation cores to natural winter temperature variations, the overwintering temperatures they experienced were manipulated by deploying cores in locations with varying snow accumulation: No Snow, Shallow Snow (30 cm) and Deep Snow (120 cm). Air temperatures during the winter period fluctuated frequently between +3 and -24 °C, and the No Snow soil temperatures reflected this variation closely, with the extreme minimum being slightly lower. Under 30 cm of snow, soil temperatures varied less and did not decrease below -12 °C. Those under deep snow were even more stable and did not decline below -2 °C. Despite these striking differences in winter thermal regimes, there were no clear differences in survival of the invertebrate fauna between treatments, including oribatid, prostigmatid and mesostigmatid mites, Araneae, Collembola, Nematocera larvae or Coleoptera. This indicates widespread tolerance, previously undocumented for the Araneae, Nematocera or Coleoptera, of
Directory of Open Access Journals (Sweden)
Mark V Albert
2012-12-01
Full Text Available Due to multiple factors such as fatigue, muscle strengthening, and neural plasticity, the responsiveness of the motor apparatus to neural commands changes over time. To enable precise movements the nervous system must adapt to compensate for these changes. Recent models of motor adaptation derive from assumptions about the way the motor apparatus changes. Characterizing these changes is difficult because motor adaptation happens at the same time, masking most of the effects of ongoing changes. Here, we analyze eye movements of monkeys with lesions to the posterior cerebellar vermis that impair adaptation. Their fluctuations better reveal the underlying changes of the motor system over time. When these measured, unadapted changes are used to derive optimal motor adaptation rules the prediction precision significantly improves. Among three models that similarly fit single-day adaptation results, the model that also matches the temporal correlations of the nonadapting saccades most accurately predicts multiple day adaptation. Saccadic gain adaptation is well matched to the natural statistics of fluctuations of the oculomotor plant.
DEFF Research Database (Denmark)
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...
Indian Academy of Sciences (India)
Enthalpy–entropy compensation is the name given to the correlation sometimes observed between the estimates of the enthalpy and entropy of a reaction obtained from temperature-dependence data. Although the mainly artefactual nature of this correlation has been known for many years, the subject enjoys periodical ...
EEG entropy measures in anesthesia
Liang, Zhenhu; Wang, Yinghua; Sun, Xue; Li, Duan; Voss, Logan J.; Sleigh, Jamie W.; Hagihira, Satoshi; Li, Xiaoli
2015-01-01
Highlights: ► Twelve entropy indices were systematically compared in monitoring depth of anesthesia and detecting burst suppression.► Renyi permutation entropy performed best in tracking EEG changes associated with different anesthesia states.► Approximate Entropy and Sample Entropy performed best in detecting burst suppression. Objective: Entropy algorithms have been widely used in analyzing EEG signals during anesthesia. However, a systematic comparison of these entropy algorithms in assessing anesthesia drugs' effect is lacking. In this study, we compare the capability of 12 entropy indices for monitoring depth of anesthesia (DoA) and detecting the burst suppression pattern (BSP), in anesthesia induced by GABAergic agents. Methods: Twelve indices were investigated, namely Response Entropy (RE) and State entropy (SE), three wavelet entropy (WE) measures [Shannon WE (SWE), Tsallis WE (TWE), and Renyi WE (RWE)], Hilbert-Huang spectral entropy (HHSE), approximate entropy (ApEn), sample entropy (SampEn), Fuzzy entropy, and three permutation entropy (PE) measures [Shannon PE (SPE), Tsallis PE (TPE) and Renyi PE (RPE)]. Two EEG data sets from sevoflurane-induced and isoflurane-induced anesthesia respectively were selected to assess the capability of each entropy index in DoA monitoring and BSP detection. To validate the effectiveness of these entropy algorithms, pharmacokinetic/pharmacodynamic (PK/PD) modeling and prediction probability (Pk) analysis were applied. The multifractal detrended fluctuation analysis (MDFA) as a non-entropy measure was compared. Results: All the entropy and MDFA indices could track the changes in EEG pattern during different anesthesia states. Three PE measures outperformed the other entropy indices, with less baseline variability, higher coefficient of determination (R2) and prediction probability, and RPE performed best; ApEn and SampEn discriminated BSP best. Additionally, these entropy measures showed an advantage in computation
Gibanov, Nikita S.; Sheremet, Mikhail A.; Oztop, Hakan F.; Al-Salem, Khaled
2018-04-01
In this study, natural convection combined with entropy generation of Fe3O4-water nanofluid within a square open cavity filled with two different porous blocks under the influence of uniform horizontal magnetic field is numerically studied. Porous blocks of different thermal properties, permeability and porosity are located on the bottom wall. The bottom wall of the cavity is kept at hot temperature Th, while upper open boundary is at constant cold temperature Tc and other walls of the cavity are supposed to be adiabatic. Governing equations with corresponding boundary conditions formulated in dimensionless stream function and vorticity using Brinkman-extended Darcy model for porous blocks have been solved numerically using finite difference method. Numerical analysis has been carried out for wide ranges of Hartmann number, nanoparticles volume fraction and length of the porous blocks. It has been found that an addition of spherical ferric oxide nanoparticles can order the flow structures inside the cavity.
Adjoint entropy vs topological entropy
Giordano Bruno, Anna
2012-01-01
Recently the adjoint algebraic entropy of endomorphisms of abelian groups was introduced and studied. We generalize the notion of adjoint entropy to continuous endomorphisms of topological abelian groups. Indeed, the adjoint algebraic entropy is defined using the family of all finite-index subgroups, while we take only the subfamily of all open finite-index subgroups to define the topological adjoint entropy. This allows us to compare the (topological) adjoint entropy with the known topologic...
Statistical tests for the Gaussian nature of primordial fluctuations through CBR experiments
International Nuclear Information System (INIS)
Luo, X.
1994-01-01
Information about the physical processes that generate the primordial fluctuations in the early Universe can be gained by testing the Gaussian nature of the fluctuations through cosmic microwave background radiation (CBR) temperature anisotropy experiments. One of the crucial aspects of density perturbations that are produced by the standard inflation scenario is that they are Gaussian, whereas seeds produced by topological defects left over from an early cosmic phase transition tend to be non-Gaussian. To carry out this test, sophisticated statistical tools are required. In this paper, we will discuss several such statistical tools, including multivariant skewness and kurtosis, Euler-Poincare characteristics, the three-point temperature correlation function, and Hotelling's T 2 statistic defined through bispectral estimates of a one-dimensional data set. The effect of noise present in the current data is discussed in detail and the COBE 53 GHz data set is analyzed. Our analysis shows that, on the large angular scale to which COBE is sensitive, the statistics are probably Gaussian. On the small angular scales, the importance of Hotelling's T 2 statistic is stressed, and the minimum sample size required to test Gaussianity is estimated. Although the current data set available from various experiments at half-degree scales is still too small, improvement of the data set by roughly a factor of 2 will be enough to test the Gaussianity statistically. On the arc min scale, we analyze the recent RING data through bispectral analysis, and the result indicates possible deviation from Gaussianity. Effects of point sources are also discussed. It is pointed out that the Gaussianity problem can be resolved in the near future by ground-based or balloon-borne experiments
Tsallis-like entropies in quantum scattering
International Nuclear Information System (INIS)
Ion, D.B.; Ion, M.L.
1998-01-01
In this work, the following entropies in quantum scattering are defined: the informational angular entropy, S θ ; Tsallis-like angular entropies, S q (θ); the angular momentum entropy, S L ; the Tsallis-like angular momentum entropies, S q (L); the angle-angular momentum entropy, S θL . These entropies are defined as natural measures of the uncertainties corresponding to the distribution probabilities. If we are interested in obtaining a measure of uncertainty of the simultaneous realization of the probability distributions, than, we have to calculate the entropy corresponding to these distributions. The expression of angle-angular momentum entropy is given. The relation between the Tsallis entropies and the angle-angular momentum entropy is derived
Energy Technology Data Exchange (ETDEWEB)
Alvarez R, J.T
1998-10-01
This thesis presents a microscopic model for the non-linear fluctuating hydrodynamic of superfluid helium ({sup 4} He), model developed by means of the Maximum Entropy Method (Maxent). In the chapter 1, it is demonstrated the necessity to developing a microscopic model for the fluctuating hydrodynamic of the superfluid helium, starting from to show a brief overview of the theories and experiments developed in order to explain the behavior of the superfluid helium. On the other hand, it is presented the Morozov heuristic method for the construction of the non-linear hydrodynamic fluctuating of simple fluid. Method that will be generalized for the construction of the non-linear fluctuating hydrodynamic of the superfluid helium. Besides, it is presented a brief summary of the content of the thesis. In the chapter 2, it is reproduced the construction of a Generalized Fokker-Planck equation, (GFP), for a distribution function associated with the coarse grained variables. Function defined with aid of a nonequilibrium statistical operator {rho}hut{sub FP} that is evaluated as Wigneris function through {rho}{sub CG} obtained by Maxent. Later this equation of GFP is reduced to a non-linear local FP equation from considering a slow and Markov process in the coarse grained variables. In this equation appears a matrix D{sub mn} defined with a nonequilibrium coarse grained statistical operator {rho}hut{sub CG}, matrix elements are used in the construction of the non-linear fluctuating hydrodynamics equations of the superfluid helium. In the chapter 3, the Lagrange multipliers are evaluated for to determine {rho}hut{sub CG} by means of the local equilibrium statistical operator {rho}hut{sub l}-tilde with the hypothesis that the system presents small fluctuations. Also are determined the currents associated with the coarse grained variables and furthermore are evaluated the matrix elements D{sub mn} but with aid of a quasi equilibrium statistical operator {rho}hut{sub qe} instead
Pa'ee, Furzani; Johnson, Giles
2017-10-01
Photoacclimation is a process by which photosynthetic capacity is regulated in response to environmental adjustments in terms of light regime. Photoacclimation is essential in determining the photosynthetic capacity to optimize light use and to avoid potentially damaging effects. Previous work in our laboratory has identified a gene, gpt2 (At1g61800) that is essential for plants to acclimate to an increase and decrease of growth irradiance, separately. To investigate the photoacclimation ability towards fluctuating natural light condition in Arabidopsis thaliana, photosynthetic capacity was measured in plants of the accession Wassileskija (WS) and in plants lacking expression of the gene At1g61800 (WS-gpt2). The experiment was carried out over a time span from early Autumn to early Spring season in 2010-2011 and 2011-2012. The seedlings were grown in an unheated greenhouse in Manchester, UK without supplementary lighting. Gas exchange measurements and chlorophyll content estimation were performed on WS and WS-gpt2 and it showed that both sets of plants were able to acclimate to fluctuating natural light condition. Therefore, it is suggested that the mechanisms of acclimation in a separate growth light condition is mechanistically distinct than the mechanism under fluctuating natural light condition.
Lechner, Joseph H.
1999-10-01
This report describes two classroom activities that help students visualize the abstract concept of entropy and apply the second law of thermodynamics to real situations. (i) A sealed "rainbow tube" contains six smaller vessels, each filled with a different brightly colored solution (low entropy). When the tube is inverted, the solutions mix together and react to form an amorphous precipitate (high entropy). The change from low entropy to high entropy is irreversible as long as the tube remains sealed. (ii) When U.S. currency is withdrawn from circulation, intact bills (low entropy) are shredded into small fragments (high entropy). Shredding is quick and easy; the reverse process is clearly nonspontaneous. It is theoretically possible, but it is time-consuming and energy-intensive, to reassemble one bill from a pile that contains fragments of hundreds of bills. We calculate the probability P of drawing pieces of only one specific bill from a mixture containing one pound of bills, each shredded into n fragments. This result can be related to Boltzmann's entropy formula S?=klnW.
Massive superclusters as a probe of the nature and amplitude of primordial density fluctuations
Energy Technology Data Exchange (ETDEWEB)
Kaiser, N.; Davis, M.
1985-10-01
It is pointed out that correlation studies of galaxy positions have been widely used in the search for information about the large-scale matter distribution. The study of rare condensations on large scales provides an approach to extend the existing knowledge of large-scale structure into the weakly clustered regime. Shane (1975) provides a description of several apparent massive condensations within the Shane-Wirtanen catalog, taking into account the Serpens-Virgo cloud and the Corona cloud. In the present study, a description is given of a model for estimating the frequency of condensations which evolve from initially Gaussian fluctuations. This model is applied to the Corona cloud to estimate its rareness and thereby estimate the rms density contrast on this mass scale. An attempt is made to find a conflict between the density fluctuations derived from the Corona cloud and independent constraints. A comparison is conducted of the estimate and the density fluctuations predicted to arise in a universe dominated by cold dark matter. 24 references.
Rahimi, Alireza; Kasaeipoor, Abbas; Malekshah, Emad Hasani; Amiri, Ali
2018-03-01
The natural convection heat transfer and fluid flow is analyzed using lattice Boltzmann numerical method. The entropy generation analysis and heatline visualization are used to study the convective flow field comprehensively. The hollow L-shaped cavity is considered and filled with SiO2-TiO2/Water-EG (60:40) hybrid nanofluid. The thermal conductivity and dynamic viscosity of nanofluid are measured experimentally. To use the experimental data of thermal conductivity and dynamic viscosity, two sets of correlations based on temperature for six different solid volume fractions of 0.5, 1, 1.5, 2, 2.5 and 3 vol% are derived. The influences of different governing parameters such different aspect ratios, solid volume fractions of nanofluid and Rayleigh numbers on the fluid flow, temperature filed, average/local Nusselt number, total/local entropy generation and heatlines are presented.
Rahimi, Alireza; Sepehr, Mohammad; Lariche, Milad Janghorban; Mesbah, Mohammad; Kasaeipoor, Abbas; Malekshah, Emad Hasani
2018-03-01
The lattice Boltzmann simulation of natural convection in H-shaped cavity filled with nanofluid is performed. The entropy generation analysis and heatline visualization are employed to analyze the considered problem comprehensively. The produced nanofluid is SiO2-TiO2/Water-EG (60:40) hybrid nanofluid, and the thermal conductivity and dynamic viscosity of used nanofluid are measured experimentally. To use the experimental data of thermal conductivity and dynamic viscosity, two sets of correlations based on temperature for six different solid volume fractions of 0.5, 1, 1.5, 2, 2.5 and 3 vol% are derived. The influences of different governing parameters such different aspect ratio, solid volume fractions of nanofluid and Rayleigh numbers on the fluid flow, temperature filed, average/local Nusselt number, total/local entropy generation and heatlines are presented.
Possible Noise Nature of Elsässer Variable z- in Highly Alfvénic Solar Wind Fluctuations
Wang, X.; Tu, C.-Y.; He, J.-S.; Wang, L.-H.; Yao, S.; Zhang, L.
2018-01-01
It has been a long-standing debate on the nature of Elsässer variable z- observed in the solar wind fluctuations. It is widely believed that z- represents inward propagating Alfvén waves and interacts nonlinearly with z+ (outward propagating Alfvén waves) to generate energy cascade. However, z- variations sometimes show a feature of convective structures. Here we present a new data analysis on autocorrelation functions of z- in order to get some definite information on its nature. We find that there is usually a large drop on the z- autocorrelation function when the solar wind fluctuations are highly Alfvénic. The large drop observed by Helios 2 spacecraft near 0.3 AU appears at the first nonzero time lag τ = 81 s, where the value of the autocorrelation coefficient drops to 25%-65% of that at τ = 0 s. Beyond the first nonzero time lag, the autocorrelation coefficient decreases gradually to zero. The drop of z- correlation function also appears in the Wind observations near 1 AU. These features of the z- correlation function may suggest that z- fluctuations consist of two components: high-frequency white noise and low-frequency pseudo structures, which correspond to flat and steep parts of z- power spectrum, respectively. This explanation is confirmed by doing a simple test on an artificial time series, which is obtained from the superposition of a random data series on its smoothed sequence. Our results suggest that in highly Alfvénic fluctuations, z- may not contribute importantly to the interactions with z+ to produce energy cascade.
Quantum fluctuations from thermal fluctuations in Jacobson formalism
Energy Technology Data Exchange (ETDEWEB)
Faizal, Mir [University of British Columbia-Okanagan, Irving K. Barber School of Arts and Sciences, Kelowna, BC (Canada); University of Lethbridge, Department of Physics and Astronomy, Lethbridge, AB (Canada); Ashour, Amani; Alcheikh, Mohammad [Damascus University, Mathematics Department, Faculty of Science, Damascus (Syrian Arab Republic); Alasfar, Lina [Universite Clermont Auvergne, Laboratoire de Physique Corpusculaire de Clermont-Ferrand, Aubiere (France); Alsaleh, Salwa; Mahroussah, Ahmed [King Saud University, Department of Physics and Astronomy, Riyadh (Saudi Arabia)
2017-09-15
In the Jacobson formalism general relativity is obtained from thermodynamics. This is done by using the Bekenstein-Hawking entropy-area relation. However, as a black hole gets smaller, its temperature will increase. This will cause the thermal fluctuations to also increase, and these will in turn correct the Bekenstein-Hawking entropy-area relation. Furthermore, with the reduction in the size of the black hole, quantum effects will also start to dominate. Just as the general relativity can be obtained from thermodynamics in the Jacobson formalism, we propose that the quantum fluctuations to the geometry can be obtained from thermal fluctuations. (orig.)
Directory of Open Access Journals (Sweden)
Elena Shadrina
2016-11-01
Full Text Available Fluctuating asymmetry (FA in nine species of small mammals (Insectivora and Rodentia was estimated using 10 cranial features (foramina for nerves and blood vessels. The main criterion was the occurrence of the fluctuating asymmetry manifestations (OFAM. A total of 2300 skulls collected in the taiga and forest-tundra of Yakutia (Northeast Asia were examined. The examined species are characterized by comparable OFAM values in the vast territories of the taiga zone; on the ecological periphery of the range an increased FA level is registered. Asymmetric manifestations in analyzed features are equally likely to occur in males and females. OFAM values in juveniles are higher than in adults; this difference is more pronounced on the periphery of the geographic range. Among juveniles, lower FA levels are observed in individuals that have bred. It can be surmised that the risk of elimination of individuals with high FA levels increases in stressful periods (active reproduction and winter. In conditions that are close to optimal, populations demonstrate relatively homogeneous FA levels, while on the periphery of the area an increase in occurrence of disturbances in developmental stability is observed, which leads, on one hand, to higher average FA for the population and, on the other hand, to heterogeneity of the population in this parameter.
Indian Academy of Sciences (India)
It is shown that (i) every probability density is the unique maximizer of relative entropy in an appropriate class and (ii) in the class of all pdf that satisfy ∫ f h i d = i for i = 1 , 2 , … , … k the maximizer of entropy is an f 0 that is proportional to exp ( ∑ c i h i ) for some choice of c i . An extension of this to a continuum of ...
Indian Academy of Sciences (India)
It is shown that (i) every probability density is the unique maximizer of relative entropy in an appropriate class and (ii) in the class of all pdf that satisfy ∫ f h i d = i for i = 1 , 2 , … , … k the maximizer of entropy is an f 0 that is proportional to exp ( ∑ c i h i ) for some choice of c i . An extension of this to a continuum of ...
Indian Academy of Sciences (India)
Abstract. It is shown that (i) every probability density is the unique maximizer of relative entropy in an appropriate class and (ii) in the class of all pdf f that satisfy. ∫ fhi dμ = λi for i = 1, 2,...,...k the maximizer of entropy is an f0 that is pro- portional to exp(. ∑ ci hi ) for some choice of ci . An extension of this to a continuum of.
Fluctuation theorem: A critical review
Malek Mansour, M.; Baras, F.
2017-10-01
Fluctuation theorem for entropy production is revisited in the framework of stochastic processes. The applicability of the fluctuation theorem to physico-chemical systems and the resulting stochastic thermodynamics were analyzed. Some unexpected limitations are highlighted in the context of jump Markov processes. We have shown that these limitations handicap the ability of the resulting stochastic thermodynamics to correctly describe the state of non-equilibrium systems in terms of the thermodynamic properties of individual processes therein. Finally, we considered the case of diffusion processes and proved that the fluctuation theorem for entropy production becomes irrelevant at the stationary state in the case of one variable systems.
Consequences of entropy bifurcation in non-Maxwellian astrophysical environments
Directory of Open Access Journals (Sweden)
M. P. Leubner
2008-07-01
Full Text Available Non-extensive systems, accounting for long-range interactions and correlations, are fundamentally related to non-Maxwellian distributions where a duality of equilibria appears in two families, the non-extensive thermodynamic equilibria and the kinetic equilibria. Both states emerge out of particular entropy generalization leading to a class of probability distributions, where bifurcation into two stationary states is naturally introduced by finite positive or negative values of the involved entropic index kappa. The limiting Boltzmann-Gibbs-Shannon state (BGS, neglecting any kind of interactions within the system, is subject to infinite entropic index and thus characterized by self-duality. Fundamental consequences of non-extensive entropy bifurcation, manifest in different astrophysical environments, as particular core-halo patterns of solar wind velocity distributions, the probability distributions of the differences of the fluctuations in plasma turbulence as well as the structure of density distributions in stellar gravitational equilibrium are discussed. In all cases a lower entropy core is accompanied by a higher entropy halo state as compared to the standard BGS solution. Data analysis and comparison with high resolution observations significantly support the theoretical requirement of non-extensive entropy generalization when dealing with systems subject to long-range interactions and correlations.
Logarithmic black hole entropy corrections and holographic Renyi entropy
International Nuclear Information System (INIS)
Mahapatra, Subhash
2018-01-01
The entanglement and Renyi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Renyi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order G D 0 . The entropic c-function and the inequalities of the Renyi entropy are also satisfied even with the correction terms. (orig.)
Effect of thermal fluctuations on a charged dilatonic black Saturn
Energy Technology Data Exchange (ETDEWEB)
Pourhassan, Behnam, E-mail: b.pourhassan@du.ac.ir [School of Physics, Damghan University, Damghan (Iran, Islamic Republic of); Faizal, Mir, E-mail: f2mir@uwaterloo.ca [Department of Physics and Astronomy, University of Lethbridge, Lethbridge, AB T1K 3M4 (Canada)
2016-04-10
In this paper, we will analyze the effect of thermal fluctuations on the thermodynamics of a charged dilatonic black Saturn. These thermal fluctuations will correct the thermodynamics of the charged dilatonic black Saturn. We will analyze the corrections to the thermodynamics of this system by first relating the fluctuations in the entropy to the fluctuations in the energy. Then, we will use the relation between entropy and a conformal field theory to analyze the fluctuations in the entropy. We will demonstrate that similar physical results are obtained from both these approaches. We will also study the effect of thermal fluctuations on the phase transition in this charged dilatonic black Saturn.
Effect of thermal fluctuations on a charged dilatonic black Saturn
Directory of Open Access Journals (Sweden)
Behnam Pourhassan
2016-04-01
Full Text Available In this paper, we will analyze the effect of thermal fluctuations on the thermodynamics of a charged dilatonic black Saturn. These thermal fluctuations will correct the thermodynamics of the charged dilatonic black Saturn. We will analyze the corrections to the thermodynamics of this system by first relating the fluctuations in the entropy to the fluctuations in the energy. Then, we will use the relation between entropy and a conformal field theory to analyze the fluctuations in the entropy. We will demonstrate that similar physical results are obtained from both these approaches. We will also study the effect of thermal fluctuations on the phase transition in this charged dilatonic black Saturn.
Strain fluctuations and elastic constants
Energy Technology Data Exchange (ETDEWEB)
Parrinello, M.; Rahman, A.
1982-03-01
It is shown that the elastic strain fluctuations are a direct measure of elastic compliances in a general anisotropic medium; depending on the ensemble in which the fluctuation is measured either the isothermal or the adiabatic compliances are obtained. These fluctuations can now be calculated in a constant enthalpy and pressure, and hence, constant entropy, ensemble due to recent develpments in the molecular dynamics techniques. A calculation for a Ni single crystal under uniform uniaxial 100 tensile or compressive load is presented as an illustration of the relationships derived between various strain fluctuations and the elastic modulii. The Born stability criteria and the behavior of strain fluctuations are shown to be related.
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…
Editorial: Entropy in Landscape Ecology
Directory of Open Access Journals (Sweden)
Samuel A. Cushman
2018-04-01
Full Text Available Entropy and the second law of thermodynamics are the central organizing principles of nature, but the ideas and implications of the second law are poorly developed in landscape ecology. The purpose of this Special Issue “Entropy in Landscape Ecology” in Entropy is to bring together current research on applications of thermodynamics in landscape ecology, to consolidate current knowledge and identify key areas for future research. The special issue contains six articles, which cover a broad range of topics including relationships between entropy and evolution, connections between fractal geometry and entropy, new approaches to calculate configurational entropy of landscapes, example analyses of computing entropy of landscapes, and using entropy in the context of optimal landscape planning. Collectively these papers provide a broad range of contributions to the nascent field of ecological thermodynamics. Formalizing the connections between entropy and ecology are in a very early stage, and that this special issue contains papers that address several centrally important ideas, and provides seminal work that will be a foundation for the future development of ecological and evolutionary thermodynamics.
Entanglement Entropy of Black Holes
Directory of Open Access Journals (Sweden)
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.
A gravitational entropy proposal
International Nuclear Information System (INIS)
Clifton, Timothy; Tavakol, Reza; Ellis, George F R
2013-01-01
We propose a thermodynamically motivated measure of gravitational entropy based on the Bel–Robinson tensor, which has a natural interpretation as the effective super-energy–momentum tensor of free gravitational fields. The specific form of this measure differs depending on whether the gravitational field is Coulomb-like or wave-like, and reduces to the Bekenstein–Hawking value when integrated over the interior of a Schwarzschild black hole. For scalar perturbations of a Robertson–Walker geometry we find that the entropy goes like the Hubble weighted anisotropy of the gravitational field, and therefore increases as structure formation occurs. This is in keeping with our expectations for the behaviour of gravitational entropy in cosmology, and provides a thermodynamically motivated arrow of time for cosmological solutions of Einstein’s field equations. It is also in keeping with Penrose’s Weyl curvature hypothesis. (paper)
Survival of rapidly fluctuating natural low winter temperatures by High Arctic soil invertebrates
DEFF Research Database (Denmark)
Convey, Peter; Abbandonato, Holly; Bergan, Frode
2015-01-01
The extreme polar environment creates challenges for its resident invertebrate communities and the stress tolerance of some of these animals has been examined over many years. However, although it is well appreciated that standard air temperature records often fail to describe accurately conditions...... experienced at microhabitat level, few studies have explicitly set out to link field conditions experienced by natural multispecies communities with the more detailed laboratory ecophysiological studies of a small number of 'representative' species. This is particularly the case during winter, when snow cover...... microhabitats. To assess survival of natural High Arctic soil invertebrate communities contained in soil and vegetation cores to natural winter temperature variations, the overwintering temperatures they experienced were manipulated by deploying cores in locations with varying snow accumulation: No Snow...
A Connection Entropy Approach to Water Resources Vulnerability Analysis in a Changing Environment
Directory of Open Access Journals (Sweden)
Zhengwei Pan
2017-11-01
Full Text Available This paper establishes a water resources vulnerability framework based on sensitivity, natural resilience and artificial adaptation, through the analyses of the four states of the water system and its accompanying transformation processes. Furthermore, it proposes an analysis method for water resources vulnerability based on connection entropy, which extends the concept of contact entropy. An example is given of the water resources vulnerability in Anhui Province of China, which analysis illustrates that, overall, vulnerability levels fluctuated and showed apparent improvement trends from 2001 to 2015. Some suggestions are also provided for the improvement of the level of water resources vulnerability in Anhui Province, considering the viewpoint of the vulnerability index.
Tran, Hai L; Lexa, Katrina W; Julien, Olivier; Young, Travis S; Walsh, Christopher T; Jacobson, Matthew P; Wells, James A
2017-02-22
Macrocycles are appealing drug candidates due to their high affinity, specificity, and favorable pharmacological properties. In this study, we explored the effects of chemical modifications to a natural product macrocycle upon its activity, 3D geometry, and conformational entropy. We chose thiocillin as a model system, a thiopeptide in the ribosomally encoded family of natural products that exhibits potent antimicrobial effects against Gram-positive bacteria. Since thiocillin is derived from a genetically encoded peptide scaffold, site-directed mutagenesis allows for rapid generation of analogues. To understand thiocillin's structure-activity relationship, we generated a site-saturation mutagenesis library covering each position along thiocillin's macrocyclic ring. We report the identification of eight unique compounds more potent than wild-type thiocillin, the best having an 8-fold improvement in potency. Computational modeling of thiocillin's macrocyclic structure revealed a striking requirement for a low-entropy macrocycle for activity. The populated ensembles of the active mutants showed a rigid structure with few adoptable conformations while inactive mutants showed a more flexible macrocycle which is unfavorable for binding. This finding highlights the importance of macrocyclization in combination with rigidifying post-translational modifications to achieve high-potency binding.
Generalized entropy production fluctuation theorems for quantum ...
Indian Academy of Sciences (India)
wipes out the previous memory of evolution and the post-measurement evolution becomes uncorrelated to the pre-measurement evolution. Thus, if one performs intermediate mea- surements along two paths, the interference effects between the two paths disappear and the quantum effects are suppressed. Hence, in the ...
Upper entropy axioms and lower entropy axioms
International Nuclear Information System (INIS)
Guo, Jin-Li; Suo, Qi
2015-01-01
The paper suggests the concepts of an upper entropy and a lower entropy. We propose a new axiomatic definition, namely, upper entropy axioms, inspired by axioms of metric spaces, and also formulate lower entropy axioms. We also develop weak upper entropy axioms and weak lower entropy axioms. Their conditions are weaker than those of Shannon–Khinchin axioms and Tsallis axioms, while these conditions are stronger than those of the axiomatics based on the first three Shannon–Khinchin axioms. The subadditivity and strong subadditivity of entropy are obtained in the new axiomatics. Tsallis statistics is a special case of satisfying our axioms. Moreover, different forms of information measures, such as Shannon entropy, Daroczy entropy, Tsallis entropy and other entropies, can be unified under the same axiomatics
Quantum random number generator based on quantum nature of vacuum fluctuations
Ivanova, A. E.; Chivilikhin, S. A.; Gleim, A. V.
2017-11-01
Quantum random number generator (QRNG) allows obtaining true random bit sequences. In QRNG based on quantum nature of vacuum, optical beam splitter with two inputs and two outputs is normally used. We compare mathematical descriptions of spatial beam splitter and fiber Y-splitter in the quantum model for QRNG, based on homodyne detection. These descriptions were identical, that allows to use fiber Y-splitters in practical QRNG schemes, simplifying the setup. Also we receive relations between the input radiation and the resulting differential current in homodyne detector. We experimentally demonstrate possibility of true random bits generation by using QRNG based on homodyne detection with Y-splitter.
On unified-entropy characterization of quantum channels
International Nuclear Information System (INIS)
Rastegin, A E
2012-01-01
We consider properties of quantum channels with the use of unified entropies. Extremal unravelings of quantum channel with respect to these entropies are examined. The concept of map entropy is extended in terms of the unified entropies. The map (q, s)-entropy is naturally defined as the unified (q, s)-entropy of a rescaled dynamical matrix of given quantum channel. Inequalities of Fannes type are obtained for introduced entropies in terms of both the trace and Frobenius norms of difference between corresponding dynamical matrices. Additivity properties of introduced map entropies are discussed. The known inequality of Lindblad with the entropy exchange is generalized to many of the unified entropies. For the tensor product of a pair of quantum channels, we derive a two-sided estimate on the output entropy of a maximally entangled input state. (paper)
Xie, Tian; Wang, Meie; Su, Chao; Chen, Weiping
2018-03-17
Soils provide the service of attenuating and detoxifying pollutants. Such ability, natural attenuation capacity (NAC), is one of the most important ecosystem services for urban soils. We improved the ecosystem-service performance index (EPX) model by integrating with entropy weight determination method to evaluate the NAC of residential soils in Beijing. Eleven parameters related to the soil process of pollutants fate and transport were selected and 115 residential soil samples were collected. The results showed that bulk density, microbial functional diversity and soil organic matter had high weights in the NAC evaluation. Urban socio-economic indicators of residential communities such as construction age, population density and property & management fee could be employed in kinetic fittings of NAC. It could be concluded urbanization had significant impacts on NAC in residential soils. The improved method revealed reasonable and practical results, and it could be served as a potential measure for application to other quantitative assessment. Copyright © 2018 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Highlights: • Double-diffusive natural convection of 2-phase flow in a porous cavity is studied. • Results are presented for different Darcy, Rayleigh and Lewis numbers. • Effects of inclination angle of enclosure on heat and mass transfer are studied. • Effects of thermal and solutal source configurations on Nu and Sh are investigated. • The entropy generation study is conducted to find the optimal source configuration. - Abstract: In the present study, steady double-diffusive natural convection of two-phase flow through a square enclosure filled with a fluid-saturated porous medium, in presence of the internal thermal and solutal source is investigated numerically. Darcy-Brinkman-Forchheimer model is used to describe the fluid flow in porous media. This research aims to obtain a deep understanding about details of physical processes involved in such flows, using both the first and the second law analysis for different internal source(s) configurations. To this end, an in-house finite volume numerical solver is developed and validated against available data in literatures. Results are presented in terms of streamlines, isotherms and concentration contours for different values of Darcy, Rayleigh and Lewis numbers. First the effect of inclination angle of the cavity on heat and mass transfer characteristics of flows is investigated in presence of an internal source with the square and rectangular shape. Next, twelve different internal source configurations with distinctive shapes, locations and arrangements are studied and their effects on Nusselt and Sherwood numbers are investigated. Finally an entropy generation analysis is conducted to identify the best internal source configuration from the viewpoint of the second law of thermodynamics.
Entropy of random entangling surfaces
Solodukhin, Sergey N.
2012-09-01
We consider the situation when a globally defined four-dimensional field system is separated on two entangled sub-systems by a dynamical (random) two-dimensional surface. The reduced density matrix averaged over ensemble of random surfaces of fixed area and the corresponding average entropy are introduced. The average entanglement entropy is analyzed for a generic conformal field theory in four dimensions. Two important particular cases are considered. In the first, both the intrinsic metric on the entangling surface and the spacetime metric are fluctuating. An important example of this type is when the entangling surface is a black hole horizon, the fluctuations of which cause necessarily the fluctuations in the spacetime geometry. In the second case, the spacetime is considered to be fixed. The detailed analysis is carried out for the random entangling surfaces embedded in flat Minkowski spacetime. In all cases, the problem reduces to an effectively two-dimensional problem of random surfaces which can be treated by means of the well-known conformal methods. Focusing on the logarithmic terms in the entropy, we predict the appearance of a new ln ln(A) term. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’.
Excess Entropy and Diffusivity
Indian Academy of Sciences (India)
First page Back Continue Last page Graphics. Excess Entropy and Diffusivity. Excess entropy scaling of diffusivity (Rosenfeld,1977). Analogous relationships also exist for viscosity and thermal conductivity.
An investigation of combustion and entropy noise
Strahle, W. C.
1977-01-01
The relative importance of entropy and direct combustion noise in turbopropulsion systems and the parameters upon which these noise sources depend were studied. Theory and experiment were employed to determine that at least with the apparatus used here, entropy noise can dominate combustion noise if there is a sufficient pressure gradient terminating the combustor. Measurements included combustor interior fluctuating pressure, near and far field fluctuating pressure, and combustor exit plane fluctuating temperatures, as well as mean pressures and temperatures. Analysis techniques included spectral, cross-correlation, cross power spectra, and ordinary and partial coherence analysis. Also conducted were combustor liner modification experiments to investigate the origin of the frequency content of combustion noise. Techniques were developed to extract nonpropagational pseudo-sound and the heat release fluctuation spectra from the data.
Entropy estimation of very short symbolic sequences
Lesne, Annick; Blanc, Jean-Luc; Pezard, Laurent
2009-04-01
While entropy per unit time is a meaningful index to quantify the dynamic features of experimental time series, its estimation is often hampered in practice by the finite length of the data. We here investigate the performance of entropy estimation procedures, relying either on block entropies or Lempel-Ziv complexity, when only very short symbolic sequences are available. Heuristic analytical arguments point at the influence of temporal correlations on the bias and statistical fluctuations, and put forward a reduced effective sequence length suitable for error estimation. Numerical studies are conducted using, as benchmarks, the wealth of different dynamic regimes generated by the family of logistic maps and stochastic evolutions generated by a Markov chain of tunable correlation time. Practical guidelines and validity criteria are proposed. For instance, block entropy leads to a dramatic overestimation for sequences of low entropy, whereas it outperforms Lempel-Ziv complexity at high entropy. As a general result, the quality of entropy estimation is sensitive to the sequence temporal correlation hence self-consistently depends on the entropy value itself, thus promoting a two-step procedure. Lempel-Ziv complexity is to be preferred in the first step and remains the best estimator for highly correlated sequences.
International Nuclear Information System (INIS)
Pinzon F, Olga Patricia; Quintero C, Paola Fernanda
2001-01-01
The ornamental trees complete a very important environmental function for the quality of the inhabitants' life in the urban areas, when offering momentous benefits as the subduing of the climate, regulation of CO 2 in the atmosphere and the scenic beauty. Thanks to the interest of the District Administration, in Bogota, in the last four years, the urban plantation of trees acquired a preponderant paper that became apparent during the biggest plantation of trees program and maintenance of green areas that it has been carried out in the history of the capital; day by day they get more importance, and they are recognized by the citizenship like fundamental values of its environment. Previously to this program, the attention received were minimum or were remembered soon after the surprising devastating consequences of phyto sanitary problems: the grooved cochineal of the acacia, the louse plant of the cypress and the bedbug of the Urapan in whose cases the ignorance of basic aspects of the biology, natural control and the harmful populations' behavior, it has forced to generally apply measured of chemical type to try to reduce the high levels population. The importance that have, the green areas in the city, it favors a continuous pursuit that allows to deepen in the knowledge of the main risk factors, current problems and potentials of the species, types and consequences of the damages and the intra and inter relationships of the arthropofauna of the urban vegetation, their relationship with the plants, as well as the incidence of biotic and abiotic in the tree phonologic behavior and in the fluctuation of the populations of this individuals in order to coming closer to the understanding of the dynamics of the populations of arthropods harmful, in such a way that is possible to design kind handling strategies with the environment, having in consideration in integrated form the conditions under the attack of arthropods harmful
Directory of Open Access Journals (Sweden)
Anna Jansson
Full Text Available Ocean acidification is causing severe changes in the inorganic carbon balance of the oceans. The pH conditions predicted for the future oceans are, however, already regularly occurring in the Baltic Sea, and the system might thus work as an analogue for future ocean acidification scenarios. The characteristics of the Baltic Sea with low buffering capacity and large natural pH fluctuations, in combination with multiple other stressors, suggest that OA effects may be severe, but remain largely unexplored. A calcifying species potentially affected by low pH conditions is the bivalve Macoma balthica (L.. We investigated larval survival and development of M. balthica by exposing the larvae to a range of pH levels: 7.2, 7.4, 7.7 and 8.1 during 20 days in order to learn what the effects of reduced pH are on the larval biology and thus also potentially for the population dynamics of this key species. We found that even a slight pH decrease causes significant negative changes during the larval phase, both by slowing growth and by decreasing survival. The growth was slower in all reduced pH treatments compared to the control treatment. The size of 250 µm that is considered indicative to imminent settling in our system was reached by 22% of the larvae grown in control conditions after 20 days, whereas in all reduced pH treatments the size of 250 µm was reached by only 7-14%. The strong impact of ocean acidification on larvae is alarming as slowly growing individuals are exposed to higher predation risk in response to the longer time they are required to spend in the plankton, further decreasing the ecological competence of the species.
Optimum design of brake friction material using hybrid entropy-GRA approach
Directory of Open Access Journals (Sweden)
Kumar Naresh
2016-01-01
Full Text Available The effect of Kevlar and natural fibres on the performance of brake friction materials was evaluated. Four friction material specimens were developed by varying the proportion of Kevlar and natural fibres. Two developed composite contained 5-10 wt.% of Kevlar fibre while in the other two the Kevlar fibre was replaced with same amount of natural fibre. SAE J661 protocol was used for the assessment of the tribological properties on a Chase testing machine. Result shows that the specimens containing Kevlar fibres shows higher friction and wear performance, whereas Kevlar replacement with natural fibre resulted in improved fade, recovery and friction fluctuations. Further hybrid entropy-GRA (grey relation analysis approach was applied to select the optimal friction materials using various performance defining attributes (PDA including friction, wear, fade, recovery, friction fluctuations and cost. The friction materials with 10 wt% of natural fibre exhibited the best overall quality.
Logarithmic corrections to entropy and Ads/CFT
Indian Academy of Sciences (India)
Abstract. We calculate the correction to the Bekenstein-Hawking entropy formula for five-dimensional AdS-Schwarzschild black holes due to thermodynamic fluctuations. The result is then compared with the boundary gauge theory entropy corrections via AdS/CFT correspondence. Keywords. AdS/CFT; blackholes. Recently ...
Logarithmic corrections to entropy and AdS/CFT
Indian Academy of Sciences (India)
Abstract. We calculate the correction to the Bekenstein-Hawking entropy formula for five-dimensional AdS-Schwarzschild black holes due to thermodynamic fluctuations. The result is then compared with the boundary gauge theory entropy corrections via AdS/CFT correspondence.
Riemannian geometry in thermodynamic fluctuation theory
International Nuclear Information System (INIS)
Ruppeiner, G.
1995-01-01
Although thermodynamic fluctuation theory originated from statistical mechanics, it may be put on a completely thermodynamic basis, in no essential need of any microscopic foundation. This review views the theory from the macroscopic perspective, emphasizing, in particular, notions of covariance and consistency, expressed naturally using the language of Riemannian geometry. Coupled with these concepts is an extension of the basic structure of thermodynamic fluctuation theory beyond the classical one of a subsystem in contact with an infinite uniform reservoir. Used here is a hierarchy of concentric subsystems, each of which samples only the thermodynamic state of the subsystem immediately larger than it. The result is a covariant thermodynamic fluctuation theory which is plausible beyond the standard second-order entropy expansion. It includes the conservation laws and is mathematically consistent when applied to fluctuations inside subsystems. Tests on known models show improvements. Perhaps most significantly, the covariant theory offers a qualitatively new tool for the study of fluctuation phenomena: the Riemannian thermodynamic curvature. The thermodynamic curvature gives, for any given thermodynamic state, a lower bound for the length scale where the classical thermodynamic fluctuation theory based on a uniform environment could conceivably hold. Straightforward computation near the critical point reveals that the curvature equals the correlation volume, a physically appealing finding. The combination of the interpretation of curvature with a well-known proportionality between the free energy and the inverse of the correlation volume yields a purely thermodynamic theory of the critical point. The scaled equation of state follows from the values of the critical exponents. The thermodynamic Riemannian metric may be put into the broader context of information theory
Text mining by Tsallis entropy
Jamaati, Maryam; Mehri, Ali
2018-01-01
Long-range correlations between the elements of natural languages enable them to convey very complex information. Complex structure of human language, as a manifestation of natural languages, motivates us to apply nonextensive statistical mechanics in text mining. Tsallis entropy appropriately ranks the terms' relevance to document subject, taking advantage of their spatial correlation length. We apply this statistical concept as a new powerful word ranking metric in order to extract keywords of a single document. We carry out an experimental evaluation, which shows capability of the presented method in keyword extraction. We find that, Tsallis entropy has reliable word ranking performance, at the same level of the best previous ranking methods.
Universal canonical entropy for gravitating systems
Indian Academy of Sciences (India)
... fluctuations, as found earlier) the canonical entropy then has a universal form including logarithmic corrections to the area law. This form is shown to be independent of the index appearing in assumption (b). The index, however, is crucial in ascertaining the domain of validity of our approach based on thermal equilibrium.
On quantum Rényi entropies: A new generalization and some properties
International Nuclear Information System (INIS)
Müller-Lennert, Martin; Dupuis, Frédéric; Szehr, Oleg; Fehr, Serge; Tomamichel, Marco
2013-01-01
The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies, or mutual information, and have found many applications in 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-processing inequalities, a duality relation, and an entropic uncertainty relation
On quantum Rényi entropies: A new generalization and some properties
Energy Technology Data Exchange (ETDEWEB)
Müller-Lennert, Martin [Department of Mathematics, ETH Zurich, 8092 Zürich (Switzerland); Dupuis, Frédéric [Department of Computer Science, Aarhus University, 8200 Aarhus (Denmark); Szehr, Oleg [Department of Mathematics, Technische Universität München, 85748 Garching (Germany); Fehr, Serge [CWI (Centrum Wiskunde and Informatica), 1090 Amsterdam (Netherlands); Tomamichel, Marco [Centre for Quantum Technologies, National University of Singapore, Singapore 117543 (Singapore)
2013-12-15
The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies, or mutual information, and have found many applications in 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-processing inequalities, a duality relation, and an entropic uncertainty relation.
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.
Intensity approximation of random fluctuation in complex systems
Yulmetyev, R. M.; Gafarov, F. M.; Yulmetyeva, D. G.; Emeljanova, N. A.
2002-01-01
The Markov and non-Markov processes in complex systems are examined with the help of dynamical information Shannon entropy method. Here we consider the essential role of two mutually independent channels of entropy involving creation of correlation and annihilation of correlation. The developed method has been used to analyze the intensity fluctuation of the complex systems of various nature: in psychology (to analyze numerical and pattern short-time human memory, to study the effect of stress on the parameters of the dynamical taping-test) and in cardiology (to analyze the random dynamics of RR-intervals in human ECG's and to diagnose various diseases of human cardiovascular systems). The received results show that the application of intensity approximation allows to improve essentially the diagnostics of parameters in the evolution of human dynamic states.
Phonon broadening in high entropy alloys
Körmann, Fritz; Ikeda, Yuji; Grabowski, Blazej; Sluiter, Marcel H. F.
2017-09-01
Refractory high entropy alloys feature outstanding properties making them a promising materials class for next-generation high-temperature applications. At high temperatures, materials properties are strongly affected by lattice vibrations (phonons). Phonons critically influence thermal stability, thermodynamic and elastic properties, as well as thermal conductivity. In contrast to perfect crystals and ordered alloys, the inherently present mass and force constant fluctuations in multi-component random alloys (high entropy alloys) can induce significant phonon scattering and broadening. Despite their importance, phonon scattering and broadening have so far only scarcely been investigated for high entropy alloys. We tackle this challenge from a theoretical perspective and employ ab initio calculations to systematically study the impact of force constant and mass fluctuations on the phonon spectral functions of 12 body-centered cubic random alloys, from binaries up to 5-component high entropy alloys, addressing the key question of how chemical complexity impacts phonons. We find that it is crucial to include both mass and force constant fluctuations. If one or the other is neglected, qualitatively wrong results can be obtained such as artificial phonon band gaps. We analyze how the results obtained for the phonons translate into thermodynamically integrated quantities, specifically the vibrational entropy. Changes in the vibrational entropy with increasing the number of elements can be as large as changes in the configurational entropy and are thus important for phase stability considerations. The set of studied alloys includes MoTa, MoTaNb, MoTaNbW, MoTaNbWV, VW, VWNb, VWTa, VWNbTa, VTaNbTi, VWNbTaTi, HfZrNb, HfMoTaTiZr.
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.
Morozov, A. N.
2017-11-01
The article reviews the possibility of describing physical time as a random Poisson process. An equation allowing the intensity of physical time fluctuations to be calculated depending on the entropy production density within irreversible natural processes has been proposed. Based on the standard solar model the work calculates the entropy production density inside the Sun and the dependence of the intensity of physical time fluctuations on the distance to the centre of the Sun. A free model parameter has been established, and the method of its evaluation has been suggested. The calculations of the entropy production density inside the Sun showed that it differs by 2-3 orders of magnitude in different parts of the Sun. The intensity of physical time fluctuations on the Earth's surface depending on the entropy production density during the sunlight-to-Earth's thermal radiation conversion has been theoretically predicted. A method of evaluation of the Kullback's measure of voltage fluctuations in small amounts of electrolyte has been proposed. Using a simple model of the Earth's surface heat transfer to the upper atmosphere, the effective Earth's thermal radiation temperature has been determined. A comparison between the theoretical values of the Kullback's measure derived from the fluctuating physical time model and the experimentally measured values of this measure for two independent electrolytic cells showed a good qualitative and quantitative concurrence of predictions of both theoretical model and experimental data.
Baumann, Hannes; Wallace, Ryan; Tagliaferri, Tristen N.; Gobler, Christopher J.
2014-01-01
Coastal marine organisms experience dynamic pH and dissolved oxygen (DO) conditions in their natural habitats, which may impact their susceptibility to long-term anthropogenic changes. Robust characterizations of all temporal scales of natural pH and DO fluctuations in different marine habitats are needed; however, appropriate time series of pH and DO are still scarce. We used multiyear (2008–2012), high-frequency (6 min) monitoring data to quantify diel, seasonal, and interannual scales of pH and DO variability in a productive, temperate tidal salt marsh (Flax Pond, Long Island, US). pHNBS and DO showed strong and similar seasonal patterns, with average (minimum) conditions declining from 8.2 (8.1) and 12.5 (11.4) mg l−1 at the end of winter to 7.6 (7.2) and 6.3 (2.8) mg l−1 in late summer, respectively. Concomitantly, average diel fluctuations increased from 0.22 and 2.2 mg l−1 (February) to 0.74 and 6.5 mg l−1 (August), respectively. Diel patterns were modulated by tides and time of day, eliciting the most extreme minima when low tides aligned with the end of the night. Simultaneous in situ pCO2 measurements showed striking fluctuations between ∼330 and ∼1,200 (early May), ∼2,200 (mid June), and ∼4,000 μatm (end of July) within single tidal cycles. These patterns also indicate that the marsh’s strong net heterotrophy influences its adjacent estuary by ‘outwelling’ acidified and hypoxic water during ebb tides. Our analyses emphasize the coupled and fluctuating nature of pH and DO conditions in productive coastal and estuarine environments, which have yet to be adequately represented by experiments.
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.
Entropy, Perception, and Relativity
National Research Council Canada - National Science Library
Jaegar, Stefan
2006-01-01
.... 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...
ECG contamination of EEG signals: effect on entropy.
Chakrabarti, Dhritiman; Bansal, Sonia
2016-02-01
Entropy™ is a proprietary algorithm which uses spectral entropy analysis of electroencephalographic (EEG) signals to produce indices which are used as a measure of depth of hypnosis. We describe a report of electrocardiographic (ECG) contamination of EEG signals leading to fluctuating erroneous Entropy values. An explanation is provided for mechanism behind this observation by describing the spread of ECG signals in head and neck and its influence on EEG/Entropy by correlating the observation with the published Entropy algorithm. While the Entropy algorithm has been well conceived, there are still instances in which it can produce erroneous values. Such erroneous values and their cause may be identified by close scrutiny of the EEG waveform if Entropy values seem out of sync with that expected at given anaesthetic levels.
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 noise: A review of theory, progress and challenges
Directory of Open Access Journals (Sweden)
Aimee S Morgans
2016-12-01
Full Text Available Combustion noise comprises two components: direct combustion noise and indirect combustion noise. The latter is the lesser studied, with entropy noise believed to be its main component. Entropy noise is generated via a sequence involving diverse flow physics. It has enjoyed a resurgence of interest over recent years, because of its increasing importance to aero-engine exhaust noise and a recognition that it can affect gas turbine combustion instabilities. Entropy noise occurs when unsteady heat release rate generates temperature fluctuations (entropy waves, and these subsequently undergo acceleration. Five stages of flow physics have been identified as being important, these being (a generation of entropy waves by unsteady heat release rate; (b advection of entropy waves through the combustor; (c acceleration of entropy waves through either a nozzle or blade row, to generate entropy noise; (d passage of entropy noise through a succession of turbine blade rows to appear at the turbine exit; and (e reflection of entropy noise back into the combustor, where it may further perturb the flame, influencing the combustor thermoacoustics. This article reviews the underlying theory, recent progress and outstanding challenges pertaining to each of these stages.
Does black-hole entropy make sense
International Nuclear Information System (INIS)
Wilkins, D.
1979-01-01
Bekenstein and Hawking saved the second law of thermodynamics near a black hole by assigning to the hole an entropy Ssub(h) proportional to the area of its event horizon. It is tempting to assume that Ssub(h) possesses all the features commonly associated with the physical entropy. Kundt has shown, however, that Ssub(h) violates several reasonable physical expectations. This criticism is reviewed, augmenting it as follows: (a) Ssub(h) is a badly behaved state function requiring knowledge of the hole's future history; and (b) close analogs of event horizons in other space-times do not possess an 'entropy'. These questions are also discussed: (c) Is Ssub(h) suitable for all regions of a black-hole space-time. And (b) should Ssub(h) be attributed to the exterior of a white hole. One can retain Ssub(h) for the interior (respectively, exterior) of a black (respectively, white) hole, but is rejected as contrary to the information-theoretic derivation of horizon entropy given by Berkenstein. The total entropy defined by Kundt (all ordinary entropy on space-section cutting through the hole, no horizon term) and that of Bekenstein-Hawking (ordinary entropy outside horizon plus horizon term) appear to be complementary concepts with separate domains of validity. In the most natural choice, an observer inside a black hole will use Kundt's entropy, and one remaining outside that of Bekenstein-Hawking. (author)
Quantum chaos: entropy signatures
International Nuclear Information System (INIS)
Miller, P.A.; Sarkar, S.; Zarum, R.
1998-01-01
A definition of quantum chaos is given in terms of entropy production rates for a quantum system coupled weakly to a reservoir. This allows the treatment of classical and quantum chaos on the same footing. In the quantum theory the entropy considered is the von Neumann entropy and in classical systems it is the Gibbs entropy. The rate of change of the coarse-grained Gibbs entropy of the classical system with time is given by the Kolmogorov-Sinai (KS) entropy. The relation between KS entropy and the rate of change of von Neumann entropy is investigated for the kicked rotator. For a system which is classically chaotic there is a linear relationship between these two entropies. Moreover it is possible to construct contour plots for the local KS entropy and compare it with the corresponding plots for the rate of change of von Neumann entropy. The quantitative and qualitative similarities of these plots are discussed for the standard map (kicked rotor) and the generalised cat maps. (author)
Information entropy of earthquake populations in northeastern Italy and western Slovenia
Bressan, G.; Barnaba, C.; Gentili, S.; Rossi, G.
2017-10-01
The spatio-temporal evolution of eight seismicity populations, preceding and following moderate earthquake sequences occurred in NE-Italy and W-Slovenia, are investigated by means of the normalized Shannon entropy and the fractal dimension. Three phases are recognized in the temporal seismic series. The period preceding the mainshock is characterized by oscillations of the Shannon entropy around a nearly constant level and by fluctuations of the fractal dimension. The phase of mainshock and aftershock sequences is characterized by a significant decrease of the Shannon entropy. A simultaneous marked decrease of the fractal dimension is observed in five cases. After the sequence, the entropy recovers the nearly constant trend before the mainshock and the fractal dimension is characterized by fluctuations. We interpreted the fluctuations of the normalized Shannon entropy and the fractal dimension caused by the coupling between the stress field and the mechanical heterogeneities of the crust that results in spatial and temporal fluctuations of the strain energy.
RNA Thermodynamic Structural Entropy.
Directory of Open Access Journals (Sweden)
Juan Antonio Garcia-Martin
Full Text Available Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe the first two accurate and efficient algorithms to compute the conformational entropy for RNA secondary structures, with respect to the Turner energy model, where free energy parameters are determined from UV absorption experiments. An algorithm to compute the derivational entropy for RNA secondary structures had previously been introduced, using stochastic context free grammars (SCFGs. However, the numerical value of derivational entropy depends heavily on the chosen context free grammar and on the training set used to estimate rule probabilities. Using data from the Rfam database, we determine that both of our thermodynamic methods, which agree in numerical value, are substantially faster than the SCFG method. Thermodynamic structural entropy is much smaller than derivational entropy, and the correlation between length-normalized thermodynamic entropy and derivational entropy is moderately weak to poor. In applications, we plot the structural entropy as a function of temperature for known thermoswitches, such as the repression of heat shock gene expression (ROSE element, we determine that the correlation between hammerhead ribozyme cleavage activity and total free energy is improved by including an additional free energy term arising from conformational entropy, and we plot the structural entropy of windows of the HIV-1 genome. Our software RNAentropy can compute structural entropy for any user-specified temperature, and supports both the Turner'99 and Turner'04 energy parameters. It follows that RNAentropy is state-of-the-art software to compute RNA secondary structure conformational entropy. Source code is available at https://github.com/clotelab/RNAentropy/; a full web server is available at http
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
Logarithmic black hole entropy corrections and holographic Rényi entropy
Mahapatra, Subhash
2018-01-01
The entanglement and Rényi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Rényi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order GD^0. The entropic c-function and the inequalities of the Rényi entropy are also satisfied even with the correction terms.
Zhu, Qiuan; Peng, Changhui; Chen, Huai; Fang, Xiuqin; Liu, Jinxun; Jiang, Hong; Yang, Yanzheng; Yang, Gang
2015-01-01
Aim The fluctuations of atmospheric methane (CH4) that have occurred in recent decades are not fully understood, particularly with regard to the contribution from wetlands. The application of spatially explicit parameters has been suggested as an effective method for reducing uncertainties in bottom-up approaches to wetland CH4 emissions, but has not been included in recent studies. Our goal was to estimate spatio-temporal patterns of global wetland CH4 emissions using a process model and then to identify the contribution of wetland emissions to atmospheric CH4fluctuations. Location Global. Methods A process-based model integrated with full descriptions of methanogenesis (TRIPLEX-GHG) was used to simulate global wetland CH4emissions. Results Global annual wetland CH4 emissions ranged from 209 to 245 Tg CH4 year−1 between 1901 and 2012, with peaks occurring in 1991 and 2012. There is a decreasing trend between 1990 and 2010 with a rate of approximately 0.48 Tg CH4 year−1, which was largely caused by emissions from tropical wetlands showing a decreasing trend of 0.44 Tg CH4 year−1 since the 1970s. Emissions from tropical, temperate and high-latitude wetlands comprised 59, 26 and 15% of global emissions, respectively. Main conclusion Global wetland CH4 emissions, the interannual variability of which was primary controlled by tropical wetlands, partially drive the atmosphericCH4 burden. The stable to decreasing trend in wetland CH4 emissions, a result of a balance of emissions from tropical and extratropical wetlands, was a particular factor in slowing the atmospheric CH4 growth rate during the 1990s. The rapid decrease in tropical wetland CH4emissions that began in 2000 was supposed to offset the increase in anthropogenic emissions and resulted in a relatively stable level of atmospheric CH4 from 2000 to 2006. Increasing wetland CH4 emissions, particularly after 2010, should be an important contributor to the growth in
Converting entropy to curvature perturbations after a cosmic bounce
Energy Technology Data Exchange (ETDEWEB)
Fertig, Angelika; Lehners, Jean-Luc; Mallwitz, Enno; Wilson-Ewing, Edward [Max Planck Institute for Gravitational Physics, Albert Einstein Institute,14476 Potsdam-Golm (Germany)
2016-10-04
We study two-field bouncing cosmologies in which primordial perturbations are created in either an ekpyrotic or a matter-dominated contraction phase. We use a non-singular ghost condensate bounce model to follow the perturbations through the bounce into the expanding phase of the universe. In contrast to the adiabatic perturbations, which on large scales are conserved across the bounce, entropy perturbations can grow significantly during the bounce phase. If they are converted into adiabatic/curvature perturbations after the bounce, they typically form the dominant contribution to the observed temperature fluctuations in the microwave background, which can have several beneficial implications. For ekpyrotic models, this mechanism loosens the constraints on the amplitude of the ekpyrotic potential while naturally suppressing the intrinsic amount of non-Gaussianity. For matter bounce models, the mechanism amplifies the scalar perturbations compared to the associated primordial gravitational waves.
Directory of Open Access Journals (Sweden)
Øyvind Grøn
2012-12-01
Full Text Available The effect of gravity upon changes of the entropy of a gravity-dominated system is discussed. In a universe dominated by vacuum energy, gravity is repulsive, and there is accelerated expansion. Furthermore, inhomogeneities are inflated and the universe approaches a state of thermal equilibrium. The difference between the evolution of the cosmic entropy in a co-moving volume in an inflationary era with repulsive gravity and a matter-dominated era with attractive gravity is discussed. The significance of conversion of gravitational energy to thermal energy in a process with gravitational clumping, in order that the entropy of the universe shall increase, is made clear. Entropy of black holes and cosmic horizons are considered. The contribution to the gravitational entropy according to the Weyl curvature hypothesis is discussed. The entropy history of the Universe is reviewed.
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.
The maximum entropy technique. System's statistical description
International Nuclear Information System (INIS)
Belashev, B.Z.; Sulejmanov, M.K.
2002-01-01
The maximum entropy technique (MENT) is applied for searching the distribution functions of physical values. MENT takes into consideration the demand of maximum entropy, the characteristics of the system and the connection conditions, naturally. It is allowed to apply MENT for statistical description of closed and open systems. The examples in which MENT had been used for the description of the equilibrium and nonequilibrium states and the states far from the thermodynamical equilibrium are considered
Sadok, Walid; Naudin, Philippe; Boussuge, Benoit; Muller, Bertrand; Welcker, Claude; Tardieu, Francois
2007-02-01
We have analysed daily patterns of leaf elongation rate (LER) in large data sets with 318 genotypes placed in naturally fluctuating temperature and evaporative demand, and examined the effect of targeted alleles on these patterns. The method consisted, firstly, in expressing elongation rate per unit thermal time, so it became temperature independent; secondly, in a joint analysis of diurnal fluctuations of elongation rate and of micrometeorological conditions in several experiments, and finally, in a comparison of daily patterns between groups of genotypes possessing targeted alleles. (1) Conditions for using thermal time at a time step of 15 min were first tested successfully in 318 recombinant inbred lines (RILs) of three mapping populations. (2) An analysis of 1989 time courses revealed a robust daily pattern of LER per unit thermal time (LERth) over several experiments. LERth was constant during the night and was reproducible (for a given RIL) over up to 10 consecutive nights in different experiments. It declined rapidly during the early morning, closely following the daily pattern of transpiration rate. (3) Groups of RILs carrying alleles conferring a high response to temperature had markedly higher night-time plateau of LER than those with low responses. Groups of RILs with high response to evaporative demand had rapid decreases in elongation rate at the transition between night and day, while this decrease was slower in groups of RILs with low response. These results open the way for using kinetics of responses to environmental stimuli as a phenotyping tool in genetic analyses.
Towards operational interpretations of generalized entropies
International Nuclear Information System (INIS)
Topsoee, Flemming
2010-01-01
The driving force behind our study has been to overcome the difficulties you encounter when you try to extend the clear and convincing operational interpretations of classical Boltzmann-Gibbs-Shannon entropy to other notions, especially to generalized entropies as proposed by Tsallis. Our approach is philosophical, based on speculations regarding the interplay between truth, belief and knowledge. The main result demonstrates that, accepting philosophically motivated assumptions, the only possible measures of entropy are those suggested by Tsallis - which, as we know, include classical entropy. This result constitutes, so it seems, a more transparent interpretation of entropy than previously available. However, further research to clarify the assumptions is still needed. Our study points to the thesis that one should never consider the notion of entropy in isolation - in order to enable a rich and technically smooth study, further concepts, such as divergence, score functions and descriptors or controls should be included in the discussion. This will clarify the distinction between Nature and Observer and facilitate a game theoretical discussion. The usefulness of this distinction and the subsequent exploitation of game theoretical results - such as those connected with the notion of Nash equilibrium - is demonstrated by a discussion of the Maximum Entropy Principle.
Coarse Graining Shannon and von Neumann Entropies
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Ana Alonso-Serrano
2017-05-01
Full Text Available The nature of coarse graining is intuitively “obvious”, but it is rather difficult to find explicit and calculable models of the coarse graining process (and the resulting entropy flow discussed in the literature. What we would like to have at hand is some explicit and calculable process that takes an arbitrary system, with specified initial entropy S, and that monotonically and controllably drives the entropy to its maximum value. This does not have to be a physical process, in fact for some purposes it is better to deal with a gedanken-process, since then it is more obvious how the “hidden information” is hiding in the fine-grain correlations that one is simply agreeing not to look at. We shall present several simple mathematically well-defined and easy to work with conceptual models for coarse graining. We shall consider both the classical Shannon and quantum von Neumann entropies, including models based on quantum decoherence, and analyse the entropy flow in some detail. When coarse graining the quantum von Neumann entropy, we find it extremely useful to introduce an adaptation of Hawking’s super-scattering matrix. These explicit models that we shall construct allow us to quantify and keep clear track of the entropy that appears when coarse graining the system and the information that can be hidden in unobserved correlations (while not the focus of the current article, in the long run, these considerations are of interest when addressing the black hole information puzzle.
Entropy and Kolmogorov complexity
Moriakov, N.V.
2016-01-01
This thesis is dedicated to studying the theory of entropy and its relation to the Kolmogorov complexity. Originating in physics, the notion of entropy was introduced to mathematics by C. E. Shannon as a way of measuring the rate at which information is coming from a data source. There are, however,
International Nuclear Information System (INIS)
Bao, Ning; Nezami, Sepehr; Ooguri, Hirosi; Stoica, Bogdan; Sully, James; Walter, Michael
2015-01-01
We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.
Indian Academy of Sciences (India)
entropy loss during protein folding plays a much larger role in determining the shape of the free energy reaction landscape than it does in most small molecule reactions. For a protein to fold, the loss of entropy must be balanced by the gain in enthalpy for the free energy to favor folding. Strong non- covalent forces from ...
International Nuclear Information System (INIS)
Saili, Noor Affizah Bujang; Mohamed, Che Abd Rahim
2013-01-01
Studies on natural radionuclides such as 210 Po and 210 Pb with the concentration of phosphorus in water column related to suspended particulate matter (SPM) were carried out at the Mersing River, Johor, Malaysia. Sixteen water samples were collected from nine stations on the 4 th July 2010. 210 Po and 210 Pb activities varied between 0.76 to 2.24 mBq/L and 0.16 to 1.60 mBq/L respectively. The phosphorus concentrations, comprising total dissolved phosphorus (TDP), soluble reactive phosphorus (SRP) and dissolved organic phosphorus (DOP), were within the ranges of 6.06 to 23.31 μg/L, 2.24 to 13.42 μg/L and 0.47 to 16.10 μ/L, respectively. The concentration of TDP and salinity shows weak positive correlation (r = 0.39), perhaps due to the shallow depth of the Mersing River. There is a high positive correlation (r = 0.85) of 210 Po activity with SPM concentration and a moderately positive correlation (r =0.59) of 210 Po and TDP in water. The K d values in suspended particulate matter are much higher compare to that in dissolved phase, proving that the adsorption of radionuclides to particles is more dominant. This implies that SPM significantly influences the variation of the P compound and both radionuclides in the Mersing River. This corresponds with agricultural activities from palm oil estates; erosion of the river bank due to river runoff; advection of suspended particulates from surface sediment due to boat and ferry traffic at the jetties; sedimentation; domestic sewage from nearby terrestrial areas; and natural processes; all of which might have resulted in their introduction to the Mersing River. (author)
International Nuclear Information System (INIS)
Reynaud, S.; Giacobino, S.; Zinn-Justin, J.
1997-01-01
This course is dedicated to present in a pedagogical manner the recent developments in peculiar fields concerned by quantum fluctuations: quantum noise in optics, light propagation through dielectric media, sub-Poissonian light generated by lasers and masers, quantum non-demolition measurements, quantum electrodynamics applied to cavities and electrical circuits involving superconducting tunnel junctions. (A.C.)
Entanglement entropy in causal set theory
Sorkin, Rafael D.; Yazdi, Yasaman K.
2018-04-01
Entanglement entropy is now widely accepted as having deep connections with quantum gravity. It is therefore desirable to understand it in the context of causal sets, especially since they provide in a natural manner the UV cutoff needed to render entanglement entropy finite. Formulating a notion of entanglement entropy in a causal set is not straightforward because the type of canonical hypersurface-data on which its definition typically relies is not available. Instead, we appeal to the more global expression given in Sorkin (2012 (arXiv:1205.2953)) which, for a Gaussian scalar field, expresses the entropy of a spacetime region in terms of the field’s correlation function within that region (its ‘Wightman function’ W(x, x') ). Carrying this formula over to the causal set, one obtains an entropy which is both finite and of a Lorentz invariant nature. We evaluate this global entropy-expression numerically for certain regions (primarily order-intervals or ‘causal diamonds’) within causal sets of 1 + 1 dimensions. For the causal-set counterpart of the entanglement entropy, we obtain, in the first instance, a result that follows a (spacetime) volume law instead of the expected (spatial) area law. We find, however, that one obtains an area law if one truncates the commutator function (‘Pauli–Jordan operator’) and the Wightman function by projecting out the eigenmodes of the Pauli–Jordan operator whose eigenvalues are too close to zero according to a geometrical criterion which we describe more fully below. In connection with these results and the questions they raise, we also study the ‘entropy of coarse-graining’ generated by thinning out the causal set, and we compare it with what one obtains by similarly thinning out a chain of harmonic oscillators, finding the same, ‘universal’ behaviour in both cases.
Enthalpy-entropy compensation: the role of solvation.
Dragan, Anatoliy I; Read, Christopher M; Crane-Robinson, Colyn
2017-05-01
Structural modifications to interacting systems frequently lead to changes in both the enthalpy (heat) and entropy of the process that compensate each other, so that the Gibbs free energy is little changed: a major barrier to the development of lead compounds in drug discovery. The conventional explanation for such enthalpy-entropy compensation (EEC) is that tighter contacts lead to a more negative enthalpy but increased molecular constraints, i.e., a compensating conformational entropy reduction. Changes in solvation can also contribute to EEC but this contribution is infrequently discussed. We review long-established and recent cases of EEC and conclude that the large fluctuations in enthalpy and entropy observed are too great to be a result of only conformational changes and must result, to a considerable degree, from variations in the amounts of water immobilized or released on forming complexes. Two systems exhibiting EEC show a correlation between calorimetric entropies and local mobilities, interpreted to mean conformational control of the binding entropy/free energy. However, a substantial contribution from solvation gives the same effect, as a consequence of a structural link between the amount of bound water and the protein flexibility. Only by assuming substantial changes in solvation-an intrinsically compensatory process-can a more complete understanding of EEC be obtained. Faced with such large, and compensating, changes in the enthalpies and entropies of binding, the best approach to engineering elevated affinities must be through the addition of ionic links, as they generate increased entropy without affecting the enthalpy.
System Entropy Measurement of Stochastic Partial Differential Systems
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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.
International Nuclear Information System (INIS)
Baccetti, Valentina; Visser, Matt
2013-01-01
Even if a probability distribution is properly normalizable, its associated Shannon (or von Neumann) entropy can easily be infinite. We carefully analyze conditions under which this phenomenon can occur. Roughly speaking, this happens when arbitrarily small amounts of probability are dispersed into an infinite number of states; we shall quantify this observation and make it precise. We develop several particularly simple, elementary, and useful bounds, and also provide some asymptotic estimates, leading to necessary and sufficient conditions for the occurrence of infinite Shannon entropy. We go to some effort to keep technical computations as simple and conceptually clear as possible. In particular, we shall see that large entropies cannot be localized in state space; large entropies can only be supported on an exponentially large number of states. We are for the time being interested in single-channel Shannon entropy in the information theoretic sense, not entropy in a stochastic field theory or quantum field theory defined over some configuration space, on the grounds that this simple problem is a necessary precursor to understanding infinite entropy in a field theoretic context. (paper)
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.
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,
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
Wavelet entropy of BOLD time series: An application to Rolandic epilepsy.
Gupta, Lalit; Jansen, Jacobus F A; Hofman, Paul A M; Besseling, René M H; de Louw, Anton J A; Aldenkamp, Albert P; Backes, Walter H
2017-12-01
To assess the wavelet entropy for the characterization of intrinsic aberrant temporal irregularities in the time series of resting-state blood-oxygen-level-dependent (BOLD) signal fluctuations. Further, to evaluate the temporal irregularities (disorder/order) on a voxel-by-voxel basis in the brains of children with Rolandic epilepsy. The BOLD time series was decomposed using the discrete wavelet transform and the wavelet entropy was calculated. Using a model time series consisting of multiple harmonics and nonstationary components, the wavelet entropy was compared with Shannon and spectral (Fourier-based) entropy. As an application, the wavelet entropy in 22 children with Rolandic epilepsy was compared to 22 age-matched healthy controls. The images were obtained by performing resting-state functional magnetic resonance imaging (fMRI) using a 3T system, an 8-element receive-only head coil, and an echo planar imaging pulse sequence ( T2*-weighted). The wavelet entropy was also compared to spectral entropy, regional homogeneity, and Shannon entropy. Wavelet entropy was found to identify the nonstationary components of the model time series. In Rolandic epilepsy patients, a significantly elevated wavelet entropy was observed relative to controls for the whole cerebrum (P = 0.03). Spectral entropy (P = 0.41), regional homogeneity (P = 0.52), and Shannon entropy (P = 0.32) did not reveal significant differences. The wavelet entropy measure appeared more sensitive to detect abnormalities in cerebral fluctuations represented by nonstationary effects in the BOLD time series than more conventional measures. This effect was observed in the model time series as well as in Rolandic epilepsy. These observations suggest that the brains of children with Rolandic epilepsy exhibit stronger nonstationary temporal signal fluctuations than controls. 2 Technical Efficacy: Stage 3 J. Magn. Reson. Imaging 2017;46:1728-1737. © 2017 International Society for Magnetic
Entropy of jammed granular matter
Briscoe, Christopher
Granular matter can be considered a non-equilibrium system, such that equilibrium statistics is insufficient to describe the dynamics. A phase transition occurs when granular materials are compressed such that a nonzero stress develops in response to a strain deformation. This transition, referred to as the jamming transition, occurs at a critical volume fraction, φc depending on friction and preparation protocol. Analysis of the jamming transition produces a phase diagram of jammed granular matter for identical spheres, characterized by the critical volume fraction, φc and the average coordination number, Z. The boundaries of the phase diagram are related to well-defined upper and lower limits in the density of disordered packings; random close packing (RCP) and random loose packing (RLP). Frictional systems, such as granular matter, exhibit an inherent path dependency resulting in the loss of energy conservation, an important facet of equilibrium statistics. It has been suggested Edwards that the volume-force (V-F) ensemble, wherein volume replaces energy as the conservative quantity, may provide a sufficient framework to create a statistical ensemble for jammed granular matter. Treating a jammed system via the V-F ensemble introduces an analogue to temperature in equilibrium systems. This analogue, "compactivity", measures how compact a system could be and governs fluctuation in the volume statistics. Randomness in statistical systems is typically characterized by entropy, the equation of state derived from the number of microstates available to the system. In equilibrium statistical mechanics, entropy provides the link between these microstates and the macroscopic thermodynamic properties of the system. Therefore, calculating the entropy within the V-F ensemble can relate the available microscopic volume for each grain to the macroscopic system properties. The entropy is shown to be minimal at RCP and maximal at the minimum RLP limit, via several methods
Directory of Open Access Journals (Sweden)
Leonid M. Martyushev
2015-06-01
Full Text Available The entropy production (inside the volume bounded by a photosphere of main-sequence stars, subgiants, giants, and supergiants is calculated based on B–V photometry data. A non-linear inverse relationship of thermodynamic fluxes and forces as well as an almost constant specific (per volume entropy production of main-sequence stars (for 95% of stars, this quantity lies within 0.5 to 2.2 of the corresponding solar magnitude is found. The obtained results are discussed from the perspective of known extreme principles related to entropy production.
Miyo, Takahiro; Oguma, Yuzuru; Charlesworth, Brian
2006-08-01
To elucidate genetic variation in susceptibility to organophosphate insecticides within natural populations of Drosophila melanogaster, we conducted an analysis of variance for mortality data sets of isofemale lines (10-286 lines) used in the previous studies. Susceptibility of isofemale lines to the three organophosphate insecticides was continuously distributed within each natural population, ranging from susceptible to resistant. Analysis of variance showed highly significant variation among isofemale lines in susceptibility to each insecticide for each natural population. Significant genetic variances in susceptibility to the three chemicals were estimated for the Katsunuma population; 0.0529-0.2722 for malathion, 0.0492-0.1603 for prothiophos, and 0.0469-0.1696 for fenitrothion. Contrary to the consistent seasonal tendency towards an increase in mean susceptibility in the fall, reported in the previous study, genetic variances in susceptibility to the three organophosphates did not change significantly in 1997 but tended to increase by 2- to 5-times in 1998. We tested whether both the observed situations, maintenance and increase in genetic variance in organophosphate resistance, can be generated under circumstances in which the levels of resistance to the three organophosphates tended to decrease, by conducting a simulation analysis, based on the hypothesis that resistant genotypes have lower fitnesses than susceptible ones under the density-independent condition. The simulation analysis generally explained the pattern in the mean susceptibility and genetic variances in susceptibility to the three organophosphates, observed in the Katsunuma population of D. melanogaster. It was suggested that the differences in the frequencies of resistance genes in the summer population could affect the patterns in genetic variance in organophosphate resistance in the fall population.
Entropy in Corporate Information Systems
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Victor Y. Tsvetkov
2014-03-01
Full Text Available This paper describes the stages of entropy formation. It depicts the basic definitions of the corporate information systems. This paper describes the quality of entropy, the duration of the entropy in the corporate information system. The article also gives a paradigmatic description of the action of information entropy in time.
Ghosh, Rikhia; Banerjee, Saikat; Hazra, Milan; Roy, Susmita; Bagchi, Biman
2014-12-01
Since the time of Kirkwood, observed deviations in magnitude of the dielectric constant of aqueous protein solution from that of neat water (˜80) and slower decay of polarization have been subjects of enormous interest, controversy, and debate. Most of the common proteins have large permanent dipole moments (often more than 100 D) that can influence structure and dynamics of even distant water molecules, thereby affecting collective polarization fluctuation of the solution, which in turn can significantly alter solution's dielectric constant. Therefore, distance dependence of polarization fluctuation can provide important insight into the nature of biological water. We explore these aspects by studying aqueous solutions of four different proteins of different characteristics and varying sizes, chicken villin headpiece subdomain (HP-36), immunoglobulin binding domain protein G (GB1), hen-egg white lysozyme (LYS), and Myoglobin (MYO). We simulate fairly large systems consisting of single protein molecule and 20000-30000 water molecules (varied according to the protein size), providing a concentration in the range of ˜2-3 mM. We find that the calculated dielectric constant of the system shows a noticeable increment in all the cases compared to that of neat water. Total dipole moment auto time correlation function of water ⟨δMW(0)δMW(t)⟩ is found to be sensitive to the nature of the protein. Surprisingly, dipole moment of the protein and total dipole moment of the water molecules are found to be only weakly coupled. Shellwise decomposition of water molecules around protein reveals higher density of first layer compared to the succeeding ones. We also calculate heuristic effective dielectric constant of successive layers and find that the layer adjacent to protein has much lower value (˜50). However, progressive layers exhibit successive increment of dielectric constant, finally reaching a value close to that of bulk 4-5 layers away. We also calculate shellwise
Minimum entropy production principle
Czech Academy of Sciences Publication Activity Database
Maes, C.; Netočný, Karel
2013-01-01
Roč. 8, č. 7 (2013), s. 9664-9677 ISSN 1941-6016 Institutional support: RVO:68378271 Keywords : MINEP Subject RIV: BE - Theoretical Physics http://www.scholarpedia.org/article/Minimum_entropy_production_principle
Energy Technology Data Exchange (ETDEWEB)
Estes, John [Blackett Laboratory, Imperial College,London SW7 2AZ (United Kingdom); Jensen, Kristan [Department of Physics and Astronomy, University of Victoria,Victoria, BC V8W 3P6 (Canada); C.N. Yang Institute for Theoretical Physics, SUNY Stony Brook,Stony Brook, NY 11794-3840 (United States); O’Bannon, Andy [Rudolf Peierls Centre for Theoretical Physics, University of Oxford,1 Keble Road, Oxford OX1 3NP (United Kingdom); Tsatis, Efstratios [8 Kotylaiou Street, Athens 11364 (Greece); Wrase, Timm [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States)
2014-05-19
We study a number of (3+1)- and (2+1)-dimensional defect and boundary conformal field theories holographically dual to supergravity theories. In all cases the defects or boundaries are planar, and the defects are codimension-one. Using holography, we compute the entanglement entropy of a (hemi-)spherical region centered on the defect (boundary). We define defect and boundary entropies from the entanglement entropy by an appropriate background subtraction. For some (3+1)-dimensional theories we find evidence that the defect/boundary entropy changes monotonically under certain renormalization group flows triggered by operators localized at the defect or boundary. This provides evidence that the g-theorem of (1+1)-dimensional field theories generalizes to higher dimensions.
Estes, John; Jensen, Kristan; O'Bannon, Andy; Tsatis, Efstratios; Wrase, Timm
2014-05-01
We study a number of (3 + 1)- and (2 + 1)-dimensional defect and boundary conformal field theories holographically dual to supergravity theories. In all cases the defects or boundaries are planar, and the defects are codimension-one. Using holography, we compute the entanglement entropy of a (hemi-)spherical region centered on the defect (boundary). We define defect and boundary entropies from the entanglement entropy by an appropriate background subtraction. For some (3 + 1)-dimensional theories we find evidence that the defect/boundary entropy changes monotonically under certain renormalization group flows triggered by operators localized at the defect or boundary. This provides evidence that the g-theorem of (1 + 1)-dimensional field theories generalizes to higher dimensions.
Microcanonical entropy for classical systems
Franzosi, Roberto
2018-03-01
The entropy definition in the microcanonical ensemble is revisited. We propose a novel definition for the microcanonical entropy that resolve the debate on the correct definition of the microcanonical entropy. In particular we show that this entropy definition fixes the problem inherent the exact extensivity of the caloric equation. Furthermore, this entropy reproduces results which are in agreement with the ones predicted with standard Boltzmann entropy when applied to macroscopic systems. On the contrary, the predictions obtained with the standard Boltzmann entropy and with the entropy we propose, are different for small system sizes. Thus, we conclude that the Boltzmann entropy provides a correct description for macroscopic systems whereas extremely small systems should be better described with the entropy that we propose here.
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MAURICIO LIMA
2001-06-01
Full Text Available The fluctuations exhibited by natural populations have fascinated ecologists for the last eighty years. However, a vigorous debate between different schools of population ecologists has hampered reaching a consensus about the causes of such numerical fluctuations. Recent findings and a more synthetic view of population change espoused by ecologists, statisticians, and mathematicians have integrated the role of nonlinear feedback (deterministic and external environmental (deterministic or stochastic processes in the dynamics of natural populations. The new challenge for population ecologists is to understand how these two different forces interact in nature. In this commentary, I review some of the basic principles of population analysis during the last 50 years. Finally, this commentary emphasize that one of the most promising approaches in population ecology will be the analysis and interpretation of time series data from several species in the same place, and the integration of demographic analysis and mathematical modeling. In both cases we need long-term data of biological populations and the factors that effect them. The potential insights gained from such an approach will help ecologists to understand better the dynamics of natural populations and will have large implications for applied issues such as conservation, management, and control of natural populationsLas fluctuaciones exhibidas por las poblaciones naturales han fascinado a los ecólogos durante los últimos ochenta años. Sin embargo, las acaloradas controversias entre las dos escuelas de ecólogos poblacionales han retrasado la explicación de dichas fluctuaciones numéricas. Recientes hallazgos y una visión más sintética del cambio poblacional lograda por los ecólogos, estadísticos y matemáticos han integrado el papel de los procesos no lineales (deterministas y los procesos externos ambientales (deterministas o estocásticos en la dinámica de las poblaciones naturales
Entropy Generation and Human Aging: Lifespan Entropy and Effect of Physical Activity Level
Silva, Carlos; Annamalai, Kalyan
2008-06-01
The first and second laws of thermodynamics were applied to biochemical reactions typical of human metabolism. An open-system model was used for a human body. Energy conservation, availability and entropy balances were performed to obtain the entropy generated for the main food components. Quantitative results for entropy generation were obtained as a function of age using the databases from the U.S. Food and Nutrition Board (FNB) and Centers for Disease Control and Prevention (CDC), which provide energy requirements and food intake composition as a function of age, weight and stature. Numerical integration was performed through human lifespan for different levels of physical activity. Results were presented and analyzed. Entropy generated over the lifespan of average individuals (natural death) was found to be 11,404 kJ/ºK per kg of body mass with a rate of generation three times higher on infants than on the elderly. The entropy generated predicts a life span of 73.78 and 81.61 years for the average U.S. male and female individuals respectively, which are values that closely match the average lifespan from statistics (74.63 and 80.36 years). From the analysis of the effect of different activity levels, it is shown that entropy generated increases with physical activity, suggesting that exercise should be kept to a “healthy minimum” if entropy generation is to be minimized.
Entropy Generation and Human Aging: Lifespan Entropy and Effect of Physical Activity Level
Directory of Open Access Journals (Sweden)
Kalyan Annamalai
2008-06-01
Full Text Available The first and second laws of thermodynamics were applied to biochemical reactions typical of human metabolism. An open-system model was used for a human body. Energy conservation, availability and entropy balances were performed to obtain the entropy generated for the main food components. Quantitative results for entropy generation were obtained as a function of age using the databases from the U.S. Food and Nutrition Board (FNB and Centers for Disease Control and Prevention (CDC, which provide energy requirements and food intake composition as a function of age, weight and stature. Numerical integration was performed through human lifespan for different levels of physical activity. Results were presented and analyzed. Entropy generated over the lifespan of average individuals (natural death was found to be 11,404 kJ/Ã‚ÂºK per kg of body mass with a rate of generation three times higher on infants than on the elderly. The entropy generated predicts a life span of 73.78 and 81.61 years for the average U.S. male and female individuals respectively, which are values that closely match the average lifespan from statistics (74.63 and 80.36 years. From the analysis of the effect of different activity levels, it is shown that entropy generated increases with physical activity, suggesting that exercise should be kept to a Ã¢Â€Âœhealthy minimumÃ¢Â€Â if entropy generation is to be minimized.
Entropy Is Simple, Qualitatively
Lambert, Frank L.
2002-10-01
Qualitatively, entropy is simple. What it is, why it is useful in understanding the behavior of macro systems or of molecular systems is easy to state: Entropy increase from a macro viewpoint is a measure of the dispersal of energy from localized to spread out at a temperature T. The conventional q in qrev/T is the energy dispersed to or from a substance or a system. On a molecular basis, entropy increase means that a system changes from having fewer accessible microstates to having a larger number of accessible microstates. Fundamentally based on statistical and quantum mechanics, this approach is superior to the non-fundamental "disorder" as a descriptor of entropy change. The foregoing in no way denies the subtlety or the difficulty presented by entropy in thermodynamics—to first-year students or to professionals. However, as an aid to beginners in their quantitative study of thermodynamics, the qualitative conclusions in this article give students the advantage of a clear bird’s-eye view of why entropy increases in a wide variety of basic cases: a substance going from 0 K to T, phase change, gas expansion, mixing of ideal gases or liquids, colligative effects, and the Gibbs equation. See Letter re: this article.
Renormalized entanglement entropy
Energy Technology Data Exchange (ETDEWEB)
Taylor, Marika; Woodhead, William [Mathematical Sciences and STAG Research Centre, University of Southampton,Highfield, Southampton, SO17 1BJ (United Kingdom)
2016-08-29
We develop a renormalization method for holographic entanglement entropy based on area renormalization of entangling surfaces. The renormalized entanglement entropy is derived for entangling surfaces in asymptotically locally anti-de Sitter spacetimes in general dimensions and for entangling surfaces in four dimensional holographic renormalization group flows. The renormalized entanglement entropy for disk regions in AdS{sub 4} spacetimes agrees precisely with the holographically renormalized action for AdS{sub 4} with spherical slicing and hence with the F quantity, in accordance with the Casini-Huerta-Myers map. We present a generic class of holographic RG flows associated with deformations by operators of dimension 3/2<Δ<5/2 for which the F quantity increases along the RG flow, hence violating the strong version of the F theorem. We conclude by explaining how the renormalized entanglement entropy can be derived directly from the renormalized partition function using the replica trick i.e. our renormalization method for the entanglement entropy is inherited directly from that of the partition function. We show explicitly how the entanglement entropy counterterms can be derived from the standard holographic renormalization counterterms for asymptotically locally anti-de Sitter spacetimes.
International Nuclear Information System (INIS)
Lemos, Jose P. S.; Zaslavskii, Oleg B.
2010-01-01
We trace the origin of the black hole entropy S, replacing a black hole by a quasiblack hole. Let the boundary of a static body approach its own gravitational radius, in such a way that a quasihorizon forms. We show that if the body is thermal with the temperature taking the Hawking value at the quasihorizon limit, it follows, in the nonextremal case, from the first law of thermodynamics that the entropy approaches the Bekenstein-Hawking value S=A/4. In this setup, the key role is played by the surface stresses on the quasihorizon and one finds that the entropy comes from the quasihorizon surface. Any distribution of matter inside the surface leads to the same universal value for the entropy in the quasihorizon limit. This can be of some help in the understanding of black hole entropy. Other similarities between black holes and quasiblack holes such as the mass formulas for both objects had been found previously. We also discuss the entropy for extremal quasiblack holes, a more subtle issue.
On Entropy Production of Repeated Quantum Measurements I. General Theory
Benoist, T.; Jakšić, V.; Pautrat, Y.; Pillet, C.-A.
2018-01-01
We study entropy production (EP) in processes involving repeated quantum measurements of finite quantum systems. Adopting a dynamical system approach, we develop a thermodynamic formalism for the EP and study fine aspects of irreversibility related to the hypothesis testing of the arrow of time. Under a suitable chaoticity assumption, we establish a Large Deviation Principle and a Fluctuation Theorem for the EP.
Language Aspects of Engineering Students' View of Entropy
Haglund, Jesper; Andersson, Staffan; Elmgren, Maja
2016-01-01
Entropy is a central concept in thermodynamics, but has been found to be challenging to students due to its abstract nature and the fact that it is not part of students' everyday language. Interviews with three pairs of engineering students (N = 6) were conducted and video recorded regarding their interpretation and use of the entropy concept, one…
Anomalous effective action, Noether current, Virasoro algebra and Horizon entropy
Energy Technology Data Exchange (ETDEWEB)
Majhi, Bibhas Ranjan [IUCAA, Ganeshkhind, Pune University Campus, Post Bag 4, Pune (India); Hebrew University of Jerusalem, Racah Institute of Physics, Jerusalem (Israel); Chakraborty, Sumanta [IUCAA, Ganeshkhind, Pune University Campus, Post Bag 4, Pune (India)
2014-05-15
Several investigations show that in a very small length scale there exist corrections to the entropy of black hole horizon. Due to fluctuations of the background metric and the external fields the action incorporates corrections. In the low energy regime, the one-loop effective action in four dimensions leads to trace anomaly. We start from the Noether current corresponding to the Einstein-Hilbert plus the one-loop effective action to calculate the charge for the diffeomorphisms which preserve the Killing horizon structure. Then a bracket for the charges is calculated. We show that the Fourier modes of the bracket are exactly similar to the Virasoro algebra. Then using the Cardy formula the entropy is evaluated. Finally, the explicit terms of the entropy expression is calculated for a classical background. It turns out that the usual expression for the entropy; i.e. the Bekenstein-Hawking form, is not modified. (orig.)
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
Energy Technology Data Exchange (ETDEWEB)
NONE
1995-08-01
The Savannah River Operations Office Strategic Plan directs Savannah River Site (SRS) to find ways to reduce operating costs, and to determine what site infrastructure must be maintained and what infrastructure is surplus. Because of the mission change, L-Lake, Par Pond, and the river water system are no longer needed to support current missions and therefore provide an opportunity for operating cost reduction. If SRS determines that L-Lake, Par Pond, and the river water system are no longer needed to support future missions and are considered surplus, appropriate NEPA documentation will be prepared. The purpose of the proposed action in this Environmental Assessment is to begin an examination of the need for the Site`s river water system by (1) developing data needed to evaluate the potential environmental impacts of further reducing or eliminating the flow demands from the Site`s river water system and; (2) evaluating the potential of reducing operating costs by allowing the water level in Par Pond to fluctuate naturally through reduced pumping. This action also includes reducing the current flow rates from L-Lake to Steel Creek to natural stream flows while maintaining full pool. The recently approved Par Pond CERCLA Interim Action Proposed Plan (IAPP) committed to evaluate in a NEPA document the environmental consequences of this proposed action. This document evaluated the remediation of human health and ecological risks associated with the three year drawdown of Par Pond. Should any of the parameters sampled in the reservoir and streams (e.g., water quality, biota, etc.) exceed established threshold levels during the implementation of the proposed action, water would again be pumped into the reservoir to minimize any impacts by bringing the water level back to an appropriate level about 58.2 m (195 ft).
International Nuclear Information System (INIS)
1995-08-01
The Savannah River Operations Office Strategic Plan directs Savannah River Site (SRS) to find ways to reduce operating costs, and to determine what site infrastructure must be maintained and what infrastructure is surplus. Because of the mission change, L-Lake, Par Pond, and the river water system are no longer needed to support current missions and therefore provide an opportunity for operating cost reduction. If SRS determines that L-Lake, Par Pond, and the river water system are no longer needed to support future missions and are considered surplus, appropriate NEPA documentation will be prepared. The purpose of the proposed action in this Environmental Assessment is to begin an examination of the need for the Site's river water system by (1) developing data needed to evaluate the potential environmental impacts of further reducing or eliminating the flow demands from the Site's river water system and; (2) evaluating the potential of reducing operating costs by allowing the water level in Par Pond to fluctuate naturally through reduced pumping. This action also includes reducing the current flow rates from L-Lake to Steel Creek to natural stream flows while maintaining full pool. The recently approved Par Pond CERCLA Interim Action Proposed Plan (IAPP) committed to evaluate in a NEPA document the environmental consequences of this proposed action. This document evaluated the remediation of human health and ecological risks associated with the three year drawdown of Par Pond. Should any of the parameters sampled in the reservoir and streams (e.g., water quality, biota, etc.) exceed established threshold levels during the implementation of the proposed action, water would again be pumped into the reservoir to minimize any impacts by bringing the water level back to an appropriate level about 58.2 m (195 ft)
Canonical entropy of three-dimensional BTZ black hole
International Nuclear Information System (INIS)
Zhao Ren; Zhang Shengli
2006-01-01
Recently, Hawking radiation of the black hole has been studied using the tunnel effect method. It is found that the radiation spectrum of the black hole is not a strictly pure thermal spectrum. How does the departure from pure thermal spectrum affect the entropy? This is a very interesting problem. In this Letter, we calculate the partition function by energy spectrum obtained from tunnel effect. Using the partition function, we compute the black hole entropy and derive the expression of the black hole entropy after considering the radiation. And we derive the entropy of charged black hole. In our calculation, we consider not only the correction to the black hole entropy due to fluctuation of energy but also the effect of the change of the black hole charges on entropy. There is no other hypothesis. Our result is more reasonable. According to the fact that the black hole entropy is not divergent, we obtain the lower limit of Banados-Teitelboim-Zanelli black hole energy. That is, the least energy of Banados-Teitelboim-Zanelli black hole, which satisfies the stationary condition in thermodynamics
Calculation of Configurational Entropy in Complex Landscapes
Directory of Open Access Journals (Sweden)
Samuel A Cushman
2018-04-01
Full Text Available Entropy and the second law of thermodynamics are fundamental concepts that underlie all natural processes and patterns. Recent research has shown how the entropy of a landscape mosaic can be calculated using the Boltzmann equation, with the entropy of a lattice mosaic equal to the logarithm of the number of ways a lattice with a given dimensionality and number of classes can be arranged to produce the same total amount of edge between cells of different classes. However, that work seemed to also suggest that the feasibility of applying this method to real landscapes was limited due to intractably large numbers of possible arrangements of raster cells in large landscapes. Here I extend that work by showing that: (1 the proportion of arrangements rather than the number with a given amount of edge length provides a means to calculate unbiased relative configurational entropy, obviating the need to compute all possible configurations of a landscape lattice; (2 the edge lengths of randomized landscape mosaics are normally distributed, following the central limit theorem; and (3 given this normal distribution it is possible to fit parametric probability density functions to estimate the expected proportion of randomized configurations that have any given edge length, enabling the calculation of configurational entropy on any landscape regardless of size or number of classes. I evaluate the boundary limits (4 for this normal approximation for small landscapes with a small proportion of a minority class and show it holds under all realistic landscape conditions. I further (5 demonstrate that this relationship holds for a sample of real landscapes that vary in size, patch richness, and evenness of area in each cover type, and (6 I show that the mean and standard deviation of the normally distributed edge lengths can be predicted nearly perfectly as a function of the size, patch richness and diversity of a landscape. Finally, (7 I show that the
A Graphical Proof of the Positive Entropy Change in Heat Transfer between Two Objects
Kiatgamolchai, Somchai
2015-01-01
It is well known that heat transfer between two objects results in a positive change in the total entropy of the two-object system. The second law of thermodynamics states that the entropy change of a naturally irreversible process is positive. In other words, if the entropy change of any process is positive, it can be inferred that such a process…
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,…
Entropy of a bit-shift channel
Baggen, Stan; Balakirsky, Vladimir; Denteneer, Dee; Egner, Sebastian; Hollmann, Henk; Tolhuizen, Ludo; Verbitskiy, Evgeny
2006-01-01
We consider a simple transformation (coding) of an iid source called a bit-shift channel. This simple transformation occurs naturally in magnetic or optical data storage. The resulting process is not Markov of any order. We discuss methods of computing the entropy of the transformed process, and
Farokhi, Saeed; Taghavi, Ray; Keshmiri, Shawn
2015-11-01
Stealth technology is developed for military aircraft to minimize their signatures. The primary attention was focused on radar signature, followed by the thermal and noise signatures of the vehicle. For radar evasion, advanced configuration designs, extensive use of carbon composites and radar-absorbing material, are developed. On thermal signature, mainly in the infra-red (IR) bandwidth, the solution was found in blended rectangular nozzles of high aspect ratio that are shielded from ground detectors. For noise, quiet and calm jets are integrated into vehicles with low-turbulence configuration design. However, these technologies are totally incapable of detecting new generation of revolutionary aircraft. These shall use all electric, distributed, propulsion system that are thermally transparent. In addition, composite skin and non-emitting sensors onboard the aircraft will lead to low signature. However, based on the second-law of thermodynamics, there is no air vehicle that can escape from leaving an entropy trail. Entropy is thus the only inevitable signature of any system, that once measured, can detect the source. By characterizing the entropy field based on its statistical properties, the source may be recognized, akin to face recognition technology. Direct measurement of entropy is cumbersome, however as a derived property, it can be easily measured. The measurement accuracy depends on the probe design and the sensors onboard. One novel air data sensor suite is introduced with promising potential to capture the entropy trail.
Entropy Production in Stochastics
Directory of Open Access Journals (Sweden)
Demetris Koutsoyiannis
2017-10-01
Full Text Available While the modern definition of entropy is genuinely probabilistic, in entropy production the classical thermodynamic definition, as in heat transfer, is typically used. Here we explore the concept of entropy production within stochastics and, particularly, two forms of entropy production in logarithmic time, unconditionally (EPLT or conditionally on the past and present having been observed (CEPLT. We study the theoretical properties of both forms, in general and in application to a broad set of stochastic processes. A main question investigated, related to model identification and fitting from data, is how to estimate the entropy production from a time series. It turns out that there is a link of the EPLT with the climacogram, and of the CEPLT with two additional tools introduced here, namely the differenced climacogram and the climacospectrum. In particular, EPLT and CEPLT are related to slopes of log-log plots of these tools, with the asymptotic slopes at the tails being most important as they justify the emergence of scaling laws of second-order characteristics of stochastic processes. As a real-world application, we use an extraordinary long time series of turbulent velocity and show how a parsimonious stochastic model can be identified and fitted using the tools developed.
Entropy conservative finite element schemes
Tadmor, E.
1986-01-01
The question of entropy stability for discrete approximations to hyperbolic systems of conservation laws is studied. The amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison. To this end, two main ingredients are used: entropy variables and the construction of certain entropy conservative schemes in terms of piecewise-linear finite element approximations. It is then shown that conservative schemes are entropy stable, if and (for three-point schemes) only if, they contain more numerical viscosity than the abovementioned entropy conservation ones.
Directory of Open Access Journals (Sweden)
Hejie Wei
2017-02-01
Full Text Available Accurately identifying the spatiotemporal variations and driving factors of ecosystem services (ES in ecological restoration is important for ecosystem management and the sustainability of nature conservation strategies. As the Green for Grain project proceeds, food provision, water regulation and climate regulation services in the Northern Shaanxi Loess Plateau (NSLP are changing and have caused broad attention. In this study, the dynamic pattern of the normalized differential vegetation index (NDVI and the main drivers of grain production (GP, water yield (WY and net primary production (NPP in the NSLP from 2000–2013 are identified by incorporating multiple data and methods, in order to provide a better understanding of how and why ES change during ecological restoration. WY was simulated by hydrological modeling, and NPP was estimated with the Carnegie Ames Stanford Approach (CASA model. The results show that vegetation restoration continued from 2000–2013, but fluctuated because of the comprehensive influence of climate and human activity. GP and NPP both exhibited significantly increasing trends, while changes in WY occurred in two stages: decline (2000–2006 and growth (2007–2013. Spatially, significantly increasing trends in NPP and WY were detected in 52.73% and 24.76% of the region, respectively, in areas that correspond with the Green for Grain project and high precipitation growth. Correlation and partial correlation analyses show that there were different dominant factors (i.e., natural vs. anthropogenic driving ES change in the NSLP from 2000–2013. The change in WY was mainly driven by precipitation, while the improvements in GP and NPP can be attributed to investments in natural capital (i.e., chemical fertilizer, agricultural machinery power and afforestation. We also found that vegetation restoration can produce positive effects on NPP, but negative effects on WY by using response analyses of WY or NPP change to NDVI
Superstatistical distributions from a maximum entropy principle.
Van der Straeten, Erik; Beck, Christian
2008-11-01
We deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the distribution of the fluctuating intensive parameter beta of a superstatistical system, given certain constraints on the complex system under consideration. We apply the theory to three examples: the superstatistical quantum-mechanical harmonic oscillator, the superstatistical classical ideal gas, and velocity time series as measured in a turbulent Taylor-Couette flow.
Case study of enthalpy-entropy noncompensation
Graziano, Giuseppe
2004-03-01
Enthalpy-entropy noncompensation characterizes the relative changes in the hydration thermodynamic functions upon "transforming" ethane into fluoromethane, chloromethane, bromomethane, and iodomethane. An analysis grounded on a simple statistical mechanical theory of hydration allows a plausible rationalization of such enthalpy-entropy noncompensation. It is shown that increasing the strength of solute-water attractive interactions modifying the chemical nature of a part of the solute molecule, but not its size, is a largely noncompensating process for the hydration of noncharged and nonhydrogen bonding species, and dominates the compensating contribution coming from the reorganization of water H bonds.
Topics in Bayesian statistics and maximum entropy
International Nuclear Information System (INIS)
Mutihac, R.; Cicuttin, A.; Cerdeira, A.; Stanciulescu, C.
1998-12-01
Notions of Bayesian decision theory and maximum entropy methods are reviewed with particular emphasis on probabilistic inference and Bayesian modeling. The axiomatic approach is considered as the best justification of Bayesian analysis and maximum entropy principle applied in natural sciences. Particular emphasis is put on solving the inverse problem in digital image restoration and Bayesian modeling of neural networks. Further topics addressed briefly include language modeling, neutron scattering, multiuser detection and channel equalization in digital communications, genetic information, and Bayesian court decision-making. (author)
Microscopic entropy and nonlocality
International Nuclear Information System (INIS)
Karpov, E.; Ordonets, G.; Petroskij, T.; Prigozhin, I.
2003-01-01
We have obtained a microscopic expression for entropy in terms of H function based on nonunitary Λ transformation which leads from the time evolution as a unitary group to a Markovian dynamics and unifies the reversible and irreversible aspects of quantum mechanics. This requires a new representation outside the Hilbert space. In terms of H, we show the entropy production and the entropy flow during the emission and absorption of radiation by an atom. Analyzing the time inversion experiment, we emphasize the importance of pre- and postcollisional correlations, which break the symmetry between incoming and outgoing waves. We consider the angle dependence of the H function in a three-dimensional situation. A model including virtual transitions is discussed in a subsequent paper
Neri, Izaak; Roldán, Édgar; Jülicher, Frank
2017-01-01
We study the statistics of infima, stopping times, and passage probabilities of entropy production in nonequilibrium steady states, and we show that they are universal. We consider two examples of stopping times: first-passage times of entropy production and waiting times of stochastic processes, which are the times when a system reaches a given state for the first time. Our main results are as follows: (i) The distribution of the global infimum of entropy production is exponential with mean equal to minus Boltzmann's constant; (ii) we find exact expressions for the passage probabilities of entropy production; (iii) we derive a fluctuation theorem for stopping-time distributions of entropy production. These results have interesting implications for stochastic processes that can be discussed in simple colloidal systems and in active molecular processes. In particular, we show that the timing and statistics of discrete chemical transitions of molecular processes, such as the steps of molecular motors, are governed by the statistics of entropy production. We also show that the extreme-value statistics of active molecular processes are governed by entropy production; for example, we derive a relation between the maximal excursion of a molecular motor against the direction of an external force and the infimum of the corresponding entropy-production fluctuations. Using this relation, we make predictions for the distribution of the maximum backtrack depth of RNA polymerases, which follow from our universal results for entropy-production infima.
Directory of Open Access Journals (Sweden)
Izaak Neri
2017-02-01
Full Text Available We study the statistics of infima, stopping times, and passage probabilities of entropy production in nonequilibrium steady states, and we show that they are universal. We consider two examples of stopping times: first-passage times of entropy production and waiting times of stochastic processes, which are the times when a system reaches a given state for the first time. Our main results are as follows: (i The distribution of the global infimum of entropy production is exponential with mean equal to minus Boltzmann’s constant; (ii we find exact expressions for the passage probabilities of entropy production; (iii we derive a fluctuation theorem for stopping-time distributions of entropy production. These results have interesting implications for stochastic processes that can be discussed in simple colloidal systems and in active molecular processes. In particular, we show that the timing and statistics of discrete chemical transitions of molecular processes, such as the steps of molecular motors, are governed by the statistics of entropy production. We also show that the extreme-value statistics of active molecular processes are governed by entropy production; for example, we derive a relation between the maximal excursion of a molecular motor against the direction of an external force and the infimum of the corresponding entropy-production fluctuations. Using this relation, we make predictions for the distribution of the maximum backtrack depth of RNA polymerases, which follow from our universal results for entropy-production infima.
Transition-strength fluctuations and the onset of chaotic motion
International Nuclear Information System (INIS)
Alhassid, Y.; Levine, R.D.
1986-01-01
The maximum-entropy formalism is used to characterize the fluctuations in transition strengths for a bound quantum-mechanical system. In the chaotic limit only one, ever present, sum rule is required as a constraint. The resulting distribution is that of Porter and Thomas, which can also be derived from random-matrix theory. For nonchaotic systems the distribution of transition strengths has a lower entropy. A possible additional constraint, operative during the onset of chaos, is proposed. The distribution of maximal entropy subject to both constraints accords with computed intensities in a system of two degrees of freedom
Remarks on entanglement entropy in string theory
Balasubramanian, Vijay; Parrikar, Onkar
2018-03-01
Entanglement entropy for spatial subregions is difficult to define in string theory because of the extended nature of strings. Here we propose a definition for bosonic open strings using the framework of string field theory. The key difference (compared to ordinary quantum field theory) is that the subregion is chosen inside a Cauchy surface in the "space of open string configurations." We first present a simple calculation of this entanglement entropy in free light-cone string field theory, ignoring subtleties related to the factorization of the Hilbert space. We reproduce the answer expected from an effective field theory point of view, namely a sum over the one-loop entanglement entropies corresponding to all the particle-excitations of the string, and further show that the full string theory regulates ultraviolet divergences in the entanglement entropy. We then revisit the question of factorization of the Hilbert space by analyzing the covariant phase-space associated with a subregion in Witten's covariant string field theory. We show that the pure gauge (i.e., BRST exact) modes in the string field become dynamical at the entanglement cut. Thus, a proper definition of the entropy must involve an extended Hilbert space, with new stringy edge modes localized at the entanglement cut.
Entropy in Born-Infeld gravity
Ozen, Gokcen Deniz; Kurekci, Sahin; Tekin, Bayram
2017-12-01
There is a class of higher derivative gravity theories that are in some sense natural extensions of cosmological Einstein's gravity with a unique maximally symmetric classical vacuum and only a massless spin-2 excitation about the vacuum and no other perturbative modes. These theories are of the Born-Infeld determinant form. We show that the macroscopic dynamical entropy as defined by Wald for bifurcate Killing horizons in these theories are equivalent to the geometric Bekenstein-Hawking entropy (or more properly Gibbons-Hawking entropy for the case of de Sitter spacetime) but given with an effective gravitational constant which encodes all the information about the background spacetime and the underlying theory. We also show that the higher curvature terms increase the entropy. We carry out the computations in generic n dimensions including the particularly interesting limits of three, four and infinite number of dimensions. We also give a preliminary discussion about the black hole entropy in generic dimensions for the Born-Infeld theories.
International Nuclear Information System (INIS)
Mendis, B G; Goodman, M C J; Taylor, A A; Halliday, D P; Shannon, M D; Major, J D; Durose, K
2013-01-01
Aberration corrected STEM EELS is used to investigate point defects in Cu 2 ZnSnS 4 (CZTS). Nano-scale clusters of Zn Cu anti-site donors are observed with the donor concentration being sufficiently high to degenerately dope the semiconductor. Uncompensated donors and acceptors result in electrostatic potential fluctuations within the material. The effect of these potential fluctuations on the photovoltaic device properties is discussed
Quantum Entropy and Complexity
Benatti, F.; Oskouei, S. Khabbazi; Abad, A. Shafiei Deh
We study the relations between the recently proposed machine-independent quantum complexity of P. Gacs [1] and the entropy of classical and quantum systems. On one hand, by restricting Gacs complexity to ergodic classical dynamical systems, we retrieve the equality between the Kolmogorov complexity rate and the Shannon entropy rate derived by A. A. Brudno [2]. On the other hand, using the quantum Shannon-McMillan theorem [3], we show that such an equality holds densely in the case of ergodic quantum spin chains.
DEFF Research Database (Denmark)
Yuri, Shtarkov; Justesen, Jørn
1997-01-01
The concept of entropy for an image on a discrete two dimensional grid is introduced. This concept is used as an information theoretic bound on the coding rate for the image. It is proved that this quantity exists as a limit for arbitrary sets satisfying certain conditions.......The concept of entropy for an image on a discrete two dimensional grid is introduced. This concept is used as an information theoretic bound on the coding rate for the image. It is proved that this quantity exists as a limit for arbitrary sets satisfying certain conditions....
International Nuclear Information System (INIS)
Ponman, T.J.
1984-01-01
For some years now two different expressions have been in use for maximum entropy image restoration and there has been some controversy over which one is appropriate for a given problem. Here two further entropies are presented and it is argued that there is no single correct algorithm. The properties of the four different methods are compared using simple 1D simulations with a view to showing how they can be used together to gain as much information as possible about the original object. (orig.)
Maximum entropy tokamak configurations
International Nuclear Information System (INIS)
Minardi, E.
1989-01-01
The new entropy concept for the collective magnetic equilibria is applied to the description of the states of a tokamak subject to ohmic and auxiliary heating. The condition for the existence of steady state plasma states with vanishing entropy production implies, on one hand, the resilience of specific current density profiles and, on the other, severe restrictions on the scaling of the confinement time with power and current. These restrictions are consistent with Goldston scaling and with the existence of a heat pinch. (author)
Gravitons and light cone fluctuations
International Nuclear Information System (INIS)
Ford, L.H.
1995-01-01
Gravitons in a squeezed vacuum state, the natural result of quantum creation in the early Universe or by black holes, will introduce metric fluctuations. These metric fluctuations will introduce fluctuations of the light cone. It is shown that when the various two-point functions of a quantized field are averaged over the metric fluctuations, the light cone singularity disappears for distinct points. The metric-averaged functions remain singular in the limit of coincident points. The metric-averaged retarded Green's function for a massless field becomes a Gaussian which is nonzero both inside and outside of the classical light cone. This implies some photons propagate faster than the classical light speed, whereas others propagate slower. The possible effects of metric fluctuations upon one-loop quantum processes are discussed and illustrated by the calculation of the one-loop electron self-energy
Wikelski, Martin; Trillmich, Fritz
1997-06-01
Body size is often assumed to represent the outcome of conflicting selection pressures of natural and sexual selection. Marine iguana (Amblyrhynchus cristatus) populations in the Galápagos exhibit 10-fold differences in body mass between island populations. There is also strong sexual size dimorphism, with males being about twice as heavy as females. To understand the evolutionary processes shaping body size in marine iguanas, we analyzed the selection differentials on body size in two island populations (max. male mass 900 g in Genovesa, 3500 g in Santa Fé). Factors that usually confound any evolutionary analysis of body sizes-predation, interspecific food competition, reproductive role division-are ruled out for marine iguanas. We show that, above hatchlings, mortality rates increased with body size in both sexes to the same extent. This effect was independent of individual age. The largest animals (males) of each island were the first to die once environmental conditions deteriorated (e.g., during El Niños). This sex-biased mortality was the result of sexual size dimorphism, but at the same time caused sexual size dimorphism to fluctuate. Mortality differed between seasons (selection differentials as low as -1.4) and acted on different absolute body sizes between islands. Both males and females did not cease growth when an optimal body size for survival was reached, as demonstrated by the fact that individual adult body size phenotypically increased in each population under favorable environmental conditions beyond naturally selected limits. But why did marine iguanas grow "too large" for survival? Due to lek mating, sexual selection constantly favored large body size in males (selection differentials up to +0.77). Females only need to reach a body size sufficient to produce surviving offspring. Thereafter, large body size of females was less favored by fertility selection than large size in males. Resulting from these different selection pressures on male
International Nuclear Information System (INIS)
Clarke, J.
1980-01-01
This paper briefly reviews sources of noise in Josephson junctions, and the limits they impose on the sensitivity of dc and rf SQUIDS. The results are strictly valid only for a resistively shunted junction (RSJ) with zero capacitance, but should be applicable to point contact junctions and microbridges in so far as these devices can be approximated by the RSJ model. Fluctuations arising from Nyquist noise in the resistive shunt of a single junction are discussed in the limit eI/sub o/R/k/sub B/T << 1 in which a classical treatment is appropriate, and then extend the treatment to the limit eI/sub o/R/k/sub B/T greater than or equal to 1 in which quantum effects become important. The Nyquist limit theory is used to calculate the noise in a dc SQUID, and the results are compared with a number of practical devices. The quantum limit is briefly considered. Results for the predicted sensitivity of rf SQUIDS are presented, and also compared with a number of practical devices. Finally, the importance of l/f noise (f is the frequency) in limiting the low frequency performance of SQUIDS is discussed
Thinning, photonic beamsplitting, and a general discrete entropy power inequality
Guha, Saikat; Shapiro, Jeffrey H.; Sanchez, Raul Garcia-Patron
2016-01-01
Many partially-successful attempts have been made to find the most natural discrete-variable version of Shannon's entropy power inequality (EPI). We develop an axiomatic framework from which we deduce the natural form of a discrete-variable EPI and an associated entropic monotonicity in a discrete-variable central limit theorem. In this discrete EPI, the geometric distribution, which has the maximum entropy among all discrete distributions with a given mean, assumes a role analogous to the Ga...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 9. Entropy à la Boltzmann. Jayanta K Bhattacharjee. General Article Volume 6 Issue 9 September 2001 pp 19-34. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/006/09/0019-0034. Author Affiliations.
Aur, Dorian; Vila-Rodriguez, Fidel
2017-01-01
Complexity measures for time series have been used in many applications to quantify the regularity of one dimensional time series, however many dynamical systems are spatially distributed multidimensional systems. We introduced Dynamic Cross-Entropy (DCE) a novel multidimensional complexity measure that quantifies the degree of regularity of EEG signals in selected frequency bands. Time series generated by discrete logistic equations with varying control parameter r are used to test DCE measures. Sliding window DCE analyses are able to reveal specific period doubling bifurcations that lead to chaos. A similar behavior can be observed in seizures triggered by electroconvulsive therapy (ECT). Sample entropy data show the level of signal complexity in different phases of the ictal ECT. The transition to irregular activity is preceded by the occurrence of cyclic regular behavior. A significant increase of DCE values in successive order from high frequencies in gamma to low frequencies in delta band reveals several phase transitions into less ordered states, possible chaos in the human brain. To our knowledge there are no reliable techniques able to reveal the transition to chaos in case of multidimensional times series. In addition, DCE based on sample entropy appears to be robust to EEG artifacts compared to DCE based on Shannon entropy. The applied technique may offer new approaches to better understand nonlinear brain activity. Copyright Â© 2016 Elsevier B.V. All rights reserved.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 9. Entropy à la Boltzmann. Jayanta K Bhattacharjee. General Article Volume 6 Issue 9 September 2001 pp 19-34. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/006/09/0019-0034 ...
DEFF Research Database (Denmark)
Hansen, Britt Rosendahl; Kuhn, Luise Theil; Bahl, Christian Robert Haffenden
2010-01-01
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...
Indian Academy of Sciences (India)
Consider the integral. taken over a reversible transformation. We shall call this function the entropy of state A.” 'Thermodynamics' by Enrico Fermi. “Let Γ be the volume of the region of motion of the states, and. This is the basic assumption of ...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 9. Entropy in Biology. Jayant B Udgaonkar. General Article Volume 6 Issue 9 September 2001 pp 61-66. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/006/09/0061-0066. Author Affiliations.
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
Primordial fluctuations from nonlinear couplings
International Nuclear Information System (INIS)
Calzetta, E.A.; Gonorazky, S.
1997-01-01
We study the spectrum of primordial fluctuations in theories where the inflaton field is nonlinearly coupled to massless fields and/or to itself. Conformally invariant theories generically predict a scale-invariant spectrum. Scales entering the theory through infrared divergences cause logarithmic corrections to the spectrum, tilting it towards the blue. We discuss in some detail whether these fluctuations are quantum or classical in nature. copyright 1997 The American Physical Society
Exact Probability Distribution versus Entropy
Directory of Open Access Journals (Sweden)
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.
A Deterministic Entropy Based on the Instantaneous Phase Space Volume
Diebner, Hans H.; Rössler, Otto E.
1998-02-01
A deterministic entropic measure is derived for the time evolution of Newtonian N-particle systems based on the volume of the instantaneously occupied phase space (IOPS). This measure is found as a natural extension of Boltzmann's entropy. The instantaneous arrangement of the particles is exploited in the form of spatial correlations. The new entropy is a bridge between the time-dependent Boltzmann entropy, formulated on the basis of densities in the one-particle phase space, and the static Gibbs entropy which uses densities in the full phase space. We apply the new concept in a molecular dynamics simulation (MDS) using an exactly time reversible "discrete Newtonian equation of motion" recently derived from the fundamental principle of least action in discretized space-time. The simulation therefore is consistent with micro-time-reversibility. Entropy becomes an exact momentary observable in both time directions in fulfillment of a dream of Boltzmann.
Entropy, neutro-entropy and anti-entropy for neutrosophic information
Patrascu, Vasile
2017-01-01
This approach presents a multi-valued representation of the neutrosophic information. It highlights the link between the bifuzzy information and neutrosophic one. The constructed deca-valued structure shows the neutrosophic information complexity. This deca-valued structure led to construction of two new concepts for the neutrosophic information: neutro-entropy and anti-entropy. These two concepts are added to the two existing: entropy and non-entropy. Thus, we obtained the following triad: e...
Entropy and information causality in general probabilistic theories
International Nuclear Information System (INIS)
Barnum, Howard; Leifer, Matthew; Spekkens, Robert; Barrett, Jonathan; Clark, Lisa Orloff; Stepanik, Nicholas; Wilce, Alex; Wilke, Robin
2010-01-01
We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality (IC) recently proposed by Pawlowski et al (2009 arXiv:0905.2292). We consider two entropic quantities, which we term measurement and mixing entropy. In the context of classical and quantum theory, these coincide, being given by the Shannon and von Neumann entropies, respectively; in general, however, they are very different. In particular, while measurement entropy is easily seen to be concave, mixing entropy need not be. In fact, as we show, mixing entropy is not concave whenever the state space is a non-simplicial polytope. Thus, the condition that measurement and mixing entropies coincide is a strong constraint on possible theories. We call theories with this property monoentropic. Measurement entropy is subadditive, but not in general strongly subadditive. Equivalently, if we define the mutual information between two systems A and B by the usual formula I(A: B)=H(A)+H(B)-H(AB), where H denotes the measurement entropy and AB is a non-signaling composite of A and B, then it can happen that I(A:BC)< I(A:B). This is relevant to IC in the sense of Pawlowski et al: we show that any monoentropic non-signaling theory in which measurement entropy is strongly subadditive, and also satisfies a version of the Holevo bound, is informationally causal, and on the other hand we observe that Popescu-Rohrlich boxes, which violate IC, also violate strong subadditivity. We also explore the interplay between measurement and mixing entropy and various natural conditions on theories that arise in quantum axiomatics.
Entropy, neutro-entropy and anti-entropy for neutrosophic information
Vasile Patrascu
2017-01-01
This article shows a deca-valued representation of neutrosophic information in which are defined the following features: truth, falsity, weak truth, weak falsity, ignorance, contradiction, saturation, neutrality, ambiguity and hesitation. Using these features, there are constructed computing formulas for entropy, neutro-entropy and anti-entropy.
Entropy Measures vs. Kolmogorov Complexity
Directory of Open Access Journals (Sweden)
Luís Antunes
2011-03-01
Full Text Available Kolmogorov complexity and Shannon entropy are conceptually different measures. However, for any recursive probability distribution, the expected value of Kolmogorov complexity equals its Shannon entropy, up to a constant. We study if a similar relationship holds for R´enyi and Tsallis entropies of order α, showing that it only holds for α = 1. Regarding a time-bounded analogue relationship, we show that, for some distributions we have a similar result. We prove that, for universal time-bounded distribution mt(x, Tsallis and Rényi entropies converge if and only if α is greater than 1. We also establish the uniform continuity of these entropies.
Information Distances versus Entropy Metric
Directory of Open Access Journals (Sweden)
Bo Hu
2017-06-01
Full Text Available Information distance has become an important tool in a wide variety of applications. Various types of information distance have been made over the years. These information distance measures are different from entropy metric, as the former is based on Kolmogorov complexity and the latter on Shannon entropy. However, for any computable probability distributions, up to a constant, the expected value of Kolmogorov complexity equals the Shannon entropy. We study the similar relationship between entropy and information distance. We also study the relationship between entropy and the normalized versions of information distances.
Maximizing entropy over Markov processes
DEFF Research Database (Denmark)
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...
Maximizing Entropy over Markov Processes
DEFF Research Database (Denmark)
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...
Energy Technology Data Exchange (ETDEWEB)
Weinberg, A.M.
1982-10-01
Utopians who use entropy to warn of a vast deterioration of energy and mineral resources seek a self-fulfilling prophesy when they work to deny society access to new energy sources, particularly nuclear power. While theoretically correct, entropy is not the relevant factor for the rest of this century. The more extreme entropists call for a return to an eotechnic society based on decentralized, renewable energy technologies, which rests on the assumptions of a loss in Gibbs Free Energy, a mineral depletion that will lead to OPEC-like manipulation, and a current technology that is destroying the environment. The author challenges these assumptions and calls for an exorcism of public fears over reactor accidents. He foresees a resurgence in public confidence in nuclear power by 1990 that will resolve Western dependence on foreign oil. (DCK)
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...
Directory of Open Access Journals (Sweden)
Hou Hucan
2017-01-01
Full Text Available Inspired by wide application of the second law of thermodynamics to flow and heat transfer devices, local entropy production analysis method was creatively introduced into energy assessment system of centrifugal water pump. Based on Reynolds stress turbulent model and energy equation model, the steady numerical simulation of the whole flow passage of one IS centrifugal pump was carried out. The local entropy production terms were calculated by user defined functions, mainly including wall entropy production, turbulent entropy production, and viscous entropy production. The numerical results indicated that the irreversible energy loss calculated by the local entropy production method agreed well with that calculated by the traditional method but with some deviations which were probably caused by high rotatability and high curvature of impeller and volute. The wall entropy production and turbulent entropy production took up large part of the whole entropy production about 48.61% and 47.91%, respectively, which indicated that wall friction and turbulent fluctuation were the major factors in affecting irreversible energy loss. Meanwhile, the entropy production rate distribution was discussed and compared with turbulent kinetic energy dissipation rate distribution, it showed that turbulent entropy production rate increased sharply at the near wall regions and both distributed more uniformly. The blade region in leading edge near suction side, trailing edge and volute tongue were the main regions to generate irreversible exergy loss. This research broadens a completely new view in evaluating energy loss and further optimizes pump using entropy production minimization.
Entropy region and convolution
Czech Academy of Sciences Publication Activity Database
Matúš, František; Csirmaz, L.
2016-01-01
Roč. 62, č. 11 (2016), s. 6007-6018 ISSN 0018-9448 R&D Projects: GA ČR GA13-20012S Institutional support: RVO:67985556 Keywords : entropy region * information-theoretic inequality * polymatroid Subject RIV: BD - Theory of Information Impact factor: 2.679, year: 2016 http://library.utia.cas.cz/separaty/2016/MTR/matus-0465564.pdf
Equipartition of entropy production
International Nuclear Information System (INIS)
Tondeur, D.
1990-01-01
This paper deals with the optimal design or operation of heat and mass transfer processes and develops the following conjecture: for a given duty, the best configuration of the process is that in which the entropy production rate is most uniformly distributed. This principle is first analyzed in detail on the simple example of tubular heat exchangers, and within the framework of linear irreversible thermodynamics. A main result is established, which states that the total entropy production is minimal when the local production is uniformly distributed (equipartition). Corollaries then result, which relate the entropy production and the variance of its distribution to economic factors such as the duty, the exchange area, the fluid flow-rates, and the temperature changes. The equipartition principle is then extended to multiple independent variables (time and space), multicomponent transfer, and non-linear but concave flux vs force relationship. Chemical Engineering examples are discussed, where the equipartition property has been applied implicitly or explicitly: design of distillation plates, cyclic distillation, optimal state of feed, and flow-sheets in chromatographic separations. Finally, a generalization of the equipartition principle is proposed, for systems with a distributed design variable (such as the size of the various elements of a system). The optimal distribution of investment is such that the investment in each element (properly amortized) is equal to the cost of irreversible energy degradation in this element. This is equivalent to saying that the ratio of these two quantities is uniformly distributed over the system, and reduces to equipartition of entropy production when the cost factors are constant over the whole system
International Nuclear Information System (INIS)
Casati, G.; Chirikov, B.V.
1996-01-01
Various fluctuations in quantum systems with discrete spectrum are discussed, including recent unpublished results. Open questions and unexplained peculiarities of quantum fluctuations are formulated [ru
Fluctuations in Cerebral Hemodynamics
National Research Council Canada - National Science Library
Latka, Miroslaw
2003-01-01
We demonstrate that the scaling properties of intracranial pressure (ICP) fluctuations and fluctuations of blood flow velocity in middle cerebral arteries are characterized by two scaling exponents...
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...
Directory of Open Access Journals (Sweden)
Bernard S. Kay
2015-12-01
Full Text Available We give a review, in the style of an essay, of the author’s 1998 matter-gravity entanglement hypothesis which, unlike the standard approach to entropy based on coarse-graining, offers a definition for the entropy of a closed system as a real and objective quantity. We explain how this approach offers an explanation for the Second Law of Thermodynamics in general and a non-paradoxical understanding of information loss during black hole formation and evaporation in particular. It also involves a radically different from usual description of black hole equilibrium states in which the total state of a black hole in a box together with its atmosphere is a pure state—entangled in just such a way that the reduced state of the black hole and of its atmosphere are each separately approximately thermal. We also briefly recall some recent work of the author which involves a reworking of the string-theory understanding of black hole entropy consistent with this alternative description of black hole equilibrium states and point out that this is free from some unsatisfactory features of the usual string theory understanding. We also recall the author’s recent arguments based on this alternative description which suggest that the Anti de Sitter space (AdS/conformal field theory (CFT correspondence is a bijection between the boundary CFT and just the matter degrees of freedom of the bulk theory.
Critical study on conventional concept of entropy
International Nuclear Information System (INIS)
Afridi, M.K.; Nizami, S.
2006-01-01
The concept of increase in entropy or disorder as a result of all natural processes has been critically reviewed on the basis of experimental facts and ongoing phenomena on our Globe. Similarly, order-disorder statements have also been judged under new and fresh look. In fact, these are not absolute but depend upon defining specific purpose and considering that whether that purpose is being served or not. The new concept has been elaborated by considering natural biological processes, spontaneous mixing of four different gases, distribution of four points in space and assembling of a packaged electronic gadget. Actually, this order-disorder dilemma is the result of not defining the specific purpose of a process which leads to so-called concept that disorder is increasing day by day in our universe. The traditional concept of entropy has been finally tested under heat exchange and probability considerations, which also yield no information to discern it as a measure of disorder. Consequently, increase of entropy translating into increase of disorder could not be applied to all natural processes especially the natural biological systems. (author)
Quantifying 'causality' in complex systems: understanding transfer entropy.
Directory of Open Access Journals (Sweden)
Fatimah Abdul Razak
Full Text Available 'Causal' direction is of great importance when dealing with complex systems. Often big volumes of data in the form of time series are available and it is important to develop methods that can inform about possible causal connections between the different observables. Here we investigate the ability of the Transfer Entropy measure to identify causal relations embedded in emergent coherent correlations. We do this by firstly applying Transfer Entropy to an amended Ising model. In addition we use a simple Random Transition model to test the reliability of Transfer Entropy as a measure of 'causal' direction in the presence of stochastic fluctuations. In particular we systematically study the effect of the finite size of data sets.
Fast Slip Velocity in a High-Entropy Alloy
Rizzardi, Q.; Sparks, G.; Maaß, R.
2018-04-01
Due to fluctuations in nearest-neighbor distances and chemistry within the unit cell, high-entropy alloys are believed to have a much higher resistance to dislocation motion than pure crystals. Here, we investigate the coarse-grained dynamics of a number of dislocations being active during a slip event. We found that the time-resolved dynamics of slip is practically identical in Au and an Al0.3CoCrFeNi high-entropy alloy, but much faster than in Nb. Differences between the FCC-crystals are seen in the spatiotemporal velocity profile, with faster acceleration and slower velocity relaxation in the high-entropy alloy. Assessing distributions that characterize the intermittently evolving plastic flow reveals material-dependent scaling exponents for size, duration, and velocity-size distributions. The results are discussed in view of the underlying dislocation mobility.
Quantifying ‘Causality’ in Complex Systems: Understanding Transfer Entropy
Abdul Razak, Fatimah; Jensen, Henrik Jeldtoft
2014-01-01
‘Causal’ direction is of great importance when dealing with complex systems. Often big volumes of data in the form of time series are available and it is important to develop methods that can inform about possible causal connections between the different observables. Here we investigate the ability of the Transfer Entropy measure to identify causal relations embedded in emergent coherent correlations. We do this by firstly applying Transfer Entropy to an amended Ising model. In addition we use a simple Random Transition model to test the reliability of Transfer Entropy as a measure of ‘causal’ direction in the presence of stochastic fluctuations. In particular we systematically study the effect of the finite size of data sets. PMID:24955766
Preimage entropy dimension of topological dynamical systems
Liu, Lei; Zhou, Xiaomin; Zhou, Xiaoyao
2014-01-01
We propose a new definition of preimage entropy dimension for continuous maps on compact metric spaces, investigate fundamental properties of the preimage entropy dimension, and compare the preimage entropy dimension with the topological entropy dimension. The defined preimage entropy dimension holds various basic properties of topological entropy dimension, for example, the preimage entropy dimension of a subsystem is bounded by that of the original system and topologically conjugated system...
Quantum Dynamical Entropies and Gács Algorithmic Entropy
Directory of Open Access Journals (Sweden)
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.
Entanglement entropy and differential entropy for massive flavors
International Nuclear Information System (INIS)
Jones, Peter A.R.; Taylor, Marika
2015-01-01
In this paper we compute the holographic entanglement entropy for massive flavors in the D3-D7 system, for arbitrary mass and various entangling region geometries. We show that the universal terms in the entanglement entropy exactly match those computed in the dual theory using conformal perturbation theory. We derive holographically the universal terms in the entanglement entropy for a CFT perturbed by a relevant operator, up to second order in the coupling; our results are valid for any entangling region geometry. We present a new method for computing the entanglement entropy of any top-down brane probe system using Kaluza-Klein holography and illustrate our results with massive flavors at finite density. Finally we discuss the differential entropy for brane probe systems, emphasising that the differential entropy captures only the effective lower-dimensional Einstein metric rather than the ten-dimensional geometry.
Entanglement entropy and differential entropy for massive flavors
Energy Technology Data Exchange (ETDEWEB)
Jones, Peter A.R. [Physics and Astronomy and STAG Research Centre, University of Southampton, Highfield, Southampton, SO17 1BJ (United Kingdom); Taylor, Marika [Mathematical Sciences and STAG Research Centre, University of Southampton, Highfield, Southampton, SO17 1BJ (United Kingdom)
2015-08-04
In this paper we compute the holographic entanglement entropy for massive flavors in the D3-D7 system, for arbitrary mass and various entangling region geometries. We show that the universal terms in the entanglement entropy exactly match those computed in the dual theory using conformal perturbation theory. We derive holographically the universal terms in the entanglement entropy for a CFT perturbed by a relevant operator, up to second order in the coupling; our results are valid for any entangling region geometry. We present a new method for computing the entanglement entropy of any top-down brane probe system using Kaluza-Klein holography and illustrate our results with massive flavors at finite density. Finally we discuss the differential entropy for brane probe systems, emphasising that the differential entropy captures only the effective lower-dimensional Einstein metric rather than the ten-dimensional geometry.
Nonequilibrium quantum fluctuations of work.
Allahverdyan, A E
2014-09-01
The concept of work is basic for statistical thermodynamics. To gain a fuller understanding of work and its (quantum) features, it needs to be represented as an average of a fluctuating quantity. Here I focus on the work done between two moments of time for a thermally isolated quantum system driven by a time-dependent Hamiltonian. I formulate two natural conditions needed for the fluctuating work to be physically meaningful for a system that starts its evolution from a nonequilibrium state. The existing definitions do not satisfy these conditions due to issues that are traced back to noncommutativity. I propose a definition of fluctuating work that is free of previous drawbacks and that applies for a wide class of nonequilibrium initial states. It allows the deduction of a generalized work-fluctuation theorem that applies for an arbitrary (out-of-equilibrium) initial state.
Quantum correction to the entropy of noncommutative BTZ black hole
Anacleto, M. A.; Brito, F. A.; Cavalcanti, A. G.; Passos, E.; Spinelly, J.
2018-02-01
In this paper we consider the generalized uncertainty principle (GUP) in the tunneling formalism via Hamilton-Jacobi method to determine the quantum-corrected Hawking temperature and entropy for noncommutative BTZ black hole. In our results we obtain several types of corrections including the expected logarithmic correction to the area entropy associated with the noncommutative BTZ black holes. We also show that the area entropy product of the noncommutative BTZ black holes is dependent on mass and by analyzing the nature of the specific heat capacity we have observed that the noncommutative BTZ black hole is stable at some range of parameters.
On Using Entropy for Enhancing Handwriting Preprocessing
Directory of Open Access Journals (Sweden)
Bernhard Peischl
2012-11-01
Full Text Available Handwriting is an important modality for Human-Computer Interaction. For medical professionals, handwriting is (still the preferred natural method of documentation. Handwriting recognition has long been a primary research area in Computer Science. With the tremendous ubiquity of smartphones, along with the renaissance of the stylus, handwriting recognition has become a new impetus. However, recognition rates are still not 100% perfect, and researchers still are constantly improving handwriting algorithms. In this paper we evaluate the performance of entropy based slant- and skew-correction, and compare the results to other methods. We selected 3700 words of 23 writers out of the Unipen-ICROW-03 benchmark set, which we annotated with their associated error angles by hand. Our results show that the entropy-based slant correction method outperforms a window based approach with an average precision of 6:02 for the entropy-based method, compared with the 7:85 for the alternative. On the other hand, the entropy-based skew correction yields a lower average precision of 2:86, compared with the average precision of 2:13 for the alternative LSM based approach.
The Entropy-Based Quantum Metric
Directory of Open Access Journals (Sweden)
Roger Balian
2014-07-01
Full Text Available The von Neumann entropy S( D ^ generates in the space of quantum density matrices D ^ the Riemannian metric ds2 = −d2S( D ^ , which is physically founded and which characterises the amount of quantum information lost by mixing D ^ and D ^ + d D ^ . A rich geometric structure is thereby implemented in quantum mechanics. It includes a canonical mapping between the spaces of states and of observables, which involves the Legendre transform of S( D ^ . The Kubo scalar product is recovered within the space of observables. Applications are given to equilibrium and non equilibrium quantum statistical mechanics. There the formalism is specialised to the relevant space of observables and to the associated reduced states issued from the maximum entropy criterion, which result from the exact states through an orthogonal projection. Von Neumann’s entropy specialises into a relevant entropy. Comparison is made with other metrics. The Riemannian properties of the metric ds2 = −d2S( D ^ are derived. The curvature arises from the non-Abelian nature of quantum mechanics; its general expression and its explicit form for q-bits are given, as well as geodesics.
Entropy and Recurrence Measures of a Financial Dynamic System by an Interacting Voter System
Directory of Open Access Journals (Sweden)
Hong-Li Niu
2015-04-01
Full Text Available A financial time series agent-based model is reproduced and investigated by the statistical physics system, the finite-range interacting voter system. The voter system originally describes the collective behavior of voters who constantly update their positions on a particular topic, which is a continuous-time Markov process. In the proposed model, the fluctuations of stock price changes are attributed to the market information interaction amongst the traders and certain similarities of investors’ behaviors. Further, the complexity of return series of the financial model is studied in comparison with two real stock indexes, the Shanghai Stock Exchange Composite Index and the Hang Seng Index, by composite multiscale entropy analysis and recurrence analysis. The empirical research shows that the simulation data for the proposed model could grasp some natural features of actual markets to some extent.
Fluctuation theorem for the effusion of an ideal gas.
Cleuren, B; Van den Broeck, C; Kawai, R
2006-08-01
The probability distribution of the entropy production for the effusion of an ideal gas between two compartments is calculated explicitly. The fluctuation theorem is verified. The analytic results are in good agreement with numerical data from hard disk molecular dynamics simulations.
Energy Technology Data Exchange (ETDEWEB)
Klein, Kristopher G.; Howes, Gregory G. [Department of Physics and Astronomy, University of Iowa, Iowa City, IA 52242 (United States); TenBarge, Jason M. [IREAP, University of Maryland, College Park, MD 20742 (United States); Podesta, John J., E-mail: kristopher-klein@uiowa.edu [Center for Space Plasma Physics, Space Science Institute, Boulder, CO 80301 (United States)
2014-04-20
Motivated by recent observations of distinct parallel and perpendicular signatures in magnetic helicity measurements segregated by wave period and angle between the local magnetic field and the solar wind velocity, this paper undertakes a comparison of three intervals of Ulysses data with synthetic time series generated from a physically motivated turbulence model. From these comparisons, it is hypothesized that the observed signatures result from a perpendicular cascade of Alfvénic fluctuations and a local, non-turbulent population of ion-cyclotron or whistler waves generated by temperature anisotropy instabilities. By constraining the model's free parameters through comparison to in situ data, it is found that, on average, ∼95% of the power near dissipative scales is contained in a perpendicular Alfvénic cascade and that the parallel fluctuations are propagating nearly unidirectionally. The effects of aliasing on magnetic helicity measurements are considered and shown to be significant near the Nyquist frequency.
Entropy: From Thermodynamics to Hydrology
Directory of Open Access Journals (Sweden)
Demetris Koutsoyiannis
2014-02-01
Full Text Available Some known results from statistical thermophysics as well as from hydrology are revisited from a different perspective trying: (a to unify the notion of entropy in thermodynamic and statistical/stochastic approaches of complex hydrological systems and (b to show the power of entropy and the principle of maximum entropy in inference, both deductive and inductive. The capability for deductive reasoning is illustrated by deriving the law of phase change transition of water (Clausius-Clapeyron from scratch by maximizing entropy in a formal probabilistic frame. However, such deductive reasoning cannot work in more complex hydrological systems with diverse elements, yet the entropy maximization framework can help in inductive inference, necessarily based on data. Several examples of this type are provided in an attempt to link statistical thermophysics with hydrology with a unifying view of entropy.
Inchin, P.; Zettergren, M. D.; Snively, J. B.; Komjathy, A.; Verkhoglyadova, O. P.
2017-12-01
Recent studies have reported magnetic field fluctuations following intense seismic hazard events [e.g. Aoyama et al., EPS, 68, 2016; Toh et al., JGR, 116, 2011]. These perturbations can be associated with ionospheric dynamo phenomena driven by seismically generated acoustic and gravity waves (AGWs). AGW-related dynamo effects can be separated from other sources of magnetic fluctuations (e.g. piezo magnetic effects, magnetospheric forcing or Rayleigh surface waves) based on time delays from event onset (corresponding closely with travel times for AGWs from ground to the ionosphere) and spectral content measured concurrently in total electron content (TEC). Modeling studies aimed at understanding these magnetic field fluctuations have demonstrated the idea that AGWs propagating through the conducting ionosphere can induce current densities sufficient to produce observable magnetic signatures [Zettergren and Snively, JGR, 120, 2017]. Here, we investigate the features of seismic-related magnetic field fluctuations in data and their generation via the effects of seismically-forced AGWs on the ionosphere [Iyemori et al., EPS, 65, 2013; Hasbi et al., JASTP, 71, 2005]. Concurrent magnetic field and TEC data are analyzed for several events: the Chilean earthquakes of 2010 and 2015, Chile's Calbuco volcano eruption and the Sumatran earthquake on March 28, 2005. We investigate the qualitative features of the disturbances as well as quantitative spectral and timing analysis of the data. For Chilean earthquakes, TEC and ground-based magnetometer data reveal fluctuations in magnetic field exhibiting 4-5 mHz frequencies, the same as in TEC. For the Calbuco volcano eruption and Sumatran earthquake both TEC and magnetic field perturbations exhibit frequencies of 4-5 mHz. The results are consistent with previous reports [Aoyama et al., EPS, 68, 2016, Hasbi et al., JASTP, 71, 2005, Iyemori et al., EPS, 65, 2013]. These observations are further interpreted through detailed numerical
Entropy and transverse section reconstruction
International Nuclear Information System (INIS)
Gullberg, G.T.
1976-01-01
A new approach to the reconstruction of a transverse section using projection data from multiple views incorporates the concept of maximum entropy. The principle of maximizing information entropy embodies the assurance of minimizing bias or prejudice in the reconstruction. Using maximum entropy is a necessary condition for the reconstructed image. This entropy criterion is most appropriate for 3-D reconstruction of objects from projections where the system is underdetermined or the data are limited statistically. This is the case in nuclear medicine time limitations in patient studies do not yield sufficient projections
Directory of Open Access Journals (Sweden)
Beretta, Gian Paolo
2008-02-01
complete and coherent resolution of the century-old dilemma on the meaning of entropy and the origin of irreversibility, including Onsager reciprocity relations and maximal-entropy-generation nonequilibrium dynamics, which we believe provides the microscopic foundations of heat, mass and momentum transfer theories, including all their implications such as Bejan's Constructal Theory of natural phenomena.
An alternative expression to the Sackur-Tetrode entropy formula for an ideal gas
Nagata, Shoichi
2018-03-01
An expression for the entropy of a monoatomic classical ideal gas is known as the Sackur-Tetrode equation. This pioneering investigation about 100 years ago incorporates quantum considerations. The purpose of this paper is to provide an alternative expression for the entropy in terms of the Heisenberg uncertainty relation. The analysis is made on the basis of fluctuation theory, for a canonical system in thermal equilibrium at temperature T. This new formula indicates manifestly that the entropy of macroscopic world is recognized as a measure of uncertainty in microscopic quantum world. The entropy in the Sackur-Tetrode equation can be re-interpreted from a different perspective viewpoint. The emphasis is on the connection between the entropy and the uncertainty relation in quantum consideration.
Katona, Gyula O H; Tardos, Gábor
2007-01-01
The present volume is a collection of survey papers in the fields of entropy, search and complexity. They summarize the latest developments in their respective areas. More than half of the papers belong to search theory which lies on the borderline of mathematics and computer science, information theory and combinatorics, respectively. Search theory has variegated applications, among others in bioinformatics. Some of these papers also have links to linear statistics and communicational complexity. Further works survey the fundamentals of information theory and quantum source coding. The volume is recommended to experienced researchers as well as young scientists and students both in mathematics and computer science
Steinberg, Peter
2008-06-01
Who is the blog written by? Peter Steinberg is a nuclear physicist at the Brookhaven National Laboratory in New York, US. He is acting project manager of the PHOBOS experiment, which used Brookhaven's Relativistic Heavy Ion Collider (RHIC) to search for unusual events produced during collisions between gold nuclei. He is also involved with the PHENIX experiment, which seeks to discover a new state of matter known as the quark-gluon plasma. In addition to his own blog Entropy Bound, Steinberg is currently blogging on a website that was set up last year to publicize the involvement of US scientists with the Large Hadron Collider (LHC) at CERN.
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.
Fluctuation theorem for Hamiltonian Systems: Le Chatelier's principle
Evans, Denis J.; Searles, Debra J.; Mittag, Emil
2001-05-01
For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.
Characterization of time series via Rényi complexity-entropy curves
Jauregui, M.; Zunino, L.; Lenzi, E. K.; Mendes, R. S.; Ribeiro, H. V.
2018-05-01
One of the most useful tools for distinguishing between chaotic and stochastic time series is the so-called complexity-entropy causality plane. This diagram involves two complexity measures: the Shannon entropy and the statistical complexity. Recently, this idea has been generalized by considering the Tsallis monoparametric generalization of the Shannon entropy, yielding complexity-entropy curves. These curves have proven to enhance the discrimination among different time series related to stochastic and chaotic processes of numerical and experimental nature. Here we further explore these complexity-entropy curves in the context of the Rényi entropy, which is another monoparametric generalization of the Shannon entropy. By combining the Rényi entropy with the proper generalization of the statistical complexity, we associate a parametric curve (the Rényi complexity-entropy curve) with a given time series. We explore this approach in a series of numerical and experimental applications, demonstrating the usefulness of this new technique for time series analysis. We show that the Rényi complexity-entropy curves enable the differentiation among time series of chaotic, stochastic, and periodic nature. In particular, time series of stochastic nature are associated with curves displaying positive curvature in a neighborhood of their initial points, whereas curves related to chaotic phenomena have a negative curvature; finally, periodic time series are represented by vertical straight lines.
Entanglement entropy and mutual information production rates in acoustic black holes.
Giovanazzi, Stefano
2011-01-07
A method to investigate acoustic Hawking radiation is proposed, where entanglement entropy and mutual information are measured from the fluctuations of the number of particles. The rate of entropy radiated per one-dimensional (1D) channel is given by S=κ/12, where κ is the sound acceleration on the sonic horizon. This entropy production is accompanied by a corresponding formation of mutual information to ensure the overall conservation of information. The predictions are confirmed using an ab initio analytical approach in transonic flows of 1D degenerate ideal Fermi fluids.
Hacisuleyman, Aysima; Erman, Burak
2017-01-01
It has recently been proposed by Gunasakaran et al. that allostery may be an intrinsic property of all proteins. Here, we develop a computational method that can determine and quantify allosteric activity in any given protein. Based on Schreiber's transfer entropy formulation, our approach leads to an information transfer landscape for the protein that shows the presence of entropy sinks and sources and explains how pairs of residues communicate with each other using entropy transfer. The model can identify the residues that drive the fluctuations of others. We apply the model to Ubiquitin, whose allosteric activity has not been emphasized until recently, and show that there are indeed systematic pathways of entropy and information transfer between residues that correlate well with the activities of the protein. We use 600 nanosecond molecular dynamics trajectories for Ubiquitin and its complex with human polymerase iota and evaluate entropy transfer between all pairs of residues of Ubiquitin and quantify the binding susceptibility changes upon complex formation. We explain the complex formation propensities of Ubiquitin in terms of entropy transfer. Important residues taking part in allosteric communication in Ubiquitin predicted by our approach are in agreement with results of NMR relaxation dispersion experiments. Finally, we show that time delayed correlation of fluctuations of two interacting residues possesses an intrinsic causality that tells which residue controls the interaction and which one is controlled. Our work shows that time delayed correlations, entropy transfer and causality are the required new concepts for explaining allosteric communication in proteins.
Renormalization group flow of entanglement entropy to thermal entropy
Kim, Ki-Seok; Park, Chanyong
2017-05-01
Utilizing the holographic technique, we investigate how the entanglement entropy evolves along the renormalization group flow. After introducing a new generalized temperature which satisfies the thermodynamicslike law even in the IR regime, we find that the renormalized entropy and the generalized temperature in the IR limit approach the thermal entropy and thermodynamic temperature of a real thermal system. This result implies that the microscopic quantum entanglement entropy in the IR region leads to the thermodynamic relation up to small quantum corrections caused by the quantum entanglement near the entangling surface. Intriguingly, this IR feature of the entanglement entropy universally happens regardless of the detail of the dual field theory and the shape of the entangling surface. We check this IR universality with a most general geometry called the hyperscaling violation geometry which is dual to a relativistic nonconformal field theory.
Entropic fluctuations in DNA sequences
Thanos, Dimitrios; Li, Wentian; Provata, Astero
2018-03-01
The Local Shannon Entropy (LSE) in blocks is used as a complexity measure to study the information fluctuations along DNA sequences. The LSE of a DNA block maps the local base arrangement information to a single numerical value. It is shown that despite this reduction of information, LSE allows to extract meaningful information related to the detection of repetitive sequences in whole chromosomes and is useful in finding evolutionary differences between organisms. More specifically, large regions of tandem repeats, such as centromeres, can be detected based on their low LSE fluctuations along the chromosome. Furthermore, an empirical investigation of the appropriate block sizes is provided and the relationship of LSE properties with the structure of the underlying repetitive units is revealed by using both computational and mathematical methods. Sequence similarity between the genomic DNA of closely related species also leads to similar LSE values at the orthologous regions. As an application, the LSE covariance function is used to measure the evolutionary distance between several primate genomes.
Directory of Open Access Journals (Sweden)
John Scales Avery
2012-04-01
Full Text Available In this essay, human society is regarded as a “superorganism”, analogous to colonies of social insects. The digestive system of the human superorganism is the global economy, which ingests both free energy and resources, and later excretes them in a degraded form. This process involves an increase in entropy. Early in the 20th century, both Frederick Soddy and Nicholas Georgescu-Roegen discussed the relationship between entropy and economics. Soddy called for an index system to regulate the money supply and a reform of the fractional reserve banking system, while Georgescu-Roegen pointed to the need for Ecological Economics, a steady-state economy, and population stabilization. As we reach the end of the fossil fuel era and as industrial growth falters, massive unemployment can only be avoided by responsible governmental action. The necessary steps include shifting labor to projects needed for a sustainable economy, dividing the available work fairly among those seeking employment, and reforming the practices of the financial sector.
On the Interplay between Entropy and Robustness of Gene Regulatory Networks
Directory of Open Access Journals (Sweden)
Bor-Sen Chen
2010-05-01
Full Text Available The interplay between entropy and robustness of gene network is a core mechanism of systems biology. The entropy is a measure of randomness or disorder of a physical system due to random parameter fluctuation and environmental noises in gene regulatory networks. The robustness of a gene regulatory network, which can be measured as the ability to tolerate the random parameter fluctuation and to attenuate the effect of environmental noise, will be discussed from the robust H∞ stabilization and filtering perspective. In this review, we will also discuss their balancing roles in evolution and potential applications in systems and synthetic biology.
Williams, Ian; Turci, Francesco; Hallett, James E.; Crowther, Peter; Cammarota, Chiara; Biroli, Giulio; Royall, C. Patrick
2018-03-01
A quasi two-dimensional colloidal suspension is studied under the influence of immobilisation (pinning) of a random fraction of its particles. We introduce a novel experimental method to perform random pinning and, with the support of numerical simulation, we find that increasing the pinning concentration smoothly arrests the system, with a cross-over from a regime of high mobility and high entropy to a regime of low mobility and low entropy. At the local level, we study fluctuations in area fraction and concentration of pins and map them to entropic structural signatures and local mobility, obtaining a measure for the local entropic fluctuations of the experimental system.
CFT and Logarithmic Corrections to the Black Hole Entropy Product Formula
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Parthapratim Pradhan
2017-01-01
Full Text Available We examine the logarithmic corrections to the black hole (BH entropy product formula of outer horizon and inner horizon by taking into account the effects of statistical quantum fluctuations around the thermal equilibrium and via conformal field theory (CFT. We argue that, in logarithmic corrections to the BH entropy product formula when calculated using CFT and taking into account the effects of quantum fluctuations around the thermal equilibrium, the formula should not be universal and it also should not be quantized. These results have been explicitly checked by giving several examples.
Analysis of Meniscus Fluctuation in a Continuous Casting Slab Mold
Zhang, Kaitian; Liu, Jianhua; Cui, Heng; Xiao, Chao
2018-03-01
A water model of slab mold was established to analyze the microscopic and macroscopic fluctuation of meniscus. The fast Fourier transform and wavelet entropy were adopted to analyze the wave amplitude, frequency, and components of fluctuation. The flow patterns under the meniscus were measured by using particle image velocimetry measurement and then the mechanisms of meniscus fluctuation were discussed. The results reflected that wavelet entropy had multi-scale and statistical properties, and it was suitable for the study of meniscus fluctuation details both in time and frequency domain. The basic wave, frequency of which exceeding 1 Hz in the condition of no mold oscillation, was demonstrated in this work. In fact, three basic waves were found: long-wave with low frequency, middle-wave with middle frequency, and short-wave with high frequency. In addition, the upper roll flow in mold had significant effect on meniscus fluctuation. When the position of flow impinged was far from the meniscus, long-wave dominated the fluctuation and the stability of meniscus was enhanced. However, when the velocity of flow was increased, the short-wave dominated the meniscus fluctuation and the meniscus stability was decreased.
Goswami, Gurupada; Mukherjee, Biswajit; Bag, Bidhan Chandra
2005-06-01
We have studied the relaxation of non-Markovian and thermodynamically closed system both in the absence and presence of non-equilibrium constraint in terms of the information entropy flux and entropy production based on the Fokker-Planck and the entropy balance equations. Our calculation shows how the relaxation time depends on noise correlation time. It also considers how the non-equilibrium constraint is affected by system parameters such as noise correlation time, strength of dissipation and frequency of dynamical system. The interplay of non-equilibrium constraint, frictional memory kernel, noise correlation time and frequency of dynamical system reveals the extremum nature of the entropy production.
International Nuclear Information System (INIS)
Goswami, Gurupada; Mukherjee, Biswajit; Bag, Bidhan Chandra
2005-01-01
We have studied the relaxation of non-Markovian and thermodynamically closed system both in the absence and presence of non-equilibrium constraint in terms of the information entropy flux and entropy production based on the Fokker-Planck and the entropy balance equations. Our calculation shows how the relaxation time depends on noise correlation time. It also considers how the non-equilibrium constraint is affected by system parameters such as noise correlation time, strength of dissipation and frequency of dynamical system. The interplay of non-equilibrium constraint, frictional memory kernel, noise correlation time and frequency of dynamical system reveals the extremum nature of the entropy production
Van Assche, W.; Yáñez, R. J.; Dehesa, J. S.
1995-08-01
The information entropy of the harmonic oscillator potential V(x)=1/2λx2 in both position and momentum spaces can be expressed in terms of the so-called ``entropy of Hermite polynomials,'' i.e., the quantity Sn(H):= -∫-∞+∞H2n(x)log H2n(x) e-x2dx. These polynomials are instances of the polynomials orthogonal with respect to the Freud weights w(x)=exp(-||x||m), m≳0. Here, a very precise and general result of the entropy of Freud polynomials recently established by Aptekarev et al. [J. Math. Phys. 35, 4423-4428 (1994)], specialized to the Hermite kernel (case m=2), leads to an important refined asymptotic expression for the information entropies of very excited states (i.e., for large n) in both position and momentum spaces, to be denoted by Sρ and Sγ, respectively. Briefly, it is shown that, for large values of n, Sρ+1/2logλ≂log(π√2n/e)+o(1) and Sγ-1/2log λ≂log(π√2n/e)+o(1), so that Sρ+Sγ≂log(2π2n/e2)+o(1) in agreement with the generalized indetermination relation of Byalinicki-Birula and Mycielski [Commun. Math. Phys. 44, 129-132 (1975)]. Finally, the rate of convergence of these two information entropies is numerically analyzed. In addition, using a Rakhmanov result, we describe a totally new proof of the leading term of the entropy of Freud polynomials which, naturally, is just a weak version of the aforementioned general result.
Thermal Expansion Anomaly Regulated by Entropy
Liu, Zi-Kui; Wang, Yi; Shang, Shunli
2014-11-01
Thermal expansion, defined as the temperature dependence of volume under constant pressure, is a common phenomenon in nature and originates from anharmonic lattice dynamics. However, it has been poorly understood how thermal expansion can show anomalies such as colossal positive, zero, or negative thermal expansion (CPTE, ZTE, or NTE), especially in quantitative terms. Here we show that changes in configurational entropy due to metastable micro(scopic)states can lead to quantitative prediction of these anomalies. We integrate the Maxwell relation, statistic mechanics, and first-principles calculations to demonstrate that when the entropy is increased by pressure, NTE occurs such as in Invar alloy (Fe3Pt, for example), silicon, ice, and water, and when the entropy is decreased dramatically by pressure, CPTE is expected such as in anti-Invar cerium, ice and water. Our findings provide a theoretic framework to understand and predict a broad range of anomalies in nature in addition to thermal expansion, which may include gigantic electrocaloric and electromechanical responses, anomalously reduced thermal conductivity, and spin distributions.
Black brane entropy and hydrodynamics
Booth, I.; Heller, M.P.; Spaliński, M.
2010-01-01
A generalization of entropy to near-equilibrium phenomena is provided by the notion of a hydrodynamic entropy current. Recent advances in holography have lead to the formulation of fluid-gravity duality, a remarkable connection between the hydrodynamics of certain strongly coupled media and dynamics
Combining Experiments and Simulations Using the Maximum Entropy Principle
DEFF Research Database (Denmark)
Boomsma, Wouter; Ferkinghoff-Borg, Jesper; Lindorff-Larsen, Kresten
2014-01-01
are not in quantitative agreement with experimental data. The principle of maximum entropy is a general procedure for constructing probability distributions in the light of new data, making it a natural tool in cases when an initial model provides results that are at odds with experiments. The number of maximum entropy...... in the context of a simple example, after which we proceed with a real-world application in the field of molecular simulations, where the maximum entropy procedure has recently provided new insight. Given the limited accuracy of force fields, macromolecular simulations sometimes produce results....... Three very recent papers have explored this problem using the maximum entropy approach, providing both new theoretical and practical insights to the problem. We highlight each of these contributions in turn and conclude with a discussion on remaining challenges....
Generalized entropy formalism and a new holographic dark energy model
Sayahian Jahromi, A.; Moosavi, S. A.; Moradpour, H.; Morais Graça, J. P.; Lobo, I. P.; Salako, I. G.; Jawad, A.
2018-05-01
Recently, the Rényi and Tsallis generalized entropies have extensively been used in order to study various cosmological and gravitational setups. Here, using a special type of generalized entropy, a generalization of both the Rényi and Tsallis entropy, together with holographic principle, we build a new model for holographic dark energy. Thereinafter, considering a flat FRW universe, filled by a pressureless component and the new obtained dark energy model, the evolution of cosmos has been investigated showing satisfactory results and behavior. In our model, the Hubble horizon plays the role of IR cutoff, and there is no mutual interaction between the cosmos components. Our results indicate that the generalized entropy formalism may open a new window to become more familiar with the nature of spacetime and its properties.
Pareto versus lognormal: a maximum entropy test.
Bee, Marco; Riccaboni, Massimo; Schiavo, Stefano
2011-08-01
It is commonly found that distributions that seem to be lognormal over a broad range change to a power-law (Pareto) distribution for the last few percentiles. The distributions of many physical, natural, and social events (earthquake size, species abundance, income and wealth, as well as file, city, and firm sizes) display this structure. We present a test for the occurrence of power-law tails in statistical distributions based on maximum entropy. This methodology allows one to identify the true data-generating processes even in the case when it is neither lognormal nor Pareto. The maximum entropy approach is then compared with other widely used methods and applied to different levels of aggregation of complex systems. Our results provide support for the theory that distributions with lognormal body and Pareto tail can be generated as mixtures of lognormally distributed units.
Entropy and the Direction of Natural Change
Indian Academy of Sciences (India)
the pages of Greek myth, the world doesn't quite work this way. More often than not, the more things change ... part of the world to faithfully recreate the conditions t.hat define the kinds of changes we're seeking to .... balloon and those of the room, the room accounting for most of the available energy. It doesn't matter at this ...
Entropy Budget for Hawking Evaporation
Directory of Open Access Journals (Sweden)
Ana Alonso-Serrano
2017-07-01
Full Text Available Blackbody radiation, emitted from a furnace and described by a Planck spectrum, contains (on average an entropy of 3 . 9 ± 2 . 5 bits per photon. Since normal physical burning is a unitary process, this amount of entropy is compensated by the same amount of “hidden information” in correlations between the photons. The importance of this result lies in the posterior extension of this argument to the Hawking radiation from black holes, demonstrating that the assumption of unitarity leads to a perfectly reasonable entropy/information budget for the evaporation process. In order to carry out this calculation, we adopt a variant of the “average subsystem” approach, but consider a tripartite pure system that includes the influence of the rest of the universe, and which allows “young” black holes to still have a non-zero entropy; which we identify with the standard Bekenstein entropy.
Entropy inequalities from reflection positivity
International Nuclear Information System (INIS)
Casini, H
2010-01-01
We investigate the question of whether the entropy and the Renyi entropies of the vacuum state reduced to a region of space can be represented in terms of correlators in quantum field theory. In this case, the positivity relations for the correlators are mapped into inequalities for the entropies. We write them using a real-time version of reflection positivity, which can be generalized to general quantum systems. Using this generalization we can prove an infinite sequence of inequalities which are obeyed by the Renyi entropies of integer index. There is one independent inequality involving any number of different subsystems. In quantum field theory the inequalities acquire a simple geometrical form and are consistent with the integer index Renyi entropies being given by vacuum expectation values of twisting operators in the Euclidean formulation. Several possible generalizations and specific examples are analyzed
Revisiting sample entropy analysis
Govindan, R. B.; Wilson, J. D.; Eswaran, H.; Lowery, C. L.; Preißl, H.
2007-03-01
We modify the definition of sample entropy (SaEn) by incorporating a time delay between the components of the block (from which the densities are estimated) and show that the modified method characterizes the complexity of the system better than the original version. We apply the modified SaEn to the standard deterministic systems and stochastic processes (uncorrelated and long range correlated (LRC) processes) and show that the underlying complexity of the system is better quantified by the modified method. We extend this analysis to the RR intervals of the normal and congestive heart failure (CHF) subjects (available via www.physionet.org) and show that there is a good degree of separation between the two groups.
Fluctuations in LC Oscillators
Directory of Open Access Journals (Sweden)
O. Ondracek
1994-03-01
Full Text Available An analysis of the phase and amplitude fluctuations in oscillators with simple resonant circuit is presented. Negative feedback is used to minimize effect of the inherent noise produced by bipolar transistor on fluctuation characteristics.
Entropy Bounds and Field Equations
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Alessandro Pesci
2015-08-01
Full Text Available For general metric theories of gravity, we compare the approach that describes/derives the field equations of gravity as a thermodynamic identity with the one which looks at them from entropy bounds. The comparison is made through the consideration of the matter entropy flux across (Rindler horizons, studied by making use of the notion of a limiting thermodynamic scale l* of matter, previously introduced in the context of entropy bounds. In doing this: (i a bound for the entropy of any lump of matter with a given energy-momentum tensor Tab is considered, in terms of a quantity, which is independent of the theory of gravity that we use; this quantity is the variation of the Clausius entropy of a suitable horizon when the element of matter crosses it; (ii by making use of the equations of motion of the theory, the same quantity is then expressed as the variation of Wald’s entropy of that horizon (and this leads to a generalized form of the generalized covariant entropy bound, applicable to general diffeomorphism-invariant theories of gravity; and (iii a notion of l* for horizons, as well as an expression for it, is given.
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.
Bubble Entropy: An Entropy Almost Free of Parameters.
Manis, George; Aktaruzzaman, Md; Sassi, Roberto
2017-11-01
Objective : A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new definition of entropy aiming to reduce the significance of this selection. Methods: We call the new definition Bubble Entropy . Bubble Entropy is based on permutation entropy, where the vectors in the embedding space are ranked. We use the bubble sort algorithm for the ordering procedure and count instead the number of swaps performed for each vector. Doing so, we create a more coarse-grained distribution and then compute the entropy of this distribution. Results: Experimental results with both real and synthetic HRV signals showed that bubble entropy presents remarkable stability and exhibits increased descriptive and discriminating power compared to all other definitions, including the most popular ones. Conclusion: The definition proposed is almost free of parameters. The most common ones are the scale factor r and the embedding dimension m . In our definition, the scale factor is totally eliminated and the importance of m is significantly reduced. The proposed method presents increased stability and discriminating power. Significance: After the extensive use of some entropy measures in physiological signals, typical values for their parameters have been suggested, or at least, widely used. However, the parameters are still there, application and dataset dependent, influencing the computed value and affecting the descriptive power. Reducing their significance or eliminating them alleviates the problem, decoupling the method from the data and the application, and eliminating subjective factors. Objective : A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new definition of entropy aiming to reduce the significance of this selection. Methods: We call the new definition Bubble Entropy . Bubble Entropy is based on permutation
The concept of entropy. Relation between action and entropy
Directory of Open Access Journals (Sweden)
J.-P.Badiali
2005-01-01
Full Text Available The Boltzmann expression for entropy represents the traditional link between thermodynamics and statistical mechanics. New theoretical developments like the Unruh effect or the black hole theory suggest a new definition of entropy. In this paper we consider the thermodynamics of black holes as seriously founded and we try to see what we can learn from it in the case of ordinary systems for which a pre-relativistic description is sufficient. We introduce a space-time model and a new definition of entropy considering the thermal equilibrium from a dynamic point of view. Then we show that for black hole and ordinary systems we have the same relation relating a change of entropy to a change of action.
Interval Entropy and Informative Distance
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Fakhroddin Misagh
2012-03-01
Full Text Available The Shannon interval entropy function as a useful dynamic measure of uncertainty for two sided truncated random variables has been proposed in the literature of reliability. In this paper, we show that interval entropy can uniquely determine the distribution function. Furthermore, we propose a measure of discrepancy between two lifetime distributions at the interval of time in base of Kullback-Leibler discrimination information. We study various properties of this measure, including its connection with residual and past measures of discrepancy and interval entropy, and we obtain its upper and lower bounds.
Directory of Open Access Journals (Sweden)
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
Detecting quantum critical points using bipartite fluctuations.
Rachel, Stephan; Laflorencie, Nicolas; Song, H Francis; Le Hur, Karyn
2012-03-16
We show that the concept of bipartite fluctuations F provides a very efficient tool to detect quantum phase transitions in strongly correlated systems. Using state-of-the-art numerical techniques complemented with analytical arguments, we investigate paradigmatic examples for both quantum spins and bosons. As compared to the von Neumann entanglement entropy, we observe that F allows us to find quantum critical points with much better accuracy in one dimension. We further demonstrate that F can be successfully applied to the detection of quantum criticality in higher dimensions with no prior knowledge of the universality class of the transition. Promising approaches to experimentally access fluctuations are discussed for quantum antiferromagnets and cold gases.
Stress-induced electric current fluctuations in rocks: a superstatistical model
Cartwright-Taylor, Alexis; Vallianatos, Filippos; Sammonds, Peter
2017-04-01
We recorded spontaneous electric current flow in non-piezoelectric Carrara marble samples during triaxial deformation. Mechanical data, ultrasonic velocities and acoustic emissions were acquired simultaneously with electric current to constrain the relationship between electric current flow, differential stress and damage. Under strain-controlled loading, spontaneous electric current signals (nA) were generated and sustained under all conditions tested. In dry samples, a detectable electric current arises only during dilatancy and the overall signal is correlated with the damage induced by microcracking. Our results show that fracture plays a key role in the generation of electric currents in deforming rocks (Cartwright-Taylor et al., in prep). We also analysed the high-frequency fluctuations of these electric current signals and found that they are not normally distributed - they exhibit power-law tails (Cartwright-Taylor et al., 2014). We modelled these distributions with q-Gaussian statistics, derived by maximising the Tsallis entropy. This definition of entropy is particularly applicable to systems which are strongly correlated and far from equilibrium. Good agreement, at all experimental conditions, between the distributions of electric current fluctuations and the q-Gaussian function with q-values far from one, illustrates the highly correlated, fractal nature of the electric source network within the samples and provides further evidence that the source of the electric signals is the developing fractal network of cracks. It has been shown (Beck, 2001) that q-Gaussian distributions can arise from the superposition of local relaxations in the presence of a slowly varying driving force, thus providing a dynamic reason for the appearance of Tsallis statistics in systems with a fluctuating energy dissipation rate. So, the probability distribution for a dynamic variable, u under some external slow forcing, β, can be obtained as a superposition of temporary local
Vibrational Effect on Entropy Generation in a Square Porous Cavity
Directory of Open Access Journals (Sweden)
Roydon Andrew Fraser
2003-12-01
Full Text Available Abstract: We investigate the nature of entropy generation for natural convection in a two-dimensional square section enclosure vibrating sinusoidally perpendicular to the applied temperature gradient in a zero-gravity field. The enclosure is assumed to fill with porous media. The Darcy momentum equation is used to model the porous media. The full governing differential equations are simplified with the Boussinesq approximation and solved by a finite volume method. Whereas the Prandtl number Pr is fixed to 1.0. Results are presented in terms of average Nusselt number (Nuav, entropy generation number (Nsav, Bejan number (Beav, and kinetic energy (KEav.
Vibrational Effect on Entropy Generation in a Square Porous Cavity
Mahmud, Shohel; Fraser, Roydon A.
2003-12-01
We investigate the nature of entropy generation for natural convection in a two-dimensional square section enclosure vibrating sinusoidally perpendicular to the applied temperature gradient in a zero-gravity field. The enclosure is assumed to fill with porous media. The Darcy momentum equation is used to model the porous media. The full governing differential equations are simplified with the Boussinesq approximation and solved by a finite volume method. Whereas the Prandtl number Pr is fixed to 1.0. Results are presented in terms of average Nusselt number (Nuav), entropy generation number (Nsav), Bejan number (Beav), and kinetic energy (KEav).
Characterization of early partial seizure onset: frequency, complexity and entropy.
Jouny, Christophe C; Bergey, Gregory K
2012-04-01
A clear classification of partial seizures onset features is not yet established. Complexity and entropy have been very widely used to describe dynamical systems, but a systematic evaluation of these measures to characterize partial seizures has never been performed. Eighteen different measures including power in frequency bands up to 300 Hz, Gabor atom density (GAD), Higuchi fractal dimension (HFD), Lempel-Ziv complexity, Shannon entropy, sample entropy, and permutation entropy, were selected to test sensitivity to partial seizure onset. Intracranial recordings from 45 patients with mesial temporal, neocortical temporal and neocortical extratemporal seizure foci were included (331 partial seizures). GAD, Lempel-Ziv complexity, HFD, high frequency activity, and sample entropy were the most reliable measures to assess early seizure onset. Increases in complexity and occurrence of high-frequency components appear to be commonly associated with early stages of partial seizure evolution from all regions. The type of measure (frequency-based, complexity or entropy) does not predict the efficiency of the method to detect seizure onset. Differences between measures such as GAD and HFD highlight the multimodal nature of partial seizure onsets. Improved methods for early seizure detection may be achieved from a better understanding of these underlying dynamics. Copyright © 2011 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.
Entropy, recycling and macroeconomics of water resources
Karakatsanis, Georgios; Mamassis, Nikos; Koutsoyiannis, Demetris
2014-05-01
We propose a macroeconomic model for water quantity and quality supply multipliers derived by water recycling (Karakatsanis et al. 2013). Macroeconomic models that incorporate natural resource conservation have become increasingly important (European Commission et al. 2012). In addition, as an estimated 80% of globally used freshwater is not reused (United Nations 2012), under increasing population trends, water recycling becomes a solution of high priority. Recycling of water resources creates two major conservation effects: (1) conservation of water in reservoirs and aquifers and (2) conservation of ecosystem carrying capacity due to wastewater flux reduction. Statistical distribution properties of the recycling efficiencies -on both water quantity and quality- for each sector are of vital economic importance. Uncertainty and complexity of water reuse in sectors are statistically quantified by entropy. High entropy of recycling efficiency values signifies greater efficiency dispersion; which -in turn- may indicate the need for additional infrastructure for the statistical distribution's both shifting and concentration towards higher efficiencies that lead to higher supply multipliers. Keywords: Entropy, water recycling, water supply multipliers, conservation, recycling efficiencies, macroeconomics References 1. European Commission (EC), Food and Agriculture Organization (FAO), International Monetary Fund (IMF), Organization of Economic Cooperation and Development (OECD), United Nations (UN) and World Bank (2012), System of Environmental and Economic Accounting (SEEA) Central Framework (White cover publication), United Nations Statistics Division 2. Karakatsanis, G., N. Mamassis, D. Koutsoyiannis and A. Efstratiades (2013), Entropy and reliability of water use via a statistical approach of scarcity, 5th EGU Leonardo Conference - Hydrofractals 2013 - STAHY '13, Kos Island, Greece, European Geosciences Union, International Association of Hydrological Sciences
Configuration Entropy Calculations for Complex Compounds Technetium
International Nuclear Information System (INIS)
Muhayatun; Susanto Imam Rahayu; Surdia, N.M.; Abdul Mutalib
2002-01-01
Recently, the study of technetium complexes is rapidly increasing, due to the benefit of 99m Tc complexes (one of Tc nuclear isomers), which are widely used for diagnostics. Study of the structure-stability relationship of Tc complexes based on solid angle has been done by Kung using a Solid Angle Factor Sum (SAS). The SAS is hypothesized to be related to stability. SAS has been used by several researchers either for synthesis or designing the reaction route of the Tc complex formation and predicting the geometry of complex structures. Although the advantages of the SAS were very gratifying, but the model does not have the theoretical basis which is able to explain the correlation of steric parameters to physicochemical properties of complexes especially to those connected to a complex's stability. To improve the SAS model, in this research the model was modified by providing a theoretical basis for SAS. The results obtained from the correlation of the SAS value to the thermodynamic stability parameters of simple complexes show the values to have a similar trend as the standard entropy (S 0 ). The entropy approximation model was created by involving some factors which are not used in Kung's model. Entropy optimization to the bond length (ML) has also been done to several complexes. The calculations of SAS value using the calculated R for more than 100 Tc complexes provide a normalized mean value of 0.8545 ± 0.0851 and have similar curve profiles as those of Kung's model. The entropy value can be obtained by multiplying the natural logarithm of the a priori degeneracy of a certain distribution (Ω) and the Boltzmann constant. The results of Ω and In Ω of the Tc complexes have a narrow range. The results of this research are able to provide a basic concept for the SAS to explain the structure-stability relationship and to improve Kung's model. (author)
Dynamical entropy for infinite quantum systems
International Nuclear Information System (INIS)
Hudetz, T.
1990-01-01
We review the recent physical application of the so-called Connes-Narnhofer-Thirring entropy, which is the successful quantum mechanical generalization of the classical Kolmogorov-Sinai entropy and, by its very conception, is a dynamical entropy for infinite quantum systems. We thus comparingly review also the physical applications of the classical dynamical entropy for infinite classical systems. 41 refs. (Author)
Beyond the Shannon-Khinchin formulation: The composability axiom and the universal-group entropy
Tempesta, Piergiulio
2016-02-01
The notion of entropy is ubiquitous both in natural and social sciences. In the last two decades, a considerable effort has been devoted to the study of new entropic forms, which generalize the standard Boltzmann-Gibbs (BG) entropy and could be applicable in thermodynamics, quantum mechanics and information theory. In Khinchin (1957), by extending previous ideas of Shannon (1948) and Shannon and Weaver (1949), Khinchin proposed a characterization of the BG entropy, based on four requirements, nowadays known as the Shannon-Khinchin (SK) axioms. The purpose of this paper is twofold. First, we show that there exists an intrinsic group-theoretical structure behind the notion of entropy. It comes from the requirement of composability of an entropy with respect to the union of two statistically independent systems, that we propose in an axiomatic formulation. Second, we show that there exists a simple universal family of trace-form entropies. This class contains many well known examples of entropies and infinitely many new ones, a priori multi-parametric. Due to its specific relation with Lazard's universal formal group of algebraic topology, the new general entropy introduced in this work will be called the universal-group entropy. A new example of multi-parametric entropy is explicitly constructed.
Phase transitions and quantum entropy
International Nuclear Information System (INIS)
Arrachea, L.; Canosa, N.; Plastino, A.; Portesi, M.; Rossignoli, R.
1990-01-01
An examination is made of the possibility to predict phase transitions of the fundamental state of finite quantum system, knowing the quantum entropy of these states, defined on the basis of the information theory. (Author). 7 refs., 3 figs
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.
Consistent histories: Description of a world with increasing entropy
Directory of Open Access Journals (Sweden)
C. H. Woo
2000-07-01
Full Text Available A distinction is made between two kinds of consistent histories: (1 robust histories consistent by virtue of decoherence, and (2 verifiable histories consistent through the existence of accessible records. It is events in verifiable histories which describe amplified quantum fluctuations. If the consistent-histories formalism is to improve on the Copenhagen interpretation by providing a self-contained quantum representation of the quasi-classical world, the appropriate quantum state must track closely all macroscopic phenomena, and the von Neumann entropy of that quantum state ought to change in the same direction as the statistical entropy of the macro-world. Since the von Neumann entropy tends to decrease under successive branchings, the evolution of an entropy-increasing quasi-classical world is not described by a process of branchings only: mergings of previously separate histories must also occur. As a consequence, the number of possible quasi-classical worlds does not have to grow indefinitely as in the many-world picture.
Mixing, entropy and competition
International Nuclear Information System (INIS)
Klimenko, A Y
2012-01-01
Non-traditional thermodynamics, applied to random behaviour associated with turbulence, mixing and competition, is reviewed and analysed. Competitive mixing represents a general framework for the study of generic properties of competitive systems and can be used to model a wide class of non-equilibrium phenomena ranging from turbulent premixed flames and invasion waves to complex competitive systems. We demonstrate consistency of the general principles of competition with thermodynamic description, review and analyse the related entropy concepts and introduce the corresponding competitive H-theorem. A competitive system can be characterized by a thermodynamic quantity—competitive potential—which determines the likely direction of evolution of the system. Contested resources tend to move between systems from lower to higher values of the competitive potential. There is, however, an important difference between conventional thermodynamics and competitive thermodynamics. While conventional thermodynamics is constrained by its zeroth law and is fundamentally transitive, the transitivity of competitive thermodynamics depends on the transitivity of the competition rules. Intransitivities are common in the real world and are responsible for complex behaviour in competitive systems. This work follows ideas and methods that have originated from the analysis of turbulent combustion, but reviews a much broader scope of issues linked to mixing and competition, including thermodynamic characterization of complex competitive systems with self-organization. The approach presented here is interdisciplinary and is addressed to the general educated readers, whereas the mathematical details can be found in the appendices. (comment)
Applications of Entropy in Finance: A Review
Directory of Open Access Journals (Sweden)
Guanqun Tong
2013-11-01
Full Text Available Although the concept of entropy is originated from thermodynamics, its concepts and relevant principles, especially the principles of maximum entropy and minimum cross-entropy, have been extensively applied in finance. In this paper, we review the concepts and principles of entropy, as well as their applications in the field of finance, especially in portfolio selection and asset pricing. Furthermore, we review the effects of the applications of entropy and compare them with other traditional and new methods.
Beyond the second law entropy production and non-equilibrium systems
Lineweaver, Charles; Niven, Robert; Regenauer-Lieb, Klaus
2014-01-01
The Second Law, a cornerstone of thermodynamics, governs the average direction of dissipative, non-equilibrium processes. But it says nothing about their actual rates or the probability of fluctuations about the average. This interdisciplinary book, written and peer-reviewed by international experts, presents recent advances in the search for new non-equilibrium principles beyond the Second Law, and their applications to a wide range of systems across physics, chemistry and biology. Beyond The Second Law brings together traditionally isolated areas of non-equilibrium research and highlights potentially fruitful connections between them, with entropy production playing the unifying role. Key theoretical concepts include the Maximum Entropy Production principle, the Fluctuation Theorem, and the Maximum Entropy method of statistical inference. Applications of these principles are illustrated in such diverse fields as climatology, cosmology, crystal growth morphology, Earth system science, environmental physics, ...
On the validity of entropy production principles for linear electrical circuits
Czech Academy of Sciences Publication Activity Database
Bruers, S.; Maes, C.; Netočný, Karel
2007-01-01
Roč. 129, - (2007), s. 725-740 ISSN 0022-4715 R&D Projects: GA ČR GA202/07/0404 Institutional research plan: CEZ:AV0Z10100520 Keywords : entropy production * variational principles * nonequilibrium fluctuations Subject RIV: BE - Theoretical Physics Impact factor: 1.605, year: 2007
Multiscale multifractal multiproperty analysis of financial time series based on Rényi entropy
Yujun, Yang; Jianping, Li; Yimei, Yang
This paper introduces a multiscale multifractal multiproperty analysis based on Rényi entropy (3MPAR) method to analyze short-range and long-range characteristics of financial time series, and then applies this method to the five time series of five properties in four stock indices. Combining the two analysis techniques of Rényi entropy and multifractal detrended fluctuation analysis (MFDFA), the 3MPAR method focuses on the curves of Rényi entropy and generalized Hurst exponent of five properties of four stock time series, which allows us to study more universal and subtle fluctuation characteristics of financial time series. By analyzing the curves of the Rényi entropy and the profiles of the logarithm distribution of MFDFA of five properties of four stock indices, the 3MPAR method shows some fluctuation characteristics of the financial time series and the stock markets. Then, it also shows a richer information of the financial time series by comparing the profile of five properties of four stock indices. In this paper, we not only focus on the multifractality of time series but also the fluctuation characteristics of the financial time series and subtle differences in the time series of different properties. We find that financial time series is far more complex than reported in some research works using one property of time series.
A geometrical origin for the covariant entropy bound
Casini, H.
2003-07-01
Causal diamond-shaped subsets of spacetime are naturally associated with operator algebras in quantum field theory, and they are also related to the Bousso covariant entropy bound. In this work we argue that the net of these causal sets to which are assigned the local operator algebras of quantum theories should be taken to be non-orthomodular if there is some lowest scale for the description of spacetime as a manifold. This geometry can be related to a reduction in the degrees of freedom of the holographic type under certain natural conditions for the local algebras. A non-orthomodular net of causal sets that implements the cutoff in a covariant manner is constructed. It gives an explanation, in a simple example, of the non-positive expansion condition for lightsheet selection in the covariant entropy bound. It also suggests a different covariant formulation of the entropy bound.
A geometrical origin for the covariant entropy bound
Energy Technology Data Exchange (ETDEWEB)
Casini, H [Centre de Physique Theorique, Campus de Luminy, F-13288 Marseille (France)
2003-07-07
Causal diamond-shaped subsets of spacetime are naturally associated with operator algebras in quantum field theory, and they are also related to the Bousso covariant entropy bound. In this work we argue that the net of these causal sets to which are assigned the local operator algebras of quantum theories should be taken to be non-orthomodular if there is some lowest scale for the description of spacetime as a manifold. This geometry can be related to a reduction in the degrees of freedom of the holographic type under certain natural conditions for the local algebras. A non-orthomodular net of causal sets that implements the cutoff in a covariant manner is constructed. It gives an explanation, in a simple example, of the non-positive expansion condition for lightsheet selection in the covariant entropy bound. It also suggests a different covariant formulation of the entropy bound.
On Interrelation of Time and Entropy
Directory of Open Access Journals (Sweden)
Leonid M. Martyushev
2017-07-01
Full Text Available A measure of time is related to the number of ways by which the human correlates the past and the future for some process. On this basis, a connection between time and entropy (information, Boltzmann–Gibbs, and thermodynamic one is established. This measure gives time such properties as universality, relativity, directionality, and non-uniformity. A number of issues of the modern science related to the finding of laws describing changes in nature are discussed. A special emphasis is made on the role of evolutionary adaptation of an observer to the surrounding world.
Intrinsic entropy perturbations from the dark sector
Celoria, Marco; Comelli, Denis; Pilo, Luigi
2018-03-01
Perfect fluids are modeled by using an effective field theory approach which naturally gives a self-consistent and unambiguous description of the intrinsic non-adiabatic contribution to pressure variations. We study the impact of intrinsic entropy perturbation on the superhorizon dynamics of the curvature perturbation Script R in the dark sector. The dark sector, made of dark matter and dark energy is described as a single perfect fluid. The non-perturbative vorticity's dynamics and the Weinberg theorem violation for perfect fluids are also studied.
Thermodynamic studies of different black holes with modifications of entropy
Haldar, Amritendu; Biswas, Ritabrata
2018-02-01
In recent years, the thermodynamic properties of black holes are topics of interests. We investigate the thermodynamic properties like surface gravity and Hawking temperature on event horizon of regular black holes viz. Hayward Class and asymptotically AdS (Anti-de Sitter) black holes. We also analyze the thermodynamic volume and naive geometric volume of asymptotically AdS black holes and show that the entropy of these black holes is simply the ratio of the naive geometric volume to thermodynamic volume. We plot the different graphs and interpret them physically. We derive the `cosmic-Censorship-Inequality' for both type of black holes. Moreover, we calculate the thermal heat capacity of aforesaid black holes and study their stabilities in different regimes. Finally, we compute the logarithmic correction to the entropy for both the black holes considering the quantum fluctuations around the thermal equilibrium and study the corresponding thermodynamics.
Quantum Fluctuations of Low Dimensional Bose-Einstein ...
African Journals Online (AJOL)
Tadesse
can be classified as quantum fluctuations and thermal (classical) fluctuations. In every physical process ... Other kinds of fluctuations that exist in nature are those induced by nonlinear dynamics. Bose-Einstein ..... enough so that no significant heat transfer happens between the system and the outside environment. On the ...
Quantum fluctuation theorem: can we go from micro to meso?
De Roeck, Wojciech
2007-06-01
Quantum extensions of the Gallavotti-Cohen fluctuation theorem (FT) for the entropy production have been discussed by several authors. There is a practical gap between microscopic forms of FT and mesoscopic (i.e. not purely Hamiltonian) forms for open systems. In a microscopic setup, it is easy to state and to prove FT. In a mesoscopic setup, it is difficult to identify fluctuations of the entropy production. (This difficulty is absent in the classical case.) We discuss a particular mesoscopic model: a Lindblad master equation, in which we state FT and, more importantly, connect it rigorously with the underlying microscopic FT. We also remark that FT is satisfied by the Lesovik-Levitov formula for statistics of charge transport. To cite this article: W. De Roeck, C. R. Physique 8 (2007).
International Nuclear Information System (INIS)
Diehl, Carl; Genheden, Samuel; Modig, Kristofer; Ryde, Ulf; Akke, Mikael
2009-01-01
The conformational entropy of proteins can make significant contributions to the free energy of ligand binding. NMR spin relaxation enables site-specific investigation of conformational entropy, via order parameters that parameterize local reorientational fluctuations of rank-2 tensors. Here we have probed the conformational entropy of lactose binding to the carbohydrate recognition domain of galectin-3 (Gal3), a protein that plays an important role in cell growth, cell differentiation, cell cycle regulation, and apoptosis, making it a potential target for therapeutic intervention in inflammation and cancer. We used 15 N spin relaxation experiments and molecular dynamics simulations to monitor the backbone amides and secondary amines of the tryptophan and arginine side chains in the ligand-free and lactose-bound states of Gal3. Overall, we observe good agreement between the experimental and computed order parameters of the ligand-free and lactose-bound states. Thus, the 15 N spin relaxation data indicate that the molecular dynamics simulations provide reliable information on the conformational entropy of the binding process. The molecular dynamics simulations reveal a correlation between the simulated order parameters and residue-specific backbone entropy, re-emphasizing that order parameters provide useful estimates of local conformational entropy. The present results show that the protein backbone exhibits an increase in conformational entropy upon binding lactose, without any accompanying structural changes
2015-09-29
maps show uniform spatial distributions for each element and are atomically resolved. NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9485 ARTICLE NATURE...suspension is mixed continuously to disperse particles within the solution as well as aid in breaking up any agglomerates . Using a Cookson Electronics
Most probable degree distribution at fixed structural entropy
Indian Academy of Sciences (India)
This result indicates that scale-free degree distributions emerge naturally when con- sidering networks ensemble with small structural entropy. The appearance of the power-law degree distribution reflects the tendency of social, technological and es- pecially biological networks toward 'ordering'. This tendency is at work ...
Maximum entropy estimation via Gauss-LP quadratures
Thély, Maxime; Sutter, Tobias; Mohajerin Esfahani, P.; Lygeros, John; Dochain, Denis; Henrion, Didier; Peaucelle, Dimitri
2017-01-01
We present an approximation method to a class of parametric integration problems that naturally appear when solving the dual of the maximum entropy estimation problem. Our method builds up on a recent generalization of Gauss quadratures via an infinite-dimensional linear program, and utilizes a
Evanescent magnetic field effects on entropy generation at the onset ...
Indian Academy of Sciences (India)
The values of relaxation time of the magnetic ﬁeld are chosen, so that the Lorentz force acts only in the transient state of entropy generation in natural convection. ... High Institute of Applied Sciences and Technology of Gabes, Omar Ibn El Khattab Street, Gabes 6029, Tunisia; National School of Engineers of Gabes, Omar ...
Evanescent magnetic field effects on entropy generation at the onset ...
Indian Academy of Sciences (India)
cent magnetic field on total entropy generation in a fluid enclosed in a square cavity by using a control ... and sources of irreversibility in a vertical non-porous channel with transverse hydromagnetic effect. Haddad et al ... numerical studies of steady heat and mass transfer by natural convection flow of a heat generating fluid ...
Dynamical glucometry: Use of multiscale entropy analysis in diabetes
Costa, Madalena D.; Henriques, Teresa; Munshi, Medha N.; Segal, Alissa R.; Goldberger, Ary L.
2014-09-01
Diabetes mellitus (DM) is one of the world's most prevalent medical conditions. Contemporary management focuses on lowering mean blood glucose values toward a normal range, but largely ignores the dynamics of glucose fluctuations. We probed analyte time series obtained from continuous glucose monitor (CGM) sensors. We show that the fluctuations in CGM values sampled every 5 min are not uncorrelated noise. Next, using multiscale entropy analysis, we quantified the complexity of the temporal structure of the CGM time series from a group of elderly subjects with type 2 DM and age-matched controls. We further probed the structure of these CGM time series using detrended fluctuation analysis. Our findings indicate that the dynamics of glucose fluctuations from control subjects are more complex than those of subjects with type 2 DM over time scales ranging from about 5 min to 5 h. These findings support consideration of a new framework, dynamical glucometry, to guide mechanistic research and to help assess and compare therapeutic interventions, which should enhance complexity of glucose fluctuations and not just lower mean and variance of blood glucose levels.
Brain entropy and human intelligence: A resting-state fMRI study
Calderone, Daniel; Morales, Leah J.
2018-01-01
Human intelligence comprises comprehension of and reasoning about an infinitely variable external environment. A brain capable of large variability in neural configurations, or states, will more easily understand and predict variable external events. Entropy measures the variety of configurations possible within a system, and recently the concept of brain entropy has been defined as the number of neural states a given brain can access. This study investigates the relationship between human intelligence and brain entropy, to determine whether neural variability as reflected in neuroimaging signals carries information about intellectual ability. We hypothesize that intelligence will be positively associated with entropy in a sample of 892 healthy adults, using resting-state fMRI. Intelligence is measured with the Shipley Vocabulary and WASI Matrix Reasoning tests. Brain entropy was positively associated with intelligence. This relation was most strongly observed in the prefrontal cortex, inferior temporal lobes, and cerebellum. This relationship between high brain entropy and high intelligence indicates an essential role for entropy in brain functioning. It demonstrates that access to variable neural states predicts complex behavioral performance, and specifically shows that entropy derived from neuroimaging signals at rest carries information about intellectual capacity. Future work in this area may elucidate the links between brain entropy in both resting and active states and various forms of intelligence. This insight has the potential to provide predictive information about adaptive behavior and to delineate the subdivisions and nature of intelligence based on entropic patterns. PMID:29432427
A Note on Burg’s Modified Entropy in Statistical Mechanics
Directory of Open Access Journals (Sweden)
Amritansu Ray
2016-02-01
Full Text Available Burg’s entropy plays an important role in this age of information euphoria, particularly in understanding the emergent behavior of a complex system such as statistical mechanics. For discrete or continuous variable, maximization of Burg’s Entropy subject to its only natural and mean constraint always provide us a positive density function though the Entropy is always negative. On the other hand, Burg’s modified entropy is a better measure than the standard Burg’s entropy measure since this is always positive and there is no computational problem for small probabilistic values. Moreover, the maximum value of Burg’s modified entropy increases with the number of possible outcomes. In this paper, a premium has been put on the fact that if Burg’s modified entropy is used instead of conventional Burg’s entropy in a maximum entropy probability density (MEPD function, the result yields a better approximation of the probability distribution. An important lemma in basic algebra and a suitable example with tables and graphs in statistical mechanics have been given to illustrate the whole idea appropriately.
Brain entropy and human intelligence: A resting-state fMRI study.
Saxe, Glenn N; Calderone, Daniel; Morales, Leah J
2018-01-01
Human intelligence comprises comprehension of and reasoning about an infinitely variable external environment. A brain capable of large variability in neural configurations, or states, will more easily understand and predict variable external events. Entropy measures the variety of configurations possible within a system, and recently the concept of brain entropy has been defined as the number of neural states a given brain can access. This study investigates the relationship between human intelligence and brain entropy, to determine whether neural variability as reflected in neuroimaging signals carries information about intellectual ability. We hypothesize that intelligence will be positively associated with entropy in a sample of 892 healthy adults, using resting-state fMRI. Intelligence is measured with the Shipley Vocabulary and WASI Matrix Reasoning tests. Brain entropy was positively associated with intelligence. This relation was most strongly observed in the prefrontal cortex, inferior temporal lobes, and cerebellum. This relationship between high brain entropy and high intelligence indicates an essential role for entropy in brain functioning. It demonstrates that access to variable neural states predicts complex behavioral performance, and specifically shows that entropy derived from neuroimaging signals at rest carries information about intellectual capacity. Future work in this area may elucidate the links between brain entropy in both resting and active states and various forms of intelligence. This insight has the potential to provide predictive information about adaptive behavior and to delineate the subdivisions and nature of intelligence based on entropic patterns.
On the definition of entropy for quantum unstable states
International Nuclear Information System (INIS)
Civitarese, Osvaldo; Gadella, Manuel
2015-01-01
The concept of entropy is central to the formulation of the quantum statistical mechanics, and it is linked to the definition of the density operator and the associated probabilities of occupation of quantum states. The extension of this scheme to accommodate for quantum decaying states is conceptually difficult, because of the nature of these states. Here we present a way to treat quantum unstable states in the context of statistical mechanics. We focuss on the definition of the entropy and avoid the use of complex temperatures
Determinism, chaos, self-organization and entropy.
Pontes, José
2016-01-01
We discuss two changes of paradigms that occurred in science along the XXth century: the end of the mechanist determinism, and the end of the apparent incompatibility between biology, where emergence of order is law, and physics, postulating a progressive loss of order in natural systems. We recognize today that three mechanisms play a major role in the building of order: the nonlinear nature of most evolution laws, along with distance to equilibrium, and with the new paradigm, that emerged in the last forty years, as we recognize that networks present collective order properties not found in the individual nodes. We also address the result presented by Blumenfeld (L.A. Blumenfeld, Problems of Biological Physics, Springer, Berlin, 1981) showing that entropy decreases resulting from building one of the most complex biological structures, the human being, are small and may be trivially compensated for compliance with thermodynamics. Life is made at the expense of very low thermodynamic cost, so thermodynamics does not pose major restrictions to the emergence of life. Besides, entropy does not capture our idea of order in biological systems. The above questions show that science is not free of confl icts and backlashes, often resulting from excessive extrapolations.
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.
Entropy and Energy in Quantum Networks
Moser, David K.
Quantum channels are functions that map density matrices to density matrices. They can be used to describe a vast array of system environment interactions for quantum mechanical systems. The focus in quantum information theory lies on the study of the information content -- the quantum entropy -- of input and output system. The property of how much information a channel can convey is called capacity. When two quantum channels are combined they act on a bigger, possibly entangled state in parallel. The effects of entanglement on the capacity of a pair of channels have been widely studied. Still, recent work showed unexpected behavior. Hastings [33] found that the capacities of two channels to transmit classical information does not simply add, but can exceed the sum of the individual quantum capacities, a property called superadditivity. We study Hastings' work and find estimates for how large the dimensions of such channels would have to be. The question of capacity relates to the behavior of quantum channels in extremal cases, when the output entropy is minimized. It is natural to wonder about the "standard" behavior of quantum channels and consider their average output entropy. We have studied this behavior in particular in cases where many relatively simple quantum channels act in parallel. When combining quantum channels in parallel, the parts of the system evolve independently of each other -- up to entanglement -- and only interact with the environment. Expanding on this idea one can think of a system where the parts not only interact with the environment but also directly with each other, a quantum channel network. Interesting cases of such systems arise naturally in the study of large biological molecules. In this case, information is often transmitted via energy pulses. Thus, the study of entropy and the study of energy overlap. Of particular interest to us are antennas in photo-active systems, they absorb light energy and transports it to a chemical
Relative information entropy in cosmology: The problem of information entanglement
Energy Technology Data Exchange (ETDEWEB)
Czinner, Viktor G., E-mail: czinner.viktor@wigner.mta.hu [Centro de Matemática, Universidade do Minho, Campus de Gualtar, 4710-057 Braga (Portugal); HAS Wigner Research Centre for Physics, H-1525 Budapest, P.O. Box 49 (Hungary); Mena, Filipe C., E-mail: fmena@math.uminho.pt [Centro de Matemática, Universidade do Minho, Campus de Gualtar, 4710-057 Braga (Portugal)
2016-07-10
The necessary information to distinguish a local inhomogeneous mass density field from its spatial average on a compact domain of the universe can be measured by relative information entropy. The Kullback–Leibler (KL) formula arises very naturally in this context, however, it provides a very complicated way to compute the mutual information between spatially separated but causally connected regions of the universe in a realistic, inhomogeneous model. To circumvent this issue, by considering a parametric extension of the KL measure, we develop a simple model to describe the mutual information which is entangled via the gravitational field equations. We show that the Tsallis relative entropy can be a good approximation in the case of small inhomogeneities, and for measuring the independent relative information inside the domain, we propose the Rényi relative entropy formula.
Entropy, pricing and macroeconomics of pumped-storage systems
Karakatsanis, Georgios; Mamassis, Nikos; Koutsoyiannis, Demetris; Efstratiadis, Andreas
2014-05-01
We propose a pricing scheme for the enhancement of macroeconomic performance of pumped-storage systems, based on the statistical properties of both geophysical and economic variables. The main argument consists in the need of a context of economic values concerning the hub energy resource; defined as the resource that comprises the reference energy currency for all involved renewable energy sources (RES) and discounts all related uncertainty. In the case of pumped-storage systems the hub resource is the reservoir's water, as a benchmark for all connected intermittent RES. The uncertainty of all involved natural and economic processes is statistically quantifiable by entropy. It is the relation between the entropies of all involved RES that shapes the macroeconomic state of the integrated pumped-storage system. Consequently, there must be consideration on the entropy of wind, solar and precipitation patterns, as well as on the entropy of economic processes -such as demand preferences on either current energy use or storage for future availability. For pumped-storage macroeconomics, a price on the reservoir's capacity scarcity should also be imposed in order to shape a pricing field with upper and lower limits for the long-term stability of the pricing range and positive net energy benefits, which is the primary issue of the generalized deployment of pumped-storage technology. Keywords: Entropy, uncertainty, pricing, hub energy resource, RES, energy storage, capacity scarcity, macroeconomics
Dissecting Protein Configurational Entropy into Conformational and Vibrational Contributions.
Chong, Song-Ho; Ham, Sihyun
2015-10-01
Quantifying how the rugged nature of the underlying free-energy landscape determines the entropic cost a protein must incur upon folding and ligand binding is a challenging problem. Here, we present a novel computational approach that dissects the protein configurational entropy on the basis of the classification of protein dynamics on the landscape into two separate components: short-term vibrational dynamics related to individual free-energy wells and long-term conformational dynamics associated with transitions between wells. We apply this method to separate the configurational entropy of the protein villin headpiece subdomain into its conformational and vibrational components. We find that the change in configurational entropy upon folding is dominated by the conformational entropy despite the fact that the magnitude of the vibrational entropy is the significantly larger component in each of the folded and unfolded states, which is in accord with the previous empirical estimations. The straightforward applicability of our method to unfolded proteins promises a wide range of applications, including those related to intrinsically disordered proteins.
Catching homologies by geometric entropy
Felice, Domenico; Franzosi, Roberto; Mancini, Stefano; Pettini, Marco
2018-02-01
A geometric entropy is defined in terms of the Riemannian volume of the parameter space of a statistical manifold associated with a given network. As such it can be a good candidate for measuring networks complexity. Here we investigate its ability to single out topological features of networks proceeding in a bottom-up manner: first we consider small size networks by analytical methods and then large size networks by numerical techniques. Two different classes of networks, the random graphs and the scale-free networks, are investigated computing their Betti numbers and then showing the capability of geometric entropy of detecting homologies.
Methods for calculating nonconcave entropies
International Nuclear Information System (INIS)
Touchette, Hugo
2010-01-01
Five different methods which can be used to analytically calculate entropies that are nonconcave as functions of the energy in the thermodynamic limit are discussed and compared. The five methods are based on the following ideas and techniques: (i) microcanonical contraction, (ii) metastable branches of the free energy, (iii) generalized canonical ensembles with specific illustrations involving the so-called Gaussian and Betrag ensembles, (iv) the restricted canonical ensemble, and (v) the inverse Laplace transform. A simple long-range spin model having a nonconcave entropy is used to illustrate each method
Population Genetics with Fluctuating Population Sizes
Chotibut, Thiparat; Nelson, David R.
2016-01-01
Standard neutral population genetics theory with a strictly fixed population size has important limitations. An alternative model that allows independently fluctuating population sizes and reproduces the standard neutral evolution is reviewed. We then study a situation such that the competing species are neutral at the equilibrium population size but population size fluctuations nevertheless favor fixation of one species over the other. In this case, a separation of timescales emerges natural...
Multivariate refined composite multiscale entropy analysis
Energy Technology Data Exchange (ETDEWEB)
Humeau-Heurtier, Anne, E-mail: anne.humeau@univ-angers.fr
2016-04-01
Multiscale entropy (MSE) has become a prevailing method to quantify signals complexity. MSE relies on sample entropy. However, MSE may yield imprecise complexity estimation at large scales, because sample entropy does not give precise estimation of entropy when short signals are processed. A refined composite multiscale entropy (RCMSE) has therefore recently been proposed. Nevertheless, RCMSE is for univariate signals only. The simultaneous analysis of multi-channel (multivariate) data often over-performs studies based on univariate signals. We therefore introduce an extension of RCMSE to multivariate data. Applications of multivariate RCMSE to simulated processes reveal its better performances over the standard multivariate MSE. - Highlights: • Multiscale entropy quantifies data complexity but may be inaccurate at large scale. • A refined composite multiscale entropy (RCMSE) has therefore recently been proposed. • Nevertheless, RCMSE is adapted to univariate time series only. • We herein introduce an extension of RCMSE to multivariate data. • It shows better performances than the standard multivariate multiscale entropy.
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
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.
Examples of Entropy-driven Ordering
Indian Academy of Sciences (India)
driven Ordering. Orientational ordering of long objects. Entropy of sliding increases. Freezing in hard-sphere systems. Vibrational entropy increases. Phase separation in hard-sphere binary mixtures with disparate sizes. More room for smaller ...
Indian Academy of Sciences (India)
mean by the 'number of states' is simply the volume (generalised to 6N dimensions) of phase space occupied by the gas molecules. The definition (1) is more natural, in .retrospect, than you might first think. For the ideal gas (see. Jayanta Bhattacharjee's article in this issue) one can carry out explicitly both the state-counting.
Quantum fluctuations and inflation
International Nuclear Information System (INIS)
Bardeen, J.M.; Bublik, G.J.
1987-01-01
The authors study the effect of quantum fluctuations on the roll-down rate of the inflation field in a semiclassical approximation; this is done by treating the inflation field as a classical random field. The quantum fluctuations are simulated by a noise term in the equation of motion. Two different inflationary scenarios (new and chaotic inflation) are considered and it is found that the roll-down rate of the median value of the inflation field is increased by the quantum fluctuations. Non-linear effects may become important in the later stages of the inflationary regime. (author)
The Wehrl entropy has Gaussian optimizers
DEFF Research Database (Denmark)
De Palma, Giacomo
2018-01-01
We determine the minimum Wehrl entropy among the quantum states with a given von Neumann entropy and prove that it is achieved by thermal Gaussian states. This result determines the relation between the von Neumann and the Wehrl entropies. The key idea is proving that the quantum-classical channel...
Algebraic entropy for differential-delay equations
Viallet, Claude M.
2014-01-01
We extend the definition of algebraic entropy to a class of differential-delay equations. The vanishing of the entropy, as a structural property of an equation, signals its integrability. We suggest a simple way to produce differential-delay equations with vanishing entropy from known integrable differential-difference equations.
Logical entropy of quantum dynamical systems
Directory of Open Access Journals (Sweden)
Ebrahimzadeh Abolfazl
2016-01-01
Full Text Available This paper introduces the concepts of logical entropy and conditional logical entropy of hnite partitions on a quantum logic. Some of their ergodic properties are presented. Also logical entropy of a quantum dynamical system is dehned and ergodic properties of dynamical systems on a quantum logic are investigated. Finally, the version of Kolmogorov-Sinai theorem is proved.
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.
Universal canonical entropy for gravitating systems
Indian Academy of Sciences (India)
Similar to this is the case of ref. [12] which also uses the saddle point approximation to express the microcanonical entropy in terms of the canonical entropy [12a]. Recalling that there is at least 'circumstantial' evidence that the microcanonical entropy has a 'universal' form [13–15], identical to that obtained in ref. [6] quoted.
Single Particle Entropy in Heated Nuclei
International Nuclear Information System (INIS)
Guttormsen, M.; Chankova, R.; Hjorth-Jensen, M.; Rekstad, J.; Siem, S.; Sunde, A. C.; Syed, N. U. H.; Agvaanluvsan, U.; Schiller, A.; Voinov, A.
2006-01-01
The thermal motion of single particles represents the largest contribution to level density (or entropy) in atomic nuclei. The concept of single particle entropy is presented and shown to be an approximate extensive (additive) quantity for mid-shell nuclei. A few applications of single particle entropy are demonstrated
Entropy of dynamical social networks
Zhao, Kun; Karsai, Marton; Bianconi, Ginestra
2012-02-01
Dynamical social networks are evolving rapidly and are highly adaptive. Characterizing the information encoded in social networks is essential to gain insight into the structure, evolution, adaptability and dynamics. Recently entropy measures have been used to quantify the information in email correspondence, static networks and mobility patterns. Nevertheless, we still lack methods to quantify the information encoded in time-varying dynamical social networks. In this talk we present a model to quantify the entropy of dynamical social networks and use this model to analyze the data of phone-call communication. We show evidence that the entropy of the phone-call interaction network changes according to circadian rhythms. Moreover we show that social networks are extremely adaptive and are modified by the use of technologies such as mobile phone communication. Indeed the statistics of duration of phone-call is described by a Weibull distribution and is significantly different from the distribution of duration of face-to-face interactions in a conference. Finally we investigate how much the entropy of dynamical social networks changes in realistic models of phone-call or face-to face interactions characterizing in this way different type human social behavior.
Hidden states and hidden entropy
International Nuclear Information System (INIS)
Betak, E.
1993-06-01
We study the properties of master equations of the pre-equilibrium exciton model. For the case when the emission is included, we have proved the entropy to be a nondecreasing function of time. The opposite statement in the recent paper of Pan et al. has been caused mainly by neglecting a part of the exciton states. (author). 17 refs
Entropy, Coding and Data Compression
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 9. Entropy, Coding and Data Compression. S Natarajan. General Article Volume 6 Issue 9 September 2001 pp 35-45. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/006/09/0035-0045 ...
Properties of von Neumann entropy
Indian Academy of Sciences (India)
disentangled) as seen by moving observers, is used to investigate the properties of von Neumann entropy, as a measure of spin–momentum entanglement. To do so, we partition the total Hilbert space into momentum and spin subspaces so that the ...
Maximum entropy beam diagnostic tomography
International Nuclear Information System (INIS)
Mottershead, C.T.
1985-01-01
This paper reviews the formalism of maximum entropy beam diagnostic tomography as applied to the Fusion Materials Irradiation Test (FMIT) prototype accelerator. The same formalism has also been used with streak camera data to produce an ultrahigh speed movie of the beam profile of the Experimental Test Accelerator (ETA) at Livermore. 11 refs., 4 figs
Vibrational entropies in metallic alloys
Ozolins, Vidvuds; Asta, Mark; Wolverton, Christopher
2000-03-01
Recently, it has been recognized that vibrational entropy can have significant effects on the phase stability of metallic alloys. Using density functional linear response calculations and molecular dynamics simulations we study three representative cases: (i) phase diagram of Al-rich Al-Sc alloys, (ii) stability of precipitate phases in CuAl_2, and (iii) phonon dynamics in bcc Zr. We find large vibrational entropy effects in all cases. In the Al-Sc system, vibrations increase the solid solubility of Sc in Al by decreasing the stability of the L12 (Al_3Sc) phase. This leads to a nearly ten-fold increase in the solid solubility of Sc in Al at T=800 K. In the Cu-Al system, our calculations predict that the tetragonal Laves phase of CuAl2 has 0.35 kB/atom higher vibrational entropy than the cubic CaF_2-type phase (the latter is predicted to be the T=0 K ground state of CuAl_2). This entropy difference causes a structural transformation in CuAl2 precipitates from the fluorite to the tetragonal Laves phase around T=500 K. Finally, we analyze the highly unusual dynamics of anharmonically stabilized bcc Zr, finding large diffuse-scattering intensity streaks between the bcc Bragg peaks.
Fully Quantum Fluctuation Theorems
Åberg, Johan
2018-02-01
Systems that are driven out of thermal equilibrium typically dissipate random quantities of energy on microscopic scales. Crooks fluctuation theorem relates the distribution of these random work costs to the corresponding distribution for the reverse process. By an analysis that explicitly incorporates the energy reservoir that donates the energy and the control system that implements the dynamic, we obtain a quantum generalization of Crooks theorem that not only includes the energy changes in the reservoir but also the full description of its evolution, including coherences. Moreover, this approach opens up the possibility for generalizations of the concept of fluctuation relations. Here, we introduce "conditional" fluctuation relations that are applicable to nonequilibrium systems, as well as approximate fluctuation relations that allow for the analysis of autonomous evolution generated by global time-independent Hamiltonians. We furthermore extend these notions to Markovian master equations, implicitly modeling the influence of the heat bath.
Fully Quantum Fluctuation Theorems
Directory of Open Access Journals (Sweden)
Johan Åberg
2018-02-01
Full Text Available Systems that are driven out of thermal equilibrium typically dissipate random quantities of energy on microscopic scales. Crooks fluctuation theorem relates the distribution of these random work costs to the corresponding distribution for the reverse process. By an analysis that explicitly incorporates the energy reservoir that donates the energy and the control system that implements the dynamic, we obtain a quantum generalization of Crooks theorem that not only includes the energy changes in the reservoir but also the full description of its evolution, including coherences. Moreover, this approach opens up the possibility for generalizations of the concept of fluctuation relations. Here, we introduce “conditional” fluctuation relations that are applicable to nonequilibrium systems, as well as approximate fluctuation relations that allow for the analysis of autonomous evolution generated by global time-independent Hamiltonians. We furthermore extend these notions to Markovian master equations, implicitly modeling the influence of the heat bath.
Fishing and stock fluctuations
National Research Council Canada - National Science Library
Laevastu, Taivo; Favorite, F
1988-01-01
.... Scarcely publicized are the multitude of causes of fish stock fluctuations. This book attempts to summarize the available knowledge on the subject and includes original work of the authors on a matter vital to the fisheries industries of the world...
Entropy production, viscosity bounds and bumpy black holes
Energy Technology Data Exchange (ETDEWEB)
Hartnoll, Sean A.; Ramirez, David M. [Department of Physics, Stanford University, Stanford, CA 94305-4060 (United States); Santos, Jorge E. [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
2016-03-24
The ratio of shear viscosity to entropy density, η/s, is computed in various holographic geometries that break translation invariance (but are isotropic). The shear viscosity does not have a hydrodynamic interpretation in such backgrounds, but does quantify the rate of entropy production due to a strain. Fluctuations of the metric components δg{sub xy} are massive about these backgrounds, leading to η/s<1/(4π) at all finite temperatures (even in Einstein gravity). As the temperature is taken to zero, different behaviors are possible. If translation symmetry breaking is irrelevant in the far IR, then η/s tends to a constant at T=0. This constant can be parametrically small. If the translation symmetry is broken in the far IR (which nonetheless develops emergent scale invariance), then η/s∼T{sup 2ν} as T→0, with ν≤1 in all cases we have considered. While these results violate simple bounds on η/s, we note that they are consistent with a possible bound on the rate of entropy production due to strain.
Scaling metabolic rate fluctuations
Labra, Fabio A.; Marquet, Pablo A.; Bozinovic, Francisco
2007-01-01
Complex ecological and economic systems show fluctuations in macroscopic quantities such as exchange rates, size of companies or populations that follow non-Gaussian tent-shaped probability distributions of growth rates with power-law decay, which suggests that fluctuations in complex systems may be governed by universal mechanisms, independent of particular details and idiosyncrasies. We propose here that metabolic rate within individual organisms may be considered as an example of an emerge...
Study of nonlinear structures in electrostatic flute type fluctuations
International Nuclear Information System (INIS)
Prasad, G.; Bora, D.; Saxena, Y.C.; Sethia, G.C.
1993-01-01
Techniques of analysing the time series with the concept of modes substituted by quantities such as dimension, Lyapunov exponent and the Kolmogorov entropy have developed in recent years. These are few tools of nonlinear dynamical system analysis. They have similar analog in plasma physics. For example, dimension analysis of turbulent fluctuations (continuous power spectrum) in fusion devices and in laboratory devices suggest that for the coherent fluctuations the calculated correlation dimension is low (nearly equal to the number of modes excited) while it is large for turbulent state. The dimension calculated is nearly equal to number of competing modes. Similarly in plasma physics we speak of unstable (growing) and damped (decaying) waves. It is analogous to Lyapunov exponent which determines the divergence (for positive Lyapunov exponent) or convergence (for negative Lyapunov exponent) of neighboring trajectories exponentially in a time series. Number of Lyapunov exponent is same as the dimension of phase space. Matric entropy of the system is sum of the positive Lyapunov exponents which determines overall stability of the system. During the study of low frequency instabilities in toroidal device we have observed that the density and potential fluctuations makes a transition from coherent multimode state (exhibiting a considerable nonlinearity as seen from the bicoherence spectrum) to a turbulent state with increase in magnetic field. We have applied the tools of non-linear dynamical system analysis on density fluctuations obtained at different magnetic field. The results of the analysis are presented. (author) 9 refs., 11 figs
Directory of Open Access Journals (Sweden)
Yu Ji
2017-03-01
Full Text Available The entropy generation analysis of fully turbulent convective heat transfer to nanofluids in a circular tube is investigated numerically using the Reynolds Averaged Navier–Stokes (RANS model. The nanofluids with particle concentration of 0%, 1%, 2%, 4% and 6% are treated as single phases of effective properties. The uniform heat flux is enforced at the tube wall. To confirm the validity of the numerical approach, the results have been compared with empirical correlations and analytical formula. The self-similarity profiles of local entropy generation are also studied, in which the peak values of entropy generation by direct dissipation, turbulent dissipation, mean temperature gradients and fluctuating temperature gradients for different Reynolds number as well as different particle concentration are observed. In addition, the effects of Reynolds number, volume fraction of nanoparticles and heat flux on total entropy generation and Bejan number are discussed. In the results, the intersection points of total entropy generation for water and four nanofluids are observed, when the entropy generation decrease before the intersection and increase after the intersection as the particle concentration increases. Finally, by definition of Ep, which combines the first law and second law of thermodynamics and attributed to evaluate the real performance of heat transfer processes, the optimal Reynolds number Reop corresponding to the best performance and the advisable Reynolds number Read providing the appropriate Reynolds number range for nanofluids in convective heat transfer can be determined.
Entropy production and isotropization in Yang-Mills theory using a quantum distribution function
Tsukiji, Hidekazu; Kunihiro, Teiji; Ohnishi, Akira; Takahashi, Toru T.
2018-01-01
We investigate the thermalization process from a glasma-like initial condition in a static box in terms of the Husimi-Wehrl (HW) entropy defined with the Husimi function, a quantum distribution function in a phase space. We calculate the semiclassical time evolution of the HW entropy in Yang-Mills field theory with the phenomenological initial field configuration given by mimicking the McLerran-Venugopalan model in a static box, which has instability triggered by initial field fluctuations. Husimi-Wehrl entropy production implies the thermalization of the system and it reflects the underlying dynamics such as chaoticity and instability. By comparing the production rate with the Kolmogorov-Sinaï rate, we find that the HW entropy production rate is significantly larger than that expected from chaoticity. We also show that the HW entropy is finally saturated when the system reaches a quasi-stationary state. The saturation time of the HW entropy is comparable with that of pressure isotropization, which is around 1 fm/c in the present calculation.
Gul, Ahmet; Erman, Burak
2018-03-01
Prediction of peptide binding on specific human leukocyte antigens (HLA) has long been studied with successful results. We herein describe the effects of entropy and dynamics by investigating the binding stabilities of 10 nanopeptides on various HLA Class I alleles using a theoretical model based on molecular dynamics simulations. The fluctuational entropies of the peptides are estimated over a temperature range of 310-460 K. The estimated entropies correlate well with experimental binding affinities of the peptides: peptides that have higher binding affinities have lower entropies compared to non-binders, which have significantly larger entropies. The computation of the entropies is based on a simple model that requires short molecular dynamics trajectories and allows for approximate but rapid determination. The paper draws attention to the long neglected dynamic aspects of peptide binding, and provides a fast computation scheme that allows for rapid scanning of large numbers of peptides on selected HLA antigens, which may be useful in defining the right peptides for personal immunotherapy.
Critical swelling of fluctuating capsules
Diamant, Haim; Haleva, Emir
2009-03-01
In many natural transport processes the solute molecules to be transported are encapsulated in semipermeable, flexible membrane vesicles of micron size. We study the swelling of such fluctuating capsules, as the number of encapsulated particles is increased, or the concentration of the outer solution is decreased. The approach to the maximum volume-to-area ratio and the associated buildup of membrane tension involve a continuous phase transition and follow universal scaling laws. The criticality and its features are model-independent, arising solely from the interplay between volume and surface degrees of freedom.ootnotetextE. Haleva and H. Diamant, Phys. Rev. Lett. 101, 078104 (2008).
Entropy and the Complexity of Graphs Revisited
Directory of Open Access Journals (Sweden)
Matthias Dehmer
2012-03-01
Full Text Available This paper presents a taxonomy and overview of approaches to the measurement of graph and network complexity. The taxonomy distinguishes between deterministic (e.g., Kolmogorov complexity and probabilistic approaches with a view to placing entropy-based probabilistic measurement in context. Entropy-based measurement is the main focus of the paper. Relationships between the different entropy functions used to measure complexity are examined; and intrinsic (e.g., classical measures and extrinsic (e.g., Körner entropy variants of entropy-based models are discussed in some detail.
Controlling the Shannon Entropy of Quantum Systems
Xing, Yifan; Wu, Jun
2013-01-01
This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking. PMID:23818819
Entropy evaporated by a black hole
International Nuclear Information System (INIS)
Zurek, W.H.
1982-01-01
It is shown that the entropy of the radiation evaporated by an uncharged, nonrotating black hole into vacuum in the course of its lifetime is approximately (4/3) times the initial entropy of this black hole. Also considered is a thermodynamically reversible process in which an increase of black-hole entropy is equal to the decrease of the entropy of its surroundings. Implications of these results for the generalized second law of thermodynamics and for the interpretation of black-hole entropy are pointed out
Towards information inequalities for generalized graph entropies.
Directory of Open Access Journals (Sweden)
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.
Entropy-Corrected Holographic Dark Energy
International Nuclear Information System (INIS)
Wei Hao
2009-01-01
The holographic dark energy (HDE) is now an interesting candidate of dark energy, which has been studied extensively in the literature. In the derivation of HDE, the black hole entropy plays an important role. In fact, the entropy-area relation can be modified due to loop quantum gravity or other reasons. With the modified entropy-area relation, we propose the so-called 'entropy-corrected holographic dark energy' (ECHDE) in the present work. We consider many aspects of ECHDE and find some interesting results. In addition, we briefly consider the so-called 'entropy-corrected agegraphic dark energy' (ECADE). (geophysics, astronomy, and astrophysics)
Fluctuation Theorem for Many-Body Pure Quantum States
Iyoda, Eiki; Kaneko, Kazuya; Sagawa, Takahiro
2017-09-01
We prove the second law of thermodynamics and the nonequilibrium fluctuation theorem for pure quantum states. The entire system obeys reversible unitary dynamics, where the initial state of the heat bath is not the canonical distribution but is a single energy eigenstate that satisfies the eigenstate-thermalization hypothesis. Our result is mathematically rigorous and based on the Lieb-Robinson bound, which gives the upper bound of the velocity of information propagation in many-body quantum systems. The entanglement entropy of a subsystem is shown connected to thermodynamic heat, highlighting the foundation of the information-thermodynamics link. We confirmed our theory by numerical simulation of hard-core bosons, and observed dynamical crossover from thermal fluctuations to bare quantum fluctuations. Our result reveals a universal scenario that the second law emerges from quantum mechanics, and can be experimentally tested by artificial isolated quantum systems such as ultracold atoms.
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;
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.
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.
Conservative models: parametric entropy vs. temporal entropy in outcomes.
Huang, Lumeng; Ritzi, Robert W; Ramanathan, Ramya
2012-01-01
The geologic architecture in aquifer systems affects the behavior of fluid flow and the dispersion of mass. The spatial distribution and connectivity of higher-permeability facies play an important role. Models that represent this geologic structure have reduced entropy in the spatial distribution of permeability relative to models without structure. The literature shows that the stochastic model with the greatest variance in the distribution of predictions (i.e., the most conservative model) will not simply be the model representing maximum disorder in the permeability field. This principle is further explored using the Shannon entropy as a single metric to quantify and compare model parametric spatial disorder to the temporal distribution of mass residence times in model predictions. The principle is most pronounced when geologic structure manifests as preferential-flow pathways through the system via connected high-permeability sediments. As per percolation theory, at certain volume fractions the full connectivity of the high-permeability sediments will not be represented unless the model is three-dimensional. At these volume fractions, two-dimensional models can profoundly underrepresent the entropy in the real, three-dimensional, aquifer system. Thus to be conservative, stochastic models must be three-dimensional and include geologic structure. © 2011, The Author(s). Ground Water © 2011, National Ground Water Association.
Effects of thermal fluctuations on non-minimal regular magnetic black hole
Energy Technology Data Exchange (ETDEWEB)
Jawad, Abdul [COMSATS Institute of Information Technology, Department of Mathematics, Lahore (Pakistan); Shahzad, M.U. [COMSATS Institute of Information Technology, Department of Mathematics, Lahore (Pakistan); University of Central Punjab, CAMS, UCP Business School, Lahore (Pakistan)
2017-05-15
We analyze the effects of thermal fluctuations on a regular black hole (RBH) of the non-minimal Einstein-Yang-Mill theory with gauge field of magnetic Wu-Yang type and a cosmological constant. We consider the logarithmic corrected entropy in order to analyze the thermal fluctuations corresponding to non-minimal RBH thermodynamics. In this scenario, we develop various important thermodynamical quantities, such as entropy, pressure, specific heats, Gibb's free energy and Helmholtz free energy. We investigate the first law of thermodynamics in the presence of logarithmic corrected entropy and non-minimal RBH. We also discuss the stability of this RBH using various frameworks such as the γ factor (the ratio of heat capacities), phase transition, grand canonical ensemble and canonical ensemble. It is observed that the non-minimal RBH becomes globally and locally more stable if we increase the value of the cosmological constant. (orig.)
Effects of thermal fluctuations on non-minimal regular magnetic black hole
International Nuclear Information System (INIS)
Jawad, Abdul; Shahzad, M.U.
2017-01-01
We analyze the effects of thermal fluctuations on a regular black hole (RBH) of the non-minimal Einstein-Yang-Mill theory with gauge field of magnetic Wu-Yang type and a cosmological constant. We consider the logarithmic corrected entropy in order to analyze the thermal fluctuations corresponding to non-minimal RBH thermodynamics. In this scenario, we develop various important thermodynamical quantities, such as entropy, pressure, specific heats, Gibb's free energy and Helmholtz free energy. We investigate the first law of thermodynamics in the presence of logarithmic corrected entropy and non-minimal RBH. We also discuss the stability of this RBH using various frameworks such as the γ factor (the ratio of heat capacities), phase transition, grand canonical ensemble and canonical ensemble. It is observed that the non-minimal RBH becomes globally and locally more stable if we increase the value of the cosmological constant. (orig.)
Analysis of swarm behaviors based on an inversion of the fluctuation theorem.
Hamann, Heiko; Schmickl, Thomas; Crailsheim, Karl
2014-01-01
A grand challenge in the field of artificial life is to find a general theory of emergent self-organizing systems. In swarm systems most of the observed complexity is based on motion of simple entities. Similarly, statistical mechanics focuses on collective properties induced by the motion of many interacting particles. In this article we apply methods from statistical mechanics to swarm systems. We try to explain the emergent behavior of a simulated swarm by applying methods based on the fluctuation theorem. Empirical results indicate that swarms are able to produce negative entropy within an isolated subsystem due to frozen accidents. Individuals of a swarm are able to locally detect fluctuations of the global entropy measure and store them, if they are negative entropy productions. By accumulating these stored fluctuations over time the swarm as a whole is producing negative entropy and the system ends up in an ordered state. We claim that this indicates the existence of an inverted fluctuation theorem for emergent self-organizing dissipative systems. This approach bears the potential of general applicability.
Principle of maximum entropy and irreversible processes
International Nuclear Information System (INIS)
Grandy, W.T. Jr.
1980-01-01
More than twenty years have passed since E.T. Jaynes pioneered the information-theoretic approach to the foundations of statistical mechanics. In the intervening period numerous applications have been worked out and new insights developed into traditional problems. Although the natural extension of these ideas to nonequilibrium statistical mechanics and irreversible processes has also been formulated, and both theory and applications have been considerably developed, much of this work has not appeared in the open literature. Yet the basic ideas and consequent theory seem to have an extraordinary unifying and illumination effect on the foundations of the many-body problem, as well as providing a transparent conceptual basis from which to view various groups of problems not previously formulated in a particularly sharp way. The aim of this review is to summarize these developements in the context of the principle of maximum entropy. (orig.)
Manufacturing of High Entropy Alloys
Jablonski, Paul D.; Licavoli, Joseph J.; Gao, Michael C.; Hawk, Jeffrey A.
2015-07-01
High entropy alloys (HEAs) have generated interest in recent years due to their unique positioning within the alloy world. By incorporating a number of elements in high proportion they have high configurational entropy, and thus they hold the promise of interesting and useful properties such as enhanced strength and phase stability. The present study investigates the microstructure of two single-phase face-centered cubic (FCC) HEAs, CoCrFeNi and CoCrFeNiMn, with special attention given to melting, homogenization and thermo-mechanical processing. Large-scale ingots were made by vacuum induction melting to avoid the extrinsic factors inherent in small-scale laboratory button samples. A computationally based homogenization heat treatment was applied to both alloys in order to eliminate segregation due to normal ingot solidification. The alloys fabricated well, with typical thermo-mechanical processing parameters being employed.
Entropy: The Markov Ordering Approach
Directory of Open Access Journals (Sweden)
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.
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 localization and extensivity in the semiclassical black hole evaporation
International Nuclear Information System (INIS)
Casini, H.
2009-01-01
I aim to quantify the distribution of information in the Hawking radiation and inside the black hole in the semiclassical evaporation process. The structure of relativistic quantum field theory does not allow one to define a localized entropy unambiguously, but rather forces one to consider the shared information (mutual information) between two different regions of space-time. Using this tool, I first show that the entropy of a thermal gas at the Unruh temperature underestimates the actual amount of (shared) information present in a region of the Rindler space. Then, I analyze the mutual information between the black hole and the late time radiation region. A well-known property of the entropy implies that this is monotonically increasing with time. This means that in the semiclassical picture it is not possible to recover the eventual purity of the initial state in the final Hawking radiation through subtle correlations established during the whole evaporation period, no matter the interactions present in the theory. I find extensivity of the entropy as a consequence of a reduction to a two dimensional conformal problem in a simple approximation. However, the extensivity of information in the radiation region in a full four dimensional calculation seems not to be guaranteed on general grounds. I also analyze the localization of shared information inside the black hole finding that a large amount of it is contained in a small, approximately flat region of space-time near the point where the horizon begins. This gives place to large violations of the entropy bounds. I show that this problem is not eased by backscattering effects and argue that a breaking of conformal invariance is necessary to delocalize the entropy. Finally, I indicate that the mutual information could lead to a way to understand the Bekenstein-Hawking black hole entropy which does not require a drastic reduction in degrees of freedom in order to regulate the entanglement entropy. On the contrary
ASSESSMENT OF MOTIVATION BY ENTROPY
Tadeusz G³owacki
2014-01-01
Motivation is inseparable from human work. It is also one of the five most important elements of the management process. The ability to determine the level of motivation would therefore be very useful in the work of every manager. This paper is an attempt to quantify motivation and evaluate its size, using the concept of entropy. The main reason to try defining a method of measuring the amount of motivation is to improve the management techniques of companies.
Collision entropy and optimal uncertainty
Bosyk, G. M.; Portesi, M.; Plastino, A.
2011-01-01
We propose an alternative measure of quantum uncertainty for pairs of arbitrary observables in the 2-dimensional case, in terms of collision entropies. We derive the optimal lower bound for this entropic uncertainty relation, which results in an analytic function of the overlap of the corresponding eigenbases. Besides, we obtain the minimum uncertainty states. We compare our relation with other formulations of the uncertainty principle.
Linearity of holographic entanglement entropy
Energy Technology Data Exchange (ETDEWEB)
Almheiri, Ahmed [Stanford Institute for Theoretical Physics, Department of Physics,Stanford University, Stanford, CA 94305 (United States); Dong, Xi [School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States); Swingle, Brian [Stanford Institute for Theoretical Physics, Department of Physics,Stanford University, Stanford, CA 94305 (United States)
2017-02-14
We consider the question of whether the leading contribution to the entanglement entropy in holographic CFTs is truly given by the expectation value of a linear operator as is suggested by the Ryu-Takayanagi formula. We investigate this property by computing the entanglement entropy, via the replica trick, in states dual to superpositions of macroscopically distinct geometries and find it consistent with evaluating the expectation value of the area operator within such states. However, we find that this fails once the number of semi-classical states in the superposition grows exponentially in the central charge of the CFT. Moreover, in certain such scenarios we find that the choice of surface on which to evaluate the area operator depends on the density matrix of the entire CFT. This nonlinearity is enforced in the bulk via the homology prescription of Ryu-Takayanagi. We thus conclude that the homology constraint is not a linear property in the CFT. We also discuss the existence of ‘entropy operators’ in general systems with a large number of degrees of freedom.
Universal mesoscopic conductance fluctuations
International Nuclear Information System (INIS)
Evangelou, S.N.
1992-01-01
The theory of conductance fluctuations in disordered metallic systems with size large compared to the mean free path of the electron but small compared to localization length is considered. It is demonstrates that fluctuations have an universal character and are due to repulsion between levels and spectral rigidity. The basic fluctuation measures for the energy spectrum in the mesoscopic regime of disordered systems are consistent with the Gaussian random matrix ensemble predictions. Although our disordered electron random matrix ensemble does not belong to the Gaussian ensemble the two ensembles turn out to be essentially similar. The level repulsion and the spectral rigidity found in nuclear spectra should also be observed in the metallic regime of Anderson localization. 7 refs. (orig.)
Directory of Open Access Journals (Sweden)
V.M. Loktev
2008-09-01
Full Text Available We analyze the spectral properties of a phenomenological model for a weakly doped two-dimensional antiferromagnet, in which the carriers move within one of the two sublattices where they were introduced. Such a constraint results in the free carrier spectra with the maxima at k=(± π/2 , ± π/2 observed in some cuprates. We consider the spectral properties of the model by taking into account fluctuations of the spins in the antiferromagnetic background. We show that such fluctuations lead to a non-pole-like structure of the single-hole Green's function and these fluctuations can be responsible for some anomalous "strange metal" properties of underdoped cuprates in the nonsuperconducting regime.
Muthukrishnan, M.; Strahle, W. C.; Neale, D. H.
1977-01-01
This paper deals with noise sources which are central to the problem of core engine noise in turbopropulsion systems. The sources dealt with are entropy noise and direct combustion noise, as well as a non-propagating psuedosound which is hydrodynamic noise. It is shown analytically and experimentally that a transition can occur from a combustion noise dominant situation to an entropy noise dominant case if the contraction of a terminating nozzle to the combustor is high enough. In the combustor tested, entropy noise is the dominant source for propagational noise if the combustor is choked at the exit. Analysis techniques include spectral, cross spectral, cross correlation, and ordinary and partial coherence analysis. Measurements include exterior and interior fluctuating and mean pressures and temperatures.
Value at risk estimation with entropy-based wavelet analysis in exchange markets
He, Kaijian; Wang, Lijun; Zou, Yingchao; Lai, Kin Keung
2014-08-01
In recent years, exchange markets are increasingly integrated together. Fluctuations and risks across different exchange markets exhibit co-moving and complex dynamics. In this paper we propose the entropy-based multivariate wavelet based approaches to analyze the multiscale characteristic in the multidimensional domain and improve further the Value at Risk estimation reliability. Wavelet analysis has been introduced to construct the entropy-based Multiscale Portfolio Value at Risk estimation algorithm to account for the multiscale dynamic correlation. The entropy measure has been proposed as the more effective measure with the error minimization principle to select the best basis when determining the wavelet families and the decomposition level to use. The empirical studies conducted in this paper have provided positive evidence as to the superior performance of the proposed approach, using the closely related Chinese Renminbi and European Euro exchange market.
Combined Power Quality Disturbances Recognition Using Wavelet Packet Entropies and S-Transform
Directory of Open Access Journals (Sweden)
Zhigang Liu
2015-08-01
Full Text Available Aiming at the combined power quality +disturbance recognition, an automated recognition method based on wavelet packet entropy (WPE and modified incomplete S-transform (MIST is proposed in this paper. By combining wavelet packet Tsallis singular entropy, energy entropy and MIST, a 13-dimension vector of different power quality (PQ disturbances including single disturbances and combined disturbances is extracted. Then, a ruled decision tree is designed to recognize the combined disturbances. The proposed method is tested and evaluated using a large number of simulated PQ disturbances and some real-life signals, which include voltage sag, swell, interruption, oscillation transient, impulsive transient, harmonics, voltage fluctuation and their combinations. In addition, the comparison of the proposed recognition approach with some existing techniques is made. The experimental results show that the proposed method can effectively recognize the single and combined PQ disturbances.
International Nuclear Information System (INIS)
Cao, Xiaobin
2011-01-01
The quasi-one-dimensional systems exhibit some unusual phenomenon, such as the Peierls instability, the pseudogap phenomena and the absence of a Fermi-Dirac distribution function line shape in the photoemission spectroscopy. Ever since the discovery of materials with highly anisotropic properties, it has been recognized that fluctuations play an important role above the three-dimensional phase transition. This regime where the precursor fluctuations are presented can be described by the so called fluctuating gap model (FGM) which was derived from the Froehlich Hamiltonian to study the low energy physics of the one-dimensional electron-phonon system. Not only is the FGM of great interest in the context of quasi-one-dimensional materials, liquid metal and spin waves above T c in ferromagnets, but also in the semiclassical approximation of superconductivity, it is possible to replace the original three-dimensional problem by a directional average over effectively one-dimensional problem which in the weak coupling limit is described by the FGM. In this work, we investigate the FGM in a wide temperature range with different statistics of the order parameter fluctuations. We derive a formally exact solution to this problem and calculate the density of states, the spectral function and the optical conductivity. In our calculation, we show that a Dyson singularity appears in the low energy density of states for Gaussian fluctuations in the commensurate case. In the incommensurate case, there is no such kind of singularity, and the zero frequency density of states varies differently as a function of the correlation lengths for different statistics of the order parameter fluctuations. Using the density of states we calculated with non-Gaussian order parameter fluctuations, we are able to calculate the static spin susceptibility which agrees with the experimental data very well. In the calculation of the spectral functions, we show that as the correlation increases, the quasi
Energy Technology Data Exchange (ETDEWEB)
Cao, Xiaobin
2011-01-15
The quasi-one-dimensional systems exhibit some unusual phenomenon, such as the Peierls instability, the pseudogap phenomena and the absence of a Fermi-Dirac distribution function line shape in the photoemission spectroscopy. Ever since the discovery of materials with highly anisotropic properties, it has been recognized that fluctuations play an important role above the three-dimensional phase transition. This regime where the precursor fluctuations are presented can be described by the so called fluctuating gap model (FGM) which was derived from the Froehlich Hamiltonian to study the low energy physics of the one-dimensional electron-phonon system. Not only is the FGM of great interest in the context of quasi-one-dimensional materials, liquid metal and spin waves above T{sub c} in ferromagnets, but also in the semiclassical approximation of superconductivity, it is possible to replace the original three-dimensional problem by a directional average over effectively one-dimensional problem which in the weak coupling limit is described by the FGM. In this work, we investigate the FGM in a wide temperature range with different statistics of the order parameter fluctuations. We derive a formally exact solution to this problem and calculate the density of states, the spectral function and the optical conductivity. In our calculation, we show that a Dyson singularity appears in the low energy density of states for Gaussian fluctuations in the commensurate case. In the incommensurate case, there is no such kind of singularity, and the zero frequency density of states varies differently as a function of the correlation lengths for different statistics of the order parameter fluctuations. Using the density of states we calculated with non-Gaussian order parameter fluctuations, we are able to calculate the static spin susceptibility which agrees with the experimental data very well. In the calculation of the spectral functions, we show that as the correlation increases, the
AdS/QCD duality and the quarkonia holographic information entropy
Braga, Nelson R. F.; da Rocha, Roldão
2018-01-01
Bottomonium and charmonium, representing quarkonia states, are scrutinized under the point of view of the information theory, in the AdS/QCD holographic setup. A logarithmic measure of information, comprised by the configurational entropy, is here employed to quantitatively study quarkonia radially excited S-wave states. The configurational entropy provides data regarding the relative dominance and the abundance of the bottomonium and charmonium states, whose underlying information is more compressed, in the Shannon's theory meaning. The derived configurational entropy, therefore, identifies the lower phenomenological prevalence of higher S-wave resonances and higher masses quarkonia in Nature.
Robust Discriminant Analysis Based on Nonparametric Maximum Entropy
He, Ran; Hu, Bao-Gang; Yuan, Xiao-Tong
In this paper, we propose a Robust Discriminant Analysis based on maximum entropy (MaxEnt) criterion (MaxEnt-RDA), which is derived from a nonparametric estimate of Renyi’s quadratic entropy. MaxEnt-RDA uses entropy as both objective and constraints; thus the structural information of classes is preserved while information loss is minimized. It is a natural extension of LDA from Gaussian assumption to any distribution assumption. Like LDA, the optimal solution of MaxEnt-RDA can also be solved by an eigen-decomposition method, where feature extraction is achieved by designing two Parzen probability matrices that characterize the within-class variation and the between-class variation respectively. Furthermore, MaxEnt-RDA makes use of high order statistics (entropy) to estimate the probability matrix so that it is robust to outliers. Experiments on toy problem , UCI datasets and face datasets demonstrate the effectiveness of the proposed method with comparison to other state-of-the-art methods.
Directory of Open Access Journals (Sweden)
Yingchao Zou
2015-06-01
Full Text Available In this paper, we propose a new entropy-optimized bivariate empirical mode decomposition (BEMD-based model for estimating portfolio value at risk (PVaR. It reveals and analyzes different components of the price fluctuation. These components are decomposed and distinguished by their different behavioral patterns and fluctuation range, by the BEMD model. The entropy theory has been introduced for the identification of the model parameters during the modeling process. The decomposed bivariate data components are calculated with the DCC-GARCH models. Empirical studies suggest that the proposed model outperforms the benchmark multivariate exponential weighted moving average (MEWMA and DCC-GARCH model, in terms of conventional out-of-sample performance evaluation criteria for the model accuracy.
From Maximum Entropy to Maximum Entropy Production: A New Approach
Directory of Open Access Journals (Sweden)
Nathaniel Virgo
2010-01-01
Full Text Available Evidence from climate science suggests that a principle of maximum thermodynamic entropy production can be used to make predictions about some physical systems. I discuss the general form of this principle and an inherent problem with it, currently unsolved by theoretical approaches: how to determine which system it should be applied to. I suggest a new way to derive the principle from statistical mechanics, and present a tentative solution to the system boundary problem. I discuss the need for experimental validation of the principle, and its impact on the way we see the relationship between thermodynamics and kinetics.
Analysis of water-level fluctuations in Wisconsin wells
Patterson, G.L.; Zaporozec, A.
1987-01-01
More than 60 percent of the residents of Wisconsin use ground water as their primary water source. Water supplies presently are abundant, but ground-water levels continually fluctuate in response to natural factors and human-related stresses. A better understanding of the magnitude, duration, and frequency of past fluctuations, and the factors controlling these fluctuations may help anticipate future changes in ground-water levels.
A possible human counterpart of the principle of increasing entropy
International Nuclear Information System (INIS)
Liang, Y.; An, K.N.; Yang, G.; Huang, J.P.
2014-01-01
It is well-known that the principle of increasing entropy holds for isolated natural systems that contain non-adaptive molecules. Here we present, for the first time, an experimental evidence for a possible human counterpart of the principle in an isolated social system that involves adaptive humans. Our work shows that the human counterpart is valid even though interactions among humans in social systems are distinctly different from those among molecules in natural systems. Thus, it becomes possible to understand social systems from this natural principle, at least to some extent.
On Thermodynamic Interpretation of Transfer Entropy
Directory of Open Access Journals (Sweden)
Don C. Price
2013-02-01
Full Text Available We propose a thermodynamic interpretation of transfer entropy near equilibrium, using a specialised Boltzmann’s principle. The approach relates conditional probabilities to the probabilities of the corresponding state transitions. This in turn characterises transfer entropy as a difference of two entropy rates: the rate for a resultant transition and another rate for a possibly irreversible transition within the system affected by an additional source. We then show that this difference, the local transfer entropy, is proportional to the external entropy production, possibly due to irreversibility. Near equilibrium, transfer entropy is also interpreted as the difference in equilibrium stabilities with respect to two scenarios: a default case and the case with an additional source. Finally, we demonstrated that such a thermodynamic treatment is not applicable to information flow, a measure of causal effect.
Curvature Entropy for Curved Profile Generation
Directory of Open Access Journals (Sweden)
Koichiro Sato
2012-03-01
Full Text Available In a curved surface design, the overall shape features that emerge from combinations of shape elements are important. However, controlling the features of the overall shape in curved profiles is difficult using conventional microscopic shape information such as dimension. Herein two types of macroscopic shape information, curvature entropy and quadrature curvature entropy, quantitatively represent the features of the overall shape. The curvature entropy is calculated by the curvature distribution, and represents the complexity of a shape (one of the overall shape features. The quadrature curvature entropy is an improvement of the curvature entropy by introducing a Markov process to evaluate the continuity of a curvature and to approximate human cognition of the shape. Additionally, a shape generation method using a genetic algorithm as a calculator and the entropy as a shape generation index is presented. Finally, the applicability of the proposed method is demonstrated using the side view of an automobile as a design example.
Large Field Inflation and Gravitational Entropy
DEFF Research Database (Denmark)
Kaloper, Nemanja; Kleban, Matthew; Lawrence, Albion
2016-01-01
species will lead to a violation of the covariant entropy bound at large $N$. If so, requiring the validity of the covariant entropy bound could limit the number of light species and their couplings, which in turn could severely constrain axion-driven inflation. Here we show that there is no such problem...... entropy of de Sitter or near-de Sitter backgrounds at leading order. Working in detail with $N$ scalar fields in de Sitter space, renormalized to one loop order, we show that the gravitational entropy automatically obeys the covariant entropy bound. Furthermore, while the axion decay constant is a strong...... in this light, and show that they are perfectly consistent with the covariant entropy bound. Thus, while quantum gravity might yet spoil large field inflation, holographic considerations in the semiclassical theory do not obstruct it....
Black hole entropy functions and attractor equations
International Nuclear Information System (INIS)
Lopes Cardoso, Gabriel; Wit, Bernard de; Mahapatra, Swapna
2007-01-01
The entropy and the attractor equations for static extremal black hole solutions follow from a variational principle based on an entropy function. In the general case such an entropy function can be derived from the reduced action evaluated in a near-horizon geometry. BPS black holes constitute special solutions of this variational principle, but they can also be derived directly from a different entropy function based on supersymmetry enhancement at the horizon. Both functions are consistent with electric/magnetic duality and for BPS black holes their corresponding OSV-type integrals give identical results at the semi-classical level. We clarify the relation between the two entropy functions and the corresponding attractor equations for N = 2 supergravity theories with higher-derivative couplings in four space-time dimensions. We discuss how non-holomorphic corrections will modify these entropy functions
Relative entropy and the RG flow
Energy Technology Data Exchange (ETDEWEB)
Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo [Centro Atómico Bariloche and CONICET,S.C. de Bariloche, Río Negro, R8402AGP (Argentina)
2017-03-16
We consider the relative entropy between vacuum states of two different theories: a conformal field theory (CFT), and the CFT perturbed by a relevant operator. By restricting both states to the null Cauchy surface in the causal domain of a sphere, we make the relative entropy equal to the difference of entanglement entropies. As a result, this difference has the positivity and monotonicity properties of relative entropy. From this it follows a simple alternative proof of the c-theorem in d=2 space-time dimensions and, for d>2, the proof that the coefficient of the area term in the entanglement entropy decreases along the renormalization group (RG) flow between fixed points. We comment on the regimes of convergence of relative entropy, depending on the space-time dimensions and the conformal dimension Δ of the perturbation that triggers the RG flow.
Magnetic fluctuations in heavy-fermion metals
DEFF Research Database (Denmark)
Mason, T.E.; Petersen, T.; Aeppli, G.
1995-01-01
, the nature of the antiferromagnetic order and magnetic fluctuations is qualitatively quite different. UPd2Al3 resembles a rare earth magnetic system with coupling of the 4f electrons to the conduction electrons manifested in a broadening of otherwise conventional spin wave excitations. This is in marked...
Unconventional entropy production in the presence of momentum-dependent forces
Kwon, Chulan; Yeo, Joonhyun; Lee, Hyun Keun; Park, Hyunggyu
2015-01-01
We investigate an unconventional nature of the entropy production (EP) in nonequilibrium systems with odd-parity variables that change signs under time reversal. We consider the Brownian motion of a particle in contact with a heat reservoir, where particle momentum is an odd-parity variable. In the presence of an {\\it external} momentum-dependent force, the EP transferred to environment is found {\\em not} equivalent to usual reservoir entropy change due to heat transfer. There appears an addi...
Quantum inflaton, primordial perturbations, and CMB fluctuations
International Nuclear Information System (INIS)
Cao, F.J.; Vega, H.J. de; Sanchez, N.G.
2004-01-01
We compute the primordial scalar, vector and tensor metric perturbations arising from quantum field inflation. Quantum field inflation takes into account the nonperturbative quantum dynamics of the inflaton consistently coupled to the dynamics of the (classical) cosmological metric. For chaotic inflation, the quantum treatment avoids the unnatural requirements of an initial state with all the energy in the zero mode. For new inflation it allows a consistent treatment of the explosive particle production due to spinodal instabilities. Quantum field inflation (under conditions that are the quantum analog of slow-roll) leads, upon evolution, to the formation of a condensate starting a regime of effective classical inflation. We compute the primordial perturbations taking the dominant quantum effects into account. The results for the scalar, vector and tensor primordial perturbations are expressed in terms of the classical inflation results. For a N-component field in a O(N) symmetric model, adiabatic fluctuations dominate while isocurvature or entropy fluctuations are negligible. The results agree with the current Wilkinson Microwave Anisotropy Probe observations and predict corrections to the power spectrum in classical inflation. Such corrections are estimated to be of the order of (m 2 /NH 2 ), where m is the inflaton mass and H the Hubble constant at the moment of horizon crossing. An upper estimate turns to be about 4% for the cosmologically relevant scales. This quantum field treatment of inflation provides the foundations to the classical inflation and permits to compute quantum corrections to it
Terrestrial Gravity Fluctuations
Directory of Open Access Journals (Sweden)
Jan Harms
2015-12-01
Full Text Available Different forms of fluctuations of the terrestrial gravity field are observed by gravity experiments. For example, atmospheric pressure fluctuations generate a gravity-noise foreground in measurements with super-conducting gravimeters. Gravity changes caused by high-magnitude earthquakes have been detected with the satellite gravity experiment GRACE, and we expect high-frequency terrestrial gravity fluctuations produced by ambient seismic fields to limit the sensitivity of ground-based gravitational-wave (GW detectors. Accordingly, terrestrial gravity fluctuations are considered noise and signal depending on the experiment. Here, we will focus on ground-based gravimetry. This field is rapidly progressing through the development of GW detectors. The technology is pushed to its current limits in the advanced generation of the LIGO and Virgo detectors, targeting gravity strain sensitivities better than 10^–23 Hz^–1/2 above a few tens of a Hz. Alternative designs for GW detectors evolving from traditional gravity gradiometers such as torsion bars, atom interferometers, and superconducting gradiometers are currently being developed to extend the detection band to frequencies below 1 Hz. The goal of this article is to provide the analytical framework to describe terrestrial gravity perturbations in these experiments. Models of terrestrial gravity perturbations related to seismic fields, atmospheric disturbances, and vibrating, rotating or moving objects, are derived and analyzed. The models are then used to evaluate passive and active gravity noise mitigation strategies in GW detectors, or alternatively, to describe their potential use in geophysics. The article reviews the current state of the field, and also presents new analyses especially with respect to the impact of seismic scattering on gravity perturbations, active gravity noise cancellation, and time-domain models of gravity perturbations from atmospheric and seismic point sources. Our
Terrestrial Gravity Fluctuations
Harms, Jan
2015-12-01
Different forms of fluctuations of the terrestrial gravity field are observed by gravity experiments. For example, atmospheric pressure fluctuations generate a gravity-noise foreground in measurements with super-conducting gravimeters. Gravity changes caused by high-magnitude earthquakes have been detected with the satellite gravity experiment GRACE, and we expect high-frequency terrestrial gravity fluctuations produced by ambient seismic fields to limit the sensitivity of ground-based gravitational-wave (GW) detectors. Accordingly, terrestrial gravity fluctuations are considered noise and signal depending on the experiment. Here, we will focus on ground-based gravimetry. This field is rapidly progressing through the development of GW detectors. The technology is pushed to its current limits in the advanced generation of the LIGO and Virgo detectors, targeting gravity strain sensitivities better than 10-23 Hz-1/2 above a few tens of a Hz. Alternative designs for GW detectors evolving from traditional gravity gradiometers such as torsion bars, atom interferometers, and superconducting gradiometers are currently being developed to extend the detection band to frequencies below 1 Hz. The goal of this article is to provide the analytical framework to describe terrestrial gravity perturbations in these experiments. Models of terrestrial gravity perturbations related to seismic fields, atmospheric disturbances, and vibrating, rotating or moving objects, are derived and analyzed. The models are then used to evaluate passive and active gravity noise mitigation strategies in GW detectors, or alternatively, to describe their potential use in geophysics. The article reviews the current state of the field, and also presents new analyses especially with respect to the impact of seismic scattering on gravity perturbations, active gravity noise cancellation, and time-domain models of gravity perturbations from atmospheric and seismic point sources. Our understanding of
Curvature Entropy for Curved Profile Generation
Ujiie, Yoshiki; Kato, Takeo; Sato, Koichiro; Matsuoka, Yoshiyuki
2012-01-01
In a curved surface design, the overall shape features that emerge from combinations of shape elements are important. However, controlling the features of the overall shape in curved profiles is difficult using conventional microscopic shape information such as dimension. Herein two types of macroscopic shape information, curvature entropy and quadrature curvature entropy, quantitatively represent the features of the overall shape. The curvature entropy is calculated by the curvature distribu...
Quantitative Entropy Study of Language Complexity
Xie, R. R.; Deng, W. B.; 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 popul...
On the minimal entropy martingale measure
Grandits, Peter; Rheinländer, Thorsten
2002-01-01
Let X be a locally bounded semimartingale. Using the theory of \\textit{BMO}-martingales we give a sufficient criterion for a martingale measure for X to minimize relative entropy among all martingale measures. This is applied to prove convergence of the q-optimal martingale measure to the minimal entropy martingale measure in entropy for $q\\downarrow 1$ under the assumption that X is continuous and that the density process of some equivalent martingale measure satisfies a reverse $\\mathit{LLo...
Permutation Entropy: New Ideas and Challenges
Directory of Open Access Journals (Sweden)
Karsten Keller
2017-03-01
Full Text Available Over recent years, some new variants of Permutation entropy have been introduced and applied to EEG analysis, including a conditional variant and variants using some additional metric information or being based on entropies that are different from the Shannon entropy. In some situations, it is not completely clear what kind of information the new measures and their algorithmic implementations provide. We discuss the new developments and illustrate them for EEG data.
Triadic conceptual structure of the maximum entropy approach to evolution.
Herrmann-Pillath, Carsten; Salthe, Stanley N
2011-03-01
Many problems in evolutionary theory are cast in dyadic terms, such as the polar oppositions of organism and environment. We argue that a triadic conceptual structure offers an alternative perspective under which the information generating role of evolution as a physical process can be analyzed, and propose a new diagrammatic approach. Peirce's natural philosophy was deeply influenced by his reception of both Darwin's theory and thermodynamics. Thus, we elaborate on a new synthesis which puts together his theory of signs and modern Maximum Entropy approaches to evolution in a process discourse. Following recent contributions to the naturalization of Peircean semiosis, pointing towards 'physiosemiosis' or 'pansemiosis', we show that triadic structures involve the conjunction of three different kinds of causality, efficient, formal and final. In this, we accommodate the state-centered thermodynamic framework to a process approach. We apply this on Ulanowicz's analysis of autocatalytic cycles as primordial patterns of life. This paves the way for a semiotic view of thermodynamics which is built on the idea that Peircean interpretants are systems of physical inference devices evolving under natural selection. In this view, the principles of Maximum Entropy, Maximum Power, and Maximum Entropy Production work together to drive the emergence of information carrying structures, which at the same time maximize information capacity as well as the gradients of energy flows, such that ultimately, contrary to Schrödinger's seminal contribution, the evolutionary process is seen to be a physical expression of the Second Law. Copyright © 2010 Elsevier Ireland Ltd. All rights reserved.
Nonextensive entropies derived from Gauss' principle
International Nuclear Information System (INIS)
Wada, Tatsuaki
2011-01-01
Gauss' principle in statistical mechanics is generalized for a q-exponential distribution in nonextensive statistical mechanics. It determines the associated stochastic and statistical nonextensive entropies which satisfy Greene-Callen principle concerning on the equivalence between microcanonical and canonical ensembles. - Highlights: → Nonextensive entropies are derived from Gauss' principle and ensemble equivalence. → Gauss' principle is generalized for a q-exponential distribution. → I have found the condition for satisfying Greene-Callen principle. → The associated statistical q-entropy is found to be normalized Tsallis entropy.
All Inequalities for the Relative Entropy
Ibinson, Ben; Linden, Noah; Winter, Andreas
2007-01-01
The relative entropy of two n-party quantum states is an important quantity exhibiting, for example, the extent to which the two states are different. The relative entropy of the states formed by reducing two n-party states to a smaller number m of parties is always less than or equal to the relative entropy of the two original n-party states. This is the monotonicity of relative entropy. Using techniques from convex geometry, we prove that monotonicity under restrictions is the only general inequality satisfied by quantum relative entropies. In doing so we make a connection to secret sharing schemes with general access structures: indeed, it turns out that the extremal rays of the cone defined by monotonicity are populated by classical secret sharing schemes. A surprising outcome is that the structure of allowed relative entropy values of subsets of multiparty states is much simpler than the structure of allowed entropy values. And the structure of allowed relative entropy values (unlike that of entropies) is the same for classical probability distributions and quantum states.
Canonical entropy of higher-dimensional Reissner-Nordstroem Black hole
International Nuclear Information System (INIS)
Zhang, L.-C.; Li, H.-F.; Zhao, R.
2007-01-01
Recently, Hawking radiation of the black hole has been studied using the tunnel effect method. It is found the radiation spectrum of the black hole is not a strictly pure thermal spectrum. How the departure from pure thermal spectrum affects the entropy? This is a very interesting problem. In this paper, we calculate the partition function by energy spectrum obtained by tunnel effect. Using the relation between the partition function and entropy, we derive the expression of entropy the general charged black hole. In our calculation, we not only consider the connection to the black hole entropy due to fluctuation of energy but also consider the effect of the change of the black hole charges on entropy. We discuss higher-dimensional Reissner-Nordstroem black hole and obtain the relation among the lower limit of energy value, the charges and energy of the black hole. We derive that higher-dimensional Reissner-Nordstroem black hole cannot approach the extreme black hole by changing its charges. (authors)
Giauque, Alexis; Birbaud, Anne Laure; Pitsch, Heinz
2007-11-01
Combustion noise is one of the main noise sources of aircraft auxiliary power unit gas turbine engines, and with the better understanding of jet and fan noise, combustion generated noise is also becoming increasingly important for the the main aircraft engines. Combustion generated noise comes from two major sources: direct noise, produced by the unsteady heat release, and indirect noise, produced by entropy fluctuations passing through pressure gradients in the turbine. Two approaches are considered to investigate the fundamental aspects of indirect noise. For the first, high order fully compressible simulations of a modulated entropy wave passing through a converging diverging nozzle are performed. The second approach uses a flow solver based on Goldstein's analogy in order to propagate the acoustic and entropy waves using the perturbed velocity, pressure, and entropy components coming from low Mach number or fully compressible calculations. The capability of these two methods to predict the acoustics produced by the modulated entropy wave are finally discussed. Numerical results are compared to the experiment performed by Bake et al. (GT2005-69029, ASME Turbo Expo 2005).
Topological entropy of autonomous flows
Energy Technology Data Exchange (ETDEWEB)
Badii, R. [Paul Scherrer Inst. (PSI), Villigen (Switzerland)
1997-06-01
When studying fluid dynamics, especially in a turbulent regime, it is crucial to estimate the number of active degrees of freedom or of localized structures in the system. The topological entropy quantifies the exponential growth of the number of `distinct` orbits in a dynamical system as a function of their length, in the infinite spatial resolution limit. Here, I illustrate a novel method for its evaluation, which extends beyond maps and is applicable to any system, including autonomous flows: these are characterized by lack of a definite absolute time scale for the orbit lengths. (author) 8 refs.
Tsallis Entropy for Geometry Simplification
Directory of Open Access Journals (Sweden)
Miguel Chover
2011-09-01
Full Text Available This paper presents a study and a comparison of the use of different information-theoretic measures for polygonal mesh simplification. Generalized measures from Information Theory such as Havrda–Charvát–Tsallis entropy and mutual information have been applied. These measures have been used in the error metric of a surfaces implification algorithm. We demonstrate that these measures are useful for simplifying three-dimensional polygonal meshes. We have also compared these metrics with the error metrics used in a geometry-based method and in an image-driven method. Quantitative results are presented in the comparison using the root-mean-square error (RMSE.
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)=-∑_{i}p_{i}logp_{i}. 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 S_{EXT} for extensive entropy, S_{IT} for the source information rate in information theory, and S_{MEP} 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.
Entropy of the electroencephalogram as applied in the M-Entropy S ...
African Journals Online (AJOL)
Background: It has been suggested that spectral entropy of the electroencephalogram as applied in the M-Entropy S/5TM Module (GE Healthcare) does not detect the effects of nitrous oxide (N2O). The aim of this study was to investigate the effect on entropy by graded increases in N2O concentrations in the presence of a ...
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.
Monotonicity of the von Neumann entropy expressed as a function of R\\'enyi entropies
Fannes, Mark
2013-01-01
The von Neumann entropy of a density matrix of dimension d, expressed in terms of the first d-1 integer order R\\'enyi entropies, is monotonically increasing in R\\'enyi entropies of even order and decreasing in those of odd order.
Entropy Stable Summation-by-Parts Formulations for Compressible Computational Fluid Dynamics
Carpenter, M.H.
2016-11-09
A systematic approach based on a diagonal-norm summation-by-parts (SBP) framework is presented for implementing entropy stable (SS) formulations of any order for the compressible Navier–Stokes equations (NSE). These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy equality for smooth problems. They are also valid for discontinuous flows provided sufficient dissipation is added at shocks and discontinuities to satisfy an entropy inequality. Admissible SBP operators include all centred diagonal-norm finite-difference (FD) operators and Legendre spectral collocation-finite element methods (LSC-FEM). Entropy stable multiblock FD and FEM operators follows immediately via nonlinear coupling operators that ensure conservation, accuracy and preserve the interior entropy estimates. Nonlinearly stable solid wall boundary conditions are also available. Existing SBP operators that lack a stability proof (e.g. weighted essentially nonoscillatory) may be combined with an entropy stable operator using a comparison technique to guarantee nonlinear stability of the pair. All capabilities extend naturally to a curvilinear form of the NSE provided that the coordinate mappings satisfy a geometric conservation law constraint. Examples are presented that demonstrate the robustness of current state-of-the-art entropy stable SBP formulations.
The Entropy of Words—Learnability and Expressivity across More than 1000 Languages
Directory of Open Access Journals (Sweden)
Christian Bentz
2017-06-01
Full Text Available The choice associated with words is a fundamental property of natural languages. It lies at the heart of quantitative linguistics, computational linguistics and language sciences more generally. Information theory gives us tools at hand to measure precisely the average amount of choice associated with words: the word entropy. Here, we use three parallel corpora, encompassing ca. 450 million words in 1916 texts and 1259 languages, to tackle some of the major conceptual and practical problems of word entropy estimation: dependence on text size, register, style and estimation method, as well as non-independence of words in co-text. We present two main findings: Firstly, word entropies display relatively narrow, unimodal distributions. There is no language in our sample with a unigram entropy of less than six bits/word. We argue that this is in line with information-theoretic models of communication. Languages are held in a narrow range by two fundamental pressures: word learnability and word expressivity, with a potential bias towards expressivity. Secondly, there is a strong linear relationship between unigram entropies and entropy rates. The entropy difference between words with and without co-textual information is narrowly distributed around ca. three bits/word. In other words, knowing the preceding text reduces the uncertainty of words by roughly the same amount across languages of the world.
Directory of Open Access Journals (Sweden)
Elías Gómez Macías
2006-01-01
Full Text Available Partiendo de óxido de magnesio comercial se preparó una suspensión acuosa, la cual se secó y calcinó para conferirle estabilidad térmica. El material, tanto fresco como usado, se caracterizó mediante DRX, área superficial BET y SEM-EPMA. El catalizador mostró una matriz de MgO tipo periclasa con CaO en la superficie. Las pruebas de actividad catalítica se efectuaron en lecho fijo empacado con partículas obtenidas mediante prensado, trituración y clasificación del material. El flujo de reactivos consistió en mezclas gas natural-aire por debajo del límite inferior de inflamabilidad. Para diferentes flujos y temperaturas de entrada de la mezcla reactiva, se midieron las concentraciones de CH4, CO2 y CO en los gases de combustión con un analizador de gases tipo infrarrojo no dispersivo (NDIR. Para alcanzar conversión total de metano se requirió aumentar la temperatura de entrada al lecho a medida que se incrementó el flujo de gases reaccionantes. Los resultados obtenidos permiten desarrollar un sistema de combustión catalítica de bajo costo con un material térmicamente estable, que promueva la alta eficiencia en la combustión de gas natural y elimine los problemas de estabilidad, seguridad y de impacto ambiental negativo inherentes a los procesos de combustión térmica convencional.
Clausius entropy for arbitrary bifurcate null surfaces
International Nuclear Information System (INIS)
Baccetti, Valentina; Visser, Matt
2014-01-01
Jacobson’s thermodynamic derivation of the Einstein equations was originally applied only to local Rindler horizons. But at least some parts of that construction can usefully be extended to give meaningful results for arbitrary bifurcate null surfaces. As presaged in Jacobson’s original article, this more general construction sharply brings into focus the questions: is entropy objectively ‘real’? Or is entropy in some sense subjective and observer-dependent? These innocent questions open a Pandora’s box of often inconclusive debate. A consensus opinion, though certainly not universally held, seems to be that Clausius entropy (thermodynamic entropy, defined via a Clausius relation dS=đQ/T) should be objectively real, but that the ontological status of statistical entropy (Shannon or von Neumann entropy) is much more ambiguous, and much more likely to be observer-dependent. This question is particularly pressing when it comes to understanding Bekenstein entropy (black hole entropy). To perhaps further add to the confusion, we shall argue that even the Clausius entropy can often be observer-dependent. In the current article we shall conclusively demonstrate that one can meaningfully assign a notion of Clausius entropy to arbitrary bifurcate null surfaces—effectively defining a ‘virtual Clausius entropy’ for arbitrary ‘virtual (local) causal horizons’. As an application, we see that we can implement a version of the generalized second law (GSL) for this virtual Clausius entropy. This version of GSL can be related to certain (nonstandard) integral variants of the null energy condition. Because the concepts involved are rather subtle, we take some effort in being careful and explicit in developing our framework. In future work we will apply this construction to generalize Jacobson’s derivation of the Einstein equations. (paper)
Ward, Joshua M; Gorenstein, Nina M; Tian, Jianhua; Martin, Stephen F; Post, Carol Beth
2010-08-18
NMR spectroscopy and molecular dynamics (MD) simulations were used to probe the structure and dynamics of complexes of three phosphotyrosine-derived peptides with the Src SH2 domain in an effort to uncover a structural explanation for enthalpy-entropy compensation observed in the binding thermodynamics. The series of phosphotyrosine peptide derivatives comprises the natural pYEEI Src SH2 ligand, a constrained mimic, in which the phosphotyrosine (pY) residue is preorganized in the bound conformation for the purpose of gaining an entropic advantage to binding, and a flexible analogue of the constrained mimic. The expected gain in binding entropy of the constrained mimic was realized; however, a balancing loss in binding enthalpy was also observed that could not be rationalized from the crystallographic structures. We examined protein dynamics to evaluate whether the observed enthalpic penalty might be the result of effects arising from altered motions in the complex. (15)N-relaxation studies and positional fluctuations from molecular dynamics indicate that the main-chain dynamics of the protein show little variation among the three complexes. Root mean squared (rms) coordinate deviations vary by less than 1.5 A for all non-hydrogen atoms for the crystal structures and in the ensemble average structures calculated from the simulations. In contrast to this striking similarity in the structures and dynamics, there are a number of large chemical shift differences from residues across the binding interface, but particularly from key Src SH2 residues that interact with pY, the "hot spot" residue, which contributes about one-half of the binding free energy. Rank-order correlations between chemical shifts and ligand binding enthalpy for several pY-binding residues, coupled with available mutagenesis and calorimetric data, suggest that subtle structural perturbations (enthalpy, leading to the observed enthalpy-entropy compensation. We find no evidence to support the premise
Fluctuations in quantum devices
Directory of Open Access Journals (Sweden)
H.Haken
2004-01-01
Full Text Available Logical gates can be formalized by Boolean algebra whose elementary operations can be realized by devices that employ the interactions of macroscopic numbers of elementary excitations such as electrons, holes, photons etc. With increasing miniaturization to the nano scale and below, quantum fluctuations become important and can no longer be ignored. Based on Heisenberg equations of motion for the creation and annihilation operators of elementary excitations, I determine the noise sources of composite quantum systems.
Physics of fashion fluctuations
Donangelo, R.; Hansen, A.; Sneppen, K.; Souza, S. R.
2000-12-01
We consider a market where many agents trade different types of products with each other. We model development of collective modes in this market, and quantify these by fluctuations that scale with time with a Hurst exponent of about 0.7. We demonstrate that individual products in the model occasionally become globally accepted means of exchange, and simultaneously become very actively traded. Thus collective features similar to money spontaneously emerge, without any a priori reason.
International Nuclear Information System (INIS)
Nizami, Lance
2010-01-01
Norwich's Entropy Theory of Perception (1975-present) is a general theory of perception, based on Shannon's Information Theory. Among many bold claims, the Entropy Theory presents a truly astounding result: that Stevens' Law with an Index of 1, an empirical power relation of direct proportionality between perceived taste intensity and stimulus concentration, arises from theory alone. Norwich's theorizing starts with several extraordinary hypotheses. First, 'multiple, parallel receptor-neuron units' without collaterals 'carry essentially the same message to the brain', i.e. the rate-level curves are identical. Second, sensation is proportional to firing rate. Third, firing rate is proportional to the taste receptor's 'resolvable uncertainty'. Fourth, the 'resolvable uncertainty' is obtained from Shannon's Information Theory. Finally, 'resolvable uncertainty' also depends upon the microscopic thermodynamic density fluctuation of the tasted solute. Norwich proves that density fluctuation is density variance, which is proportional to solute concentration, all based on the theory of fluctuations in fluid composition from Tolman's classic physics text, 'The Principles of Statistical Mechanics'. Altogether, according to Norwich, perceived taste intensity is theoretically proportional to solute concentration. Such a universal rule for taste, one that is independent of solute identity, personal physiological differences, and psychophysical task, is truly remarkable and is well-deserving of scrutiny. Norwich's crucial step was the derivation of density variance. That step was meticulously reconstructed here. It transpires that the appropriate fluctuation is Tolman's mean-square fractional density fluctuation, not density variance as used by Norwich. Tolman's algebra yields a 'Stevens Index' of -1 rather than 1. As 'Stevens Index' empirically always exceeds zero, the Index of -1 suggests that it is risky to infer psychophysical laws of sensory response from information theory
Fractal Tempo Fluctuation and Pulse Prediction.
Rankin, Summer K; Large, Edward W; Fink, Philip W
2009-06-01
WE INVESTIGATED PEOPLES' ABILITY TO ADAPT TO THE fluctuating tempi of music performance. In Experiment 1, four pieces from different musical styles were chosen, and performances were recorded from a skilled pianist who was instructed to play with natural expression. Spectral and rescaled range analyses on interbeat interval time-series revealed long-range (1/ f type) serial correlations and fractal scaling in each piece. Stimuli for Experiment 2 included two of the performances from Experiment 1, with mechanical versions serving as controls. Participants tapped the beat at ¼- and ⅛-note metrical levels, successfully adapting to large tempo fluctuations in both performances. Participants predicted the structured tempo fluctuations, with superior performance at the ¼-note level. Thus, listeners may exploit long-range correlations and fractal scaling to predict tempo changes in music.
International Nuclear Information System (INIS)
Diaz-Mendez, S.E.; Sierra-Grajeda, J.M.T.; Hernandez-Guerrero, A.; Rodriguez-Lelis, J.M.
2013-01-01
Generally speaking, an ecosystem is seen as a complex set, it is composed by different biotic and abiotic parts. Naturally, each part has specifics functions related with mass and energy, those functions have influence between the parts directly and indirectly, and these functions are subjected to the basic laws of thermodynamics. If each part of the ecosystem is taken as thermodynamics system its entropy generation could be evaluated, then the total entropy generation of the ecosystem must be sum of the entropy generation in each part, to be in accordance with the Gouy-Stodola theorem. With this in mind, in this work an environmental indicator, for any kind of ecosystems, can be determined as a function of the ratio of total entropy generation for reference state, for instance a healthy forest; and the entropy generation of new different state of the same ecosystem can take, for instance a deforestation. Thus, thermodynamics concepts are applied to study the eutrophication of freshwater ecosystems; the strategy is based on techniques that integrate assumptions of the methodology of entropy generation inside ecosystems. The results show that if the amount of entropy generation is small respect a reference state; the sustainability of the ecosystem will be greater. - Highlights: • We estimate an environmental impact indicator using the concept of entropy generation. • It can be a useful tool for assessing the environmental impacts of the society over the environment. • It can be a useful tool to compare new technologies and improve their efficiencies even more. • It can help for a better understanding of the concept of entropy and its role among various classes of processes. • It can help to reduce environmental concerns and increase the sustainability of the planet
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…
Entropy change of biological dynamics in COPD
Cao, Zhixin; Sun, Baoqing; Lo, Iek Long; Liu, Tzu-Ming; Zheng, Jun; Sun, Shixue; Shi, Yan; Zhang, Xiaohua Douglas
2017-01-01
In this century, the rapid development of large data storage technologies, mobile network technology, and portable medical devices makes it possible to measure, record, store, and track analysis of large amount of data in human physiological signals. Entropy is a key metric for quantifying the irregularity contained in physiological signals. In this review, we focus on how entropy changes in various physiological signals in COPD. Our review concludes that the entropy change relies on the types of physiological signals under investigation. For major physiological signals related to respiratory diseases, such as airflow, heart rate variability, and gait variability, the entropy of a patient with COPD is lower than that of a healthy person. However, in case of hormone secretion and respiratory sound, the entropy of a patient is higher than that of a healthy person. For mechanomyogram signal, the entropy increases with the increased severity of COPD. This result should give valuable guidance for the use of entropy for physiological signals measured by wearable medical device as well as for further research on entropy in COPD. PMID:29066881
Invariant of dynamical systems: A generalized entropy
International Nuclear Information System (INIS)
Meson, A.M.; Vericat, F.
1996-01-01
In this work the concept of entropy of a dynamical system, as given by Kolmogorov, is generalized in the sense of Tsallis. It is shown that this entropy is an isomorphism invariant, being complete for Bernoulli schemes. copyright 1996 American Institute of Physics
Entropies, Partitionings and Heart Rate Variability
Czech Academy of Sciences Publication Activity Database
Paluš, Milan; Zebrowski, J.
2009-01-01
Roč. 51, č. 2 (2009), s. 65-72 ISSN 0001-7604 Institutional research plan: CEZ:AV0Z10300504 Keywords : coarse-grained entropy rate * HR variability * entropy Subject RIV: BB - Applied Statistics, Operational Research http://www.activitas.org/index.php/nervosa/article/view/25
Quantum aspects of black hole entropy
Indian Academy of Sciences (India)
Quantum corrections to the semiclassical Bekenstein–Hawking area law for black hole entropy, obtained within the quantum geometry framework, are treated in some detail. Their ramiﬁcation for the holographic entropy bound for bounded stationary spacetimes is discussed. Four dimensional supersymmetric extremal black ...
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…
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…
Problems in black-hole entropy interpretation
International Nuclear Information System (INIS)
Liberati, S.
1997-01-01
In this work some proposals for black-hole entropy interpretation are exposed and investigated. In particular, the author will firstly consider the so-called 'entanglement entropy' interpretation, in the framework of the brick wall model and the divergence problem arising in the one-loop calculations of various thermodynamical quantities, like entropy, internal energy and heat capacity. It is shown that the assumption of equality of entanglement entropy and Bekenstein-Hawking one appears to give inconsistent results. These will be a starting point for a different interpretation of black.hole entropy based on peculiar topological structures of manifolds with 'intrinsic' thermodynamical features. It is possible to show an exact relation between black-hole gravitational entropy and topology of these Euclidean space-times. the expression for the Euler characteristic, through the Gauss-Bonnet integral, and the one for entropy for gravitational instantons are proposed in a form which makes the relation between these self-evident. Using this relation he propose a generalization of the Bekenstein-Hawking entropy in which the former and Euler characteristic are related in the equation S = χA / 8. Finally, he try to expose some conclusions and hypotheses about possible further development of this research
Towards operational interpretations of generalized entropies
DEFF Research Database (Denmark)
Topsøe, Flemming
Operationelle fortolkninger af nye entropimål, f.eks. af Tsallis entropi, angives med udgangspunkt i erkendelsesteoretiske betragtninger.......Operationelle fortolkninger af nye entropimål, f.eks. af Tsallis entropi, angives med udgangspunkt i erkendelsesteoretiske betragtninger....
Quantum aspects of black hole entropy
Indian Academy of Sciences (India)
Abstract. 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.
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…
Quantum horizon fluctuations of an evaporating black hole
International Nuclear Information System (INIS)
Roura, Albert
2007-01-01
The quantum fluctuations of a black hole spacetime are studied within a low-energy effective field theory approach to quantum gravity. Our approach accounts for both intrinsic metric fluctuations and those induced by matter fields interacting with the gravitational field. Here we will concentrate on spherically symmetric fluctuations of the black hole horizon. Our results suggest that for a sufficiently massive evaporating black hole, fluctuations can accumulate over time and become significant well before reaching Planckian scales. In addition, we provide the sketch of a proof that the symmetrized two-point function of the stress-tensor operator smeared over a null hypersurface is actually divergent and discuss the implications for the analysis of horizon fluctuations. Finally, a natural way to probe quantum metric fluctuations near the horizon is briefly described
Minimum Entropy-Based Cascade Control for Governing Hydroelectric Turbines
Directory of Open Access Journals (Sweden)
Mifeng Ren
2014-06-01
Full Text Available In this paper, an improved cascade control strategy is presented for hydroturbine speed governors. Different from traditional proportional-integral-derivative (PID control and model predictive control (MPC strategies, the performance index of the outer controller is constructed by integrating the entropy and mean value of the tracking error with the constraints on control energy. The inner controller is implemented by a proportional controller. Compared with the conventional PID-P and MPC-P cascade control methods, the proposed cascade control strategy can effectively decrease fluctuations of hydro-turbine speed under non-Gaussian disturbance conditions in practical hydropower plants. Simulation results show the advantages of the proposed cascade control method.
Entropy corresponding to the interior of a Schwarzschild black hole
Directory of Open Access Journals (Sweden)
Bibhas Ranjan Majhi
2017-07-01
Full Text Available Interior volume within the horizon of a black hole is a non-trivial concept which turns out to be very important to explain several issues in the context of quantum nature of black hole. Here we show that the entropy, contained by the maximum interior volume for massless modes, is proportional to the Bekenstein–Hawking expression. The proportionality constant is less than unity implying the horizon bears maximum entropy than that by the interior. The derivation is very systematic and free of any ambiguity. To do so the precise value of the energy of the modes, living in the interior, is derived by constraint analysis. Finally, the implications of the result are discussed.
Entropy corresponding to the interior of a Schwarzschild black hole
Majhi, Bibhas Ranjan; Samanta, Saurav
2017-07-01
Interior volume within the horizon of a black hole is a non-trivial concept which turns out to be very important to explain several issues in the context of quantum nature of black hole. Here we show that the entropy, contained by the maximum interior volume for massless modes, is proportional to the Bekenstein-Hawking expression. The proportionality constant is less than unity implying the horizon bears maximum entropy than that by the interior. The derivation is very systematic and free of any ambiguity. To do so the precise value of the energy of the modes, living in the interior, is derived by constraint analysis. Finally, the implications of the result are discussed.
The Entropy Production Distribution in Non-Markovian Thermal Baths
Directory of Open Access Journals (Sweden)
José Inés Jiménez-Aquino
2014-03-01
Full Text Available In this work we study the distribution function for the total entropy production of a Brownian particle embedded in a non-Markovian thermal bath. The problem is studied in the overdamped approximation of the generalized Langevin equation, which accounts for a friction memory kernel characteristic of a Gaussian colored noise. The problem is studied in two physical situations: (i when the particle in the harmonic trap is subjected to an arbitrary time-dependent driving force; and (ii when the minimum of the harmonic trap is arbitrarily dragged out of equilibrium by an external force. By assuming a natural non Markovian canonical distribution for the initial conditions, the distribution function for the total entropy production becomes a non Gaussian one. Its characterization is then given through the first three cumulants.
Study on spectral entropy of two-phase flow density wave instability
International Nuclear Information System (INIS)
Zhang Zuoyi
1992-05-01
By using mathematic proof, spectral entropy calculations for simple examples and a practical two-phase flow system, it has been proved that under the same stochastic input, the output spectral entropy of a stable linear system is in maximum, while for an unstable linear system, its entropy is in relative lower level. Because the spectral entropy describes the output uncertainty of a system and the second law of thermodynamics rules the direction of natural tendency, the spontaneous process can develop only toward the direction of uncertainty increasing, and the opposite is impossible. It seems that the physical mechanism of the stability of a system can be explained as following: Any deviation from its original state of a stable system will reduce the spectral entropy and violate the natural tendency so that the system will return to original state. On the contrary, the deviation from its original state of an unstable system will increase the spectral entropy that will enhance the deviation and the system will be further away from its original state
Energy Technology Data Exchange (ETDEWEB)
Pourhassan, Behnam [Damghan University, School of Physics, Damghan (Iran, Islamic Republic of); Faizal, Mir [University of British Columbia-Okanagan, Irving K. Barber School of Arts and Sciences, Kelowna, BC (Canada); University of Lethbridge, Department of Physics and Astronomy, Lethbridge, AB (Canada)
2017-02-15
In this paper, we analyze the effects of thermal fluctuations on a STU black hole. We observe that these thermal fluctuations can affect the stability of a STU black hole. We will also analyze the effects of these thermal fluctuations on the thermodynamics of a STU black hole. Furthermore, in the Jacobson formalism such a modification will produce a deformation of the geometry of the STU black hole. Hence, we use the AdS/CFT correspondence to analyze the effect of such a deformation on the dual quark-gluon plasma. So, we explicitly analyze the effect of thermal fluctuations on the shear viscosity to entropy ratio in the quark-gluon plasma, and we analyze the effects of thermal fluctuations on this ratio. (orig.)
International Nuclear Information System (INIS)
Anttila, Jani; Annila, Arto
2011-01-01
A course of a game is formulated as a physical process that will consume free energy in the least time. Accordingly, the rate of entropy increase is the payoff function that will subsume all forms of free energy that motivate diverse decisions. Also other concepts of game theory are related to their profound physical counterparts. When the physical portrayal of behavior is mathematically analyzed, the course of a game is found to be inherently unpredictable because each move affects motives in the future. Despite the non-holonomic character of the natural process, the objective of consuming free energy in the least time will direct an extensive-form game toward a Lyapunov-stable point that satisfies the minimax theorem. -- Highlights: → Behavior in the context of game theory is described as a natural process. → The rate of entropy increase, derived from statistical physics of open systems, is identified as the payoff function. → Entropy as the payoff function also clarifies motives of collaboration and subjective nature of decision making. → Evolutionary equation of motion that accounts for the course of a game is inherently unpredictable.
Black hole entropy, curved space and monsters
International Nuclear Information System (INIS)
Hsu, Stephen D.H.; Reeb, David
2008-01-01
We investigate the microscopic origin of black hole entropy, in particular the gap between the maximum entropy of ordinary matter and that of black holes. Using curved space, we construct configurations with entropy greater than the area A of a black hole of equal mass. These configurations have pathological properties and we refer to them as monsters. When monsters are excluded we recover the entropy bound on ordinary matter S 3/4 . This bound implies that essentially all of the microstates of a semiclassical black hole are associated with the growth of a slightly smaller black hole which absorbs some additional energy. Our results suggest that the area entropy of black holes is the logarithm of the number of distinct ways in which one can form the black hole from ordinary matter and smaller black holes, but only after the exclusion of monster states
The role of entropy in magnetotail dynamics
Energy Technology Data Exchange (ETDEWEB)
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.
What is the entropy of the universe?
Energy Technology Data Exchange (ETDEWEB)
Frampton, Paul H [Department of Physics and Astronomy, UNC-Chapel Hill, NC 27599 (United States); Hsu, Stephen D H; Reeb, David [Institute of Theoretical Science, University of Oregon, Eugene, OR 97403 (United States); Kephart, Thomas W, E-mail: frampton@physics.unc.ed, E-mail: hsu@uoregon.ed, E-mail: tom.kephart@gmail.co, E-mail: dreeb@uoregon.ed [Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235 (United States)
2009-07-21
Standard calculations suggest that the entropy of our universe is dominated by black holes, whose entropy is of order their area in Planck units, although they comprise only a tiny fraction of its total energy. Statistical entropy is the logarithm of the number of microstates consistent with the observed macroscopic properties of a system, hence a measure of uncertainty about its precise state. Therefore, assuming unitarity in black hole evaporation, the standard results suggest that the largest uncertainty in the future quantum state of the universe is due to the Hawking radiation from evaporating black holes. However, the entropy of the matter precursors to astrophysical black holes is enormously less than that given by area entropy. If unitarity relates the future radiation states to the black hole precursor states, then the standard results are highly misleading, at least for an observer that can differentiate the individual states of the Hawking radiation.
Entropy of black holes with multiple horizons
He, Yun; Ma, Meng-Sen; Zhao, Ren
2018-05-01
We examine the entropy of black holes in de Sitter space and black holes surrounded by quintessence. These black holes have multiple horizons, including at least the black hole event horizon and a horizon outside it (cosmological horizon for de Sitter black holes and "quintessence horizon" for the black holes surrounded by quintessence). Based on the consideration that the two horizons are not independent each other, we conjecture that the total entropy of these black holes should not be simply the sum of entropies of the two horizons, but should have an extra term coming from the correlations between the two horizons. Different from our previous works, in this paper we consider the cosmological constant as the variable and employ an effective method to derive the explicit form of the entropy. We also try to discuss the thermodynamic stabilities of these black holes according to the entropy and the effective temperature.
Constant conditional entropy and related hypotheses
International Nuclear Information System (INIS)
Ferrer-i-Cancho, Ramon; Dębowski, Łukasz; Moscoso del Prado Martín, Fermín
2013-01-01
Constant entropy rate (conditional entropies must remain constant as the sequence length increases) and uniform information density (conditional probabilities must remain constant as the sequence length increases) are two information theoretic principles that are argued to underlie a wide range of linguistic phenomena. Here we revise the predictions of these principles in the light of Hilberg’s law on the scaling of conditional entropy in language and related laws. We show that constant entropy rate (CER) and two interpretations for uniform information density (UID), full UID and strong UID, are inconsistent with these laws. Strong UID implies CER but the reverse is not true. Full UID, a particular case of UID, leads to costly uncorrelated sequences that are totally unrealistic. We conclude that CER and its particular cases are incomplete hypotheses about the scaling of conditional entropies. (letter)
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.
What is the entropy of the universe?
International Nuclear Information System (INIS)
Frampton, Paul H; Hsu, Stephen D H; Reeb, David; Kephart, Thomas W
2009-01-01
Standard calculations suggest that the entropy of our universe is dominated by black holes, whose entropy is of order their area in Planck units, although they comprise only a tiny fraction of its total energy. Statistical entropy is the logarithm of the number of microstates consistent with the observed macroscopic properties of a system, hence a measure of uncertainty about its precise state. Therefore, assuming unitarity in black hole evaporation, the standard results suggest that the largest uncertainty in the future quantum state of the universe is due to the Hawking radiation from evaporating black holes. However, the entropy of the matter precursors to astrophysical black holes is enormously less than that given by area entropy. If unitarity relates the future radiation states to the black hole precursor states, then the standard results are highly misleading, at least for an observer that can differentiate the individual states of the Hawking radiation.
Entropy Parameter M in Modeling a Flow Duration Curve
Directory of Open Access Journals (Sweden)
Yu Zhang
2017-12-01
Full Text Available A flow duration curve (FDC is widely used for predicting water supply, hydropower, environmental flow, sediment load, and pollutant load. Among different methods of constructing an FDC, the entropy-based method, developed recently, is appealing because of its several desirable characteristics, such as simplicity, flexibility, and statistical basis. This method contains a parameter, called entropy parameter M, which constitutes the basis for constructing the FDC. Since M is related to the ratio of the average streamflow to the maximum streamflow which, in turn, is related to the drainage area, it may be possible to determine M a priori and construct an FDC for ungauged basins. This paper, therefore, analyzed the characteristics of M in both space and time using streamflow data from 73 gauging stations in the Brazos River basin, Texas, USA. Results showed that the M values were impacted by reservoir operation and possibly climate change. The values were fluctuating, but relatively stable, after the operation of the reservoirs. Parameter M was found to change inversely with the ratio of average streamflow to the maximum streamflow. When there was an extreme event, there occurred a jump in the M value. Further, spatially, M had a larger value if the drainage area was small.
Entropy production and transport in relation to Tokamak temperature profiles
International Nuclear Information System (INIS)
Martinell, J.J.; Almaguer, J.A.; Herrera, J.J.E.
1992-01-01
The consequences of using the idea of entropy production rate minimization are examined in relation to the shape of radial temperature profiles and the scaling of transport coefficients with temperature in Tokamak discharges. This is done under the assumption that physical processes occur in such a way as to produce relaxed states where an extremal of some relevant quantity (in this case the entropy production) is obtained. The conditions under which the temperature profiles adopt the Gaussian-like shapes observed in Tokamak plasmas are studied. This is possible only for certain scalings of the thermal conductivity with temperature favouring certain models of anomalous transport against others. These results are also dependent on whether or not the current density profile is assumed to be determined by the temperature profile, as in Ohmically heated discharges with constant electric field. In the former case an anomalous electrical resistivity is needed in order to obtain the correct temperature profiles for known models of anomalous thermal conductivity. When the current density is an independent function of radius the electrical resistivity can be classical, and for the thermal diffusivity this approach favours the models based on magnetic fluctuations exhibiting the Ohkawa scaling, as well as a model that employs profile consistency in its derivations. These cases should be relevant to discharges with auxiliary heating. (Author)
Shannon versus Kullback-Leibler entropies in nonequilibrium random motion
International Nuclear Information System (INIS)
Garbaczewski, Piotr
2005-01-01
We analyze dynamical properties of the Shannon information entropy of a continuous probability distribution, which is driven by a standard diffusion process. This entropy choice is confronted with another option, employing the conditional Kullback-Leibler entropy. Both entropies discriminate among various probability distributions, either statically or in the time domain. An asymptotic approach towards equilibrium is typically monotonic in terms of the Kullback entropy. The Shannon entropy time rate needs not to be positive and is a sensitive indicator of the power transfer processes (removal/supply) due to an active environment. In the case of Smoluchowski diffusions, the Kullback entropy time rate coincides with the Shannon entropy 'production' rate
Entropy-driven crystal formation on highly strained substrates
Savage, John R.
2013-05-20
In heteroepitaxy, lattice mismatch between the deposited material and the underlying surface strongly affects nucleation and growth processes. The effect of mismatch is well studied in atoms with growth kinetics typically dominated by bond formation with interaction lengths on the order of one lattice spacing. In contrast, less is understood about how mismatch affects crystallization of larger particles, such as globular proteins and nanoparticles, where interparticle interaction energies are often comparable to thermal fluctuations and are short ranged, extending only a fraction of the particle size. Here, using colloidal experiments and simulations, we find particles with short-range attractive interactions form crystals on isotropically strained lattices with spacings significantly larger than the interaction length scale. By measuring the free-energy cost of dimer formation on monolayers of increasing uniaxial strain, we show the underlying mismatched substrate mediates an entropy-driven attractive interaction extending well beyond the interaction length scale. Remarkably, because this interaction arises from thermal fluctuations, lowering temperature causes such substrate-mediated attractive crystals to dissolve. Such counterintuitive results underscore the crucial role of entropy in heteroepitaxy in this technologically important regime. Ultimately, this entropic component of lattice mismatched crystal growth could be used to develop unique methods for heterogeneous nucleation and growth of single crystals for applications ranging from protein crystallization to controlling the assembly of nanoparticles into ordered, functional superstructures. In particular, the construction of substrates with spatially modulated strain profiles would exploit this effect to direct self-assembly, whereby nucleation sites and resulting crystal morphology can be controlled directly through modifications of the substrate.
Glass Transition, Crystallization of Glass-Forming Melts, and Entropy
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Jürn W. P. Schmelzer
2018-02-01
Full Text Available A critical analysis of possible (including some newly proposed definitions of the vitreous state and the glass transition is performed and an overview of kinetic criteria of vitrification is presented. On the basis of these results, recent controversial discussions on the possible values of the residual entropy of glasses are reviewed. Our conclusion is that the treatment of vitrification as a process of continuously breaking ergodicity with entropy loss and a residual entropy tending to zero in the limit of zero absolute temperature is in disagreement with the absolute majority of experimental and theoretical investigations of this process and the nature of the vitreous state. This conclusion is illustrated by model computations. In addition to the main conclusion derived from these computations, they are employed as a test for several suggestions concerning the behavior of thermodynamic coefficients in the glass transition range. Further, a brief review is given on possible ways of resolving the Kauzmann paradox and its implications with respect to the validity of the third law of thermodynamics. It is shown that neither in its primary formulations nor in its consequences does the Kauzmann paradox result in contradictions with any basic laws of nature. Such contradictions are excluded by either crystallization (not associated with a pseudospinodal as suggested by Kauzmann or a conventional (and not an ideal glass transition. Some further so far widely unexplored directions of research on the interplay between crystallization and glass transition are anticipated, in which entropy may play—beyond the topics widely discussed and reviewed here—a major role.
Gambling with Superconducting Fluctuations
Foltyn, Marek; Zgirski, Maciej
2015-08-01
Josephson junctions and superconducting nanowires, when biased close to superconducting critical current, can switch to a nonzero voltage state by thermal or quantum fluctuations. The process is understood as an escape of a Brownian particle from a metastable state. Since this effect is fully stochastic, we propose to use it for generating random numbers. We present protocol for obtaining random numbers and test the experimentally harvested data for their fidelity. Our work is prerequisite for using the Josephson junction as a tool for stochastic (probabilistic) determination of physical parameters such as magnetic flux, temperature, and current.
Entropy Generation Analysis of Desalination Technologies
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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.
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 of self-gravitating radiation
International Nuclear Information System (INIS)
Sorkin, R.D.; Wald, R.M.; Jiu, Z.Z.
1981-01-01
The entropy of self-gravitating radiation confined to a spherical box of radius R is examined in the context of general relativity. It is expected that configurations (i.e., initial data) which extremize total entropy will be spherically symmetric, time symmetric distributions of radiation in local thermodynamic equilibrium. Assuming this is the case, it is proved that extrema of S coincide precisely with static equilibrium configurations of the radiation fluid. Furthermore, dynamically stable equilibrium configurations are shown to coincide with local maxima of S. The equilibrium configurations and their entropies are calculated and their properties are discussed. However, it is shown that entropies higher than these local extrema can be achieved and, indeed, arbitrarily high entropies can be attained by configurations inside of or outside but arbitrarily near their own Schwarzschild radius. However, consideration is limited to configurations which are outside their own Schwarzschild radius by at least one radiation wavelength, then the entropy is bounded and it is found Ssub(max) < is approximately equal to MR, where M is the total mass. This supports the validity for self-gravitating systems of the Bekenstein upper limit on the entropy to energy ratio of material bodies. (author)
Entropy change of biological dynamics in COPD
Directory of Open Access Journals (Sweden)
Jin Y
2017-10-01
Full Text Available Yu Jin,1,* Chang Chen,1,* Zhixin Cao,2 Baoqing Sun,3 Iek Long Lo,4 Tzu-Ming Liu,1 Jun Zheng,1 Shixue Sun,1 Yan Shi,5 Xiaohua Douglas Zhang1 1Faculty of Health Sciences, University of Macau, Taipa, Macau, 2Beijing Engineering Research Center of Diagnosis and Treatment of Respiratory and Critical Care Medicine, Beijing Chaoyang Hospital, Beijing, 3State Key Laboratory of Respiratory Disease, The First Affiliated Hospital of Guangzhou Medical University, Guangzhou, 4Department of Geriatrics, Centro Hospital Conde de Sao Januario, Macau, 5School of Automation Science and Electrical Engineering, Beihang University, Beijing, China *These authors contributed equally to this work Abstract: In this century, the rapid development of large data storage technologies, mobile network technology, and portable medical devices makes it possible to measure, record, store, and track analysis of large amount of data in human physiological signals. Entropy is a key metric for quantifying the irregularity contained in physiological signals. In this review, we focus on how entropy changes in various physiological signals in COPD. Our review concludes that the entropy change relies on the types of physiological signals under investigation. For major physiological signals related to respiratory diseases, such as airflow, heart rate variability, and gait variability, the entropy of a patient with COPD is lower than that of a healthy person. However, in case of hormone secretion and respiratory sound, the entropy of a patient is higher than that of a healthy person. For mechanomyogram signal, the entropy increases with the increased severity of COPD. This result should give valuable guidance for the use of entropy for physiological signals measured by wearable medical device as well as for further research on entropy in COPD. Keywords: entropy, heart rate variability, physiological signal, respiratory pattern, COPD, irregularity
Entropy vs. Majorization: What Determines Complexity?
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William Seitz
2014-07-01
Full Text Available The evolution of a microcanonical statistical ensemble of states of isolated systems from order to disorder as determined by increasing entropy, is compared to an alternative evolution that is determined by mixing character. The fact that the partitions of an integer N are in one-to-one correspondence with macrostates for N distinguishable objects is noted. Orders for integer partitions are given, including the original order by Young and the Boltzmann order by entropy. Mixing character (represented by Young diagrams is seen to be a partially ordered quality rather than a quantity (See Ruch, 1975. The majorization partial order is reviewed as is its Hasse diagram representation known as the Young Diagram Lattice (YDL.Two lattices that show allowed transitions between macrostates are obtained from the YDL: we term these the mixing lattice and the diversity lattice. We study the dynamics (time evolution on the two lattices, namely the sequence of steps on the lattices (i.e., the path or trajectory that leads from low entropy, less mixed states to high entropy, highly mixed states. These paths are sequences of macrostates with monotonically increasing entropy. The distributions of path lengths on the two lattices are obtained via Monte Carlo methods, and surprisingly both distributions appear Gaussian. However, the width of the path length distribution for diversity is the square root of the mixing case, suggesting a qualitative difference in their temporal evolution. Another surprising result is that some macrostates occur in many paths while others do not. The evolution at low entropy and at high entropy is quite simple, but at intermediate entropies, the number of possible evolutionary paths is extremely large (due to the extensive branching of the lattices. A quantitative complexity measure associated with incomparability of macrostates in the mixing partial order is proposed, complementing Kolmogorov complexity and Shannon entropy.
Entropy/information flux in Hawking radiation
Alonso-Serrano, Ana; Visser, Matt
2018-01-01
Blackbody radiation contains (on average) an entropy of 3.9 ± 2.5 bits per photon. If the emission process is unitary, then this entropy is exactly compensated by "hidden information" in the correlations. We extend this argument to the Hawking radiation from GR black holes, demonstrating that the assumption of unitarity leads to a perfectly reasonable entropy/information budget. The key technical aspect of our calculation is a variant of the "average subsystem" approach developed by Page, which we extend beyond bipartite pure systems, to a tripartite pure system that considers the influence of the environment.
Density estimation by maximum quantum entropy
Energy Technology Data Exchange (ETDEWEB)
Silver, R.N.; Wallstrom, T.; Martz, H.F.
1993-11-01
A new Bayesian method for non-parametric density estimation is proposed, based on a mathematical analogy to quantum statistical physics. The mathematical procedure is related to maximum entropy methods for inverse problems and image reconstruction. The information divergence enforces global smoothing toward default models, convexity, positivity, extensivity and normalization. The novel feature is the replacement of classical entropy by quantum entropy, so that local smoothing is enforced by constraints on differential operators. The linear response of the estimate is proportional to the covariance. The hyperparameters are estimated by type-II maximum likelihood (evidence). The method is demonstrated on textbook data sets.
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.
Option price calibration from Renyi entropy
International Nuclear Information System (INIS)
Brody, Dorje C.; Buckley, Ian R.C.; Constantinou, Irene C.
2007-01-01
The calibration of the risk-neutral density function for the future asset price, based on the maximisation of the entropy measure of Renyi, is proposed. Whilst the conventional approach based on the use of logarithmic entropy measure fails to produce the observed power-law distribution when calibrated against option prices, the approach outlined here is shown to produce the desired form of the distribution. Procedures for the maximisation of the Renyi entropy under constraints are outlined in detail, and a number of interesting properties of the resulting power-law distributions are also derived. The result is applied to efficiently evaluate prices of path-independent derivatives
Permutation Entropy for Random Binary Sequences
Directory of Open Access Journals (Sweden)
Lingfeng Liu
2015-12-01
Full Text Available In this paper, we generalize the permutation entropy (PE measure to binary sequences, which is based on Shannon’s entropy, and theoretically analyze this measure for random binary sequences. We deduce the theoretical value of PE for random binary sequences, which can be used to measure the randomness of binary sequences. We also reveal the relationship between this PE measure with other randomness measures, such as Shannon’s entropy and Lempel–Ziv complexity. The results show that PE is consistent with these two measures. Furthermore, we use PE as one of the randomness measures to evaluate the randomness of chaotic binary sequences.
Emission and Absorption Entropy Generation in Semiconductors
DEFF Research Database (Denmark)
Reck, Kasper; Varpula, Aapo; Prunnila, Mika
2013-01-01
While emission and absorption entropy generation is well known in black bodies, it has not previously been studied in semiconductors, even though semiconductors are widely used for solar light absorption in modern solar cells [1]. We present an analysis of the entropy generation in semiconductor...... materials due to emission and absorption of electromagnetic radiation. It is shown that the emission and absorption entropy generation reduces the fundamental limit on the efficiency of any semiconductor solar cell even further than the Landsberg limit. The results are derived from purely thermodynamical...
On the Conditional Entropy of Wireless Networks
DEFF Research Database (Denmark)
Coon, Justin P.; Badiu, Mihai Alin; Gündüz, Deniz
2018-01-01
The characterization of topological uncertainty in wireless networks using the formalism of graph entropy has received interest in the spatial networks community. In this paper, we develop lower bounds on the entropy of a wireless network by conditioning on potential network observables. Two...... approaches are considered: 1) conditioning on subgraphs, and 2) conditioning on node positions. The first approach is shown to yield a relatively tight bound on the network entropy. The second yields a loose bound, in general, but it provides insight into the dependence between node positions (modelled using...
Remarks on Bousso's covariant entropy bound
Mayo, A E
2002-01-01
Bousso's covariant entropy bound is put to the test in the context of a non-singular cosmological solution of general relativity found by Bekenstein. Although the model complies with every assumption made in Bousso's original conjecture, the entropy bound is violated due to the occurrence of negative energy density associated with the interaction of some the matter components in the model. We demonstrate how this property allows for the test model to 'elude' a proof of Bousso's conjecture which was given recently by Flanagan, Marolf and Wald. This corroborates the view that the covariant entropy bound should be applied only to stable systems for which every matter component carries positive energy density.
Black hole entropy and quantum information
Duff, M J
2006-01-01
We review some recently established connections between the mathematics of black hole entropy in string theory and that of multipartite entanglement in quantum information theory. In the case of N=2 black holes and the entanglement of three qubits, the quartic [SL(2)]^3 invariant, Cayley's hyperdeterminant, provides both the black hole entropy and the measure of tripartite entanglement. In the case of N=8 black holes and the entanglement of seven qubits, the quartic E_7 invariant of Cartan provides both the black hole entropy and the measure of a particular tripartite entanglement encoded in the Fano plane.
Cytoskeleton dynamics: Fluctuations within the network
International Nuclear Information System (INIS)
Bursac, Predrag; Fabry, Ben; Trepat, Xavier; Lenormand, Guillaume; Butler, James P.; Wang, Ning; Fredberg, Jeffrey J.; An, Steven S.
2007-01-01
Out-of-equilibrium systems, such as the dynamics of a living cytoskeleton (CSK), are inherently noisy with fluctuations arising from the stochastic nature of the underlying biochemical and molecular events. Recently, such fluctuations within the cell were characterized by observing spontaneous nano-scale motions of an RGD-coated microbead bound to the cell surface [Bursac et al., Nat. Mater. 4 (2005) 557-561]. While these reported anomalous bead motions represent a molecular level reorganization (remodeling) of microstructures in contact with the bead, a precise nature of these cytoskeletal constituents and forces that drive their remodeling dynamics are largely unclear. Here, we focused upon spontaneous motions of an RGD-coated bead and, in particular, assessed to what extent these motions are attributable to (i) bulk cell movement (cell crawling), (ii) dynamics of focal adhesions, (iii) dynamics of lipid membrane, and/or (iv) dynamics of the underlying actin CSK driven by myosin motors
Maximum Entropy and Theory Construction: A Reply to Favretti
Directory of Open Access Journals (Sweden)
John Harte
2018-04-01
Full Text Available In the maximum entropy theory of ecology (METE, the form of a function describing the distribution of abundances over species and metabolic rates over individuals in an ecosystem is inferred using the maximum entropy inference procedure. Favretti shows that an alternative maximum entropy model exists that assumes the same prior knowledge and makes predictions that differ from METE’s. He shows that both cannot be correct and asserts that his is the correct one because it can be derived from a classic microstate-counting calculation. I clarify here exactly what the core entities and definitions are for METE, and discuss the relevance of two critical issues raised by Favretti: the existence of a counting procedure for microstates and the choices of definition of the core elements of a theory. I emphasize that a theorist controls how the core entities of his or her theory are defined, and that nature is the final arbiter of the validity of a theory.
Energy Flows in Low-Entropy Complex Systems
Directory of Open Access Journals (Sweden)
Eric J. Chaisson
2015-12-01
Full Text Available Nature’s many complex systems—physical, biological, and cultural—are islands of low-entropy order within increasingly disordered seas of surrounding, high-entropy chaos. Energy is a principal facilitator of the rising complexity of all such systems in the expanding Universe, including galaxies, stars, planets, life, society, and machines. A large amount of empirical evidence—relating neither entropy nor information, rather energy—suggests that an underlying simplicity guides the emergence and growth of complexity among many known, highly varied systems in the 14-billion-year-old Universe, from big bang to humankind. Energy flows are as centrally important to life and society as they are to stars and galaxies. In particular, the quantity energy rate density—the rate of energy flow per unit mass—can be used to explicate in a consistent, uniform, and unifying way a huge collection of diverse complex systems observed throughout Nature. Operationally, those systems able to utilize optimal amounts of energy tend to survive and those that cannot are non-randomly eliminated.
Tail Risk Constraints and Maximum Entropy
Directory of Open Access Journals (Sweden)
Donald Geman
2015-06-01
Full Text Available Portfolio selection in the financial literature has essentially been analyzed under two central assumptions: full knowledge of the joint probability distribution of the returns of the securities that will comprise the target portfolio; and investors’ preferences are expressed through a utility function. In the real world, operators build portfolios under risk constraints which are expressed both by their clients and regulators and which bear on the maximal loss that may be generated over a given time period at a given confidence level (the so-called Value at Risk of the position. Interestingly, in the finance literature, a serious discussion of how much or little is known from a probabilistic standpoint about the multi-dimensional density of the assets’ returns seems to be of limited relevance. Our approach in contrast is to highlight these issues and then adopt throughout a framework of entropy maximization to represent the real world ignorance of the “true” probability distributions, both univariate and multivariate, of traded securities’ returns. In this setting, we identify the optimal portfolio under a number of downside risk constraints. Two interesting results are exhibited: (i the left- tail constraints are sufficiently powerful to override all other considerations in the conventional theory; (ii the “barbell portfolio” (maximal certainty/ low risk in one set of holdings, maximal uncertainty in another, which is quite familiar to traders, naturally emerges in our construction.
Kurhe, Deepti N; Dagade, Dilip H; Jadhav, Jyoti P; Govindwar, Sanjay P; Patil, Kesharsingh J
2009-12-31
Densities and osmotic coefficient measurements for dilute aqueous solutions of glycine, l-leucine, and glycylglycine have been reported at 298.15 K. The partial molar volumes and activity coefficients of solute as well as solvent have been estimated using the density and osmotic coefficient data, respectively. Excess and mixing thermodynamic properties, such as Gibbs free energy, enthalpy, and entropy changes, have been obtained using the activity data from this study and the heat data reported in the literature. The concentration enthalpy-entropy compensation effects have been observed for the studied systems, and the compensation temperatures are reported. It has been observed that the excess free energy change for all the studied systems is almost the same over the studied concentration range, showing that the differences in properties of such solutions are largely decided by the enthalpy-entropy effects. These results, along with partial entropy data, show the effects of the presence of hydrophobic interactions and water structure making effect in the case of aqueous solutions of l-leucine. The application of the Starikov-Norden enthalpy-entropy compensation model yielded information about a "hidden Carnot cycle" and the existence of multiple microphases. Application of the Kirkwood-Buff (KB) theory of solutions for the studied systems yields pair correlation functions between the components. The variation of Kirkwood-Buff integrals with concentration further signifies the concentration dependence of the hydrophobic hydration and interactions in the solution phase. The osmotic second virial coefficients have also been obtained using the KB theory and show good agreement with those obtained using the McMillan-Mayer theory of solutions. The mean square concentration fluctuations is estimated using the KB theory, which gives information about the microheterogeneity in the solution phase, which further reflects the presence of hydration and solute association.
Unification of field theory and maximum entropy methods for learning probability densities.
Kinney, Justin B
2015-09-01
The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive solution. Maximum entropy estimation and Bayesian field theory are two such approaches. Both have origins in statistical physics, but the relationship between them has remained unclear. Here I unify these two methods by showing that every maximum entropy density estimate can be recovered in the infinite smoothness limit of an appropriate Bayesian field theory. I also show that Bayesian field theory estimation can be performed without imposing any boundary conditions on candidate densities, and that the infinite smoothness limit of these theories recovers the most common types of maximum entropy estimates. Bayesian field theory thus provides a natural test of the maximum entropy null hypothesis and, furthermore, returns an alternative (lower entropy) density estimate when the maximum entropy hypothesis is falsified. The computations necessary for this approach can be performed rapidly for one-dimensional data, and software for doing this is provided.
Using Link Disconnection Entropy Disorder to Detect Fast Moving Nodes in MANETs.
Alvarez, Carlos F; Palafox, Luis E; Aguilar, Leocundo; Sanchez, Mauricio A; Martinez, Luis G
2016-01-01
Mobile ad-hoc networks (MANETs) are dynamic by nature; this dynamism comes from node mobility, traffic congestion, and other transmission conditions. Metrics to evaluate the effects of those conditions shine a light on node's behavior in an ad-hoc network, helping to identify the node or nodes with better conditions of connection. In this paper, we propose a relative index to evaluate a single node reliability, based on the link disconnection entropy disorder using neighboring nodes as reference. Link disconnection entropy disorder is best used to identify fast moving nodes or nodes with unstable communications, this without the need of specialized sensors such as GPS. Several scenarios were studied to verify the index, measuring the effects of Speed and traffic density on the link disconnection entropy disorder. Packet delivery ratio is associated to the metric detecting a strong relationship, enabling the use of the link disconnection entropy disorder to evaluate the stability of a node to communicate with other nodes. To expand the utilization of the link entropy disorder, we identified nodes with higher speeds in network simulations just by using the link entropy disorder.
The maximum entropy production and maximum Shannon information entropy in enzyme kinetics
Dobovišek, Andrej; Markovič, Rene; Brumen, Milan; Fajmut, Aleš
2018-04-01
We demonstrate that the maximum entropy production principle (MEPP) serves as a physical selection principle for the description of the most probable non-equilibrium steady states in simple enzymatic reactions. A theoretical approach is developed, which enables maximization of the density of entropy production with respect to the enzyme rate constants for the enzyme reaction in a steady state. Mass and Gibbs free energy conservations are considered as optimization constraints. In such a way computed optimal enzyme rate constants in a steady state yield also the most uniform probability distribution of the enzyme states. This accounts for the maximal Shannon information entropy. By means of the stability analysis it is also demonstrated that maximal density of entropy production in that enzyme reaction requires flexible enzyme structure, which enables rapid transitions between different enzyme states. These results are supported by an example, in which density of entropy production and Shannon information entropy are numerically maximized for the enzyme Glucose Isomerase.
On extremals of the entropy production by ‘Langevin–Kramers’ dynamics
International Nuclear Information System (INIS)
Muratore-Ginanneschi, Paolo
2014-01-01
We refer as ‘Langevin–Kramers’ dynamics to a class of stochastic differential systems exhibiting a degenerate ‘metriplectic’ structure. This means that the drift field can be decomposed into a symplectic and a gradient-like component with respect to a pseudo-metric tensor associated with random fluctuations affecting increments of only a sub-set of the degrees of freedom. Systems in this class are often encountered in applications as elementary models of Hamiltonian dynamics in a heat bath eventually relaxing to a Boltzmann steady state. Entropy production control in Langevin–Kramers models differs from the now well-understood case of Langevin–Smoluchowski dynamics for two reasons. First, the definition of entropy production stemming from fluctuation theorems specifies a cost functional which does not act coercively on all degrees of freedom of control protocols. Second, the presence of a symplectic structure imposes a non-local constraint on the class of admissible controls. Using Pontryagin control theory and restricting the attention to additive noise, we show that smooth protocols attaining extremal values of the entropy production appear generically in continuous parametric families as a consequence of a trade-off between smoothness of the admissible protocols and non-coercivity of the cost functional. Uniqueness is, however, always recovered in the over-damped limit as extremal equations reduce at leading order to the Monge–Ampère–Kantorovich optimal mass-transport equations. (paper)
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mail: schroer@cbpf.br
2002-08-01
The lightfront quantization of the 70s is reviewed in the more rigorous setting of lightfront (LF) restriction of free fields in which the lightfront is considered to be linear extension of the upper causal horizon of a wedge region. Particular attention is given to the change of localization structure in passing from the wedge to its horizon which results in the emergence of a transverse quantum mechanical substructure of the QFT on the horizon and its lightfront extension. The vacuum fluctuations of QFT on the LF are compressed into the direction of the lightray (where they become associated with a chiral QFT) and lead to the notion of area density of a 'split localization' entropy. To overcome the limitation of this restriction approach and include interacting theories with non-canonical short distance behavior, we introduce a new concept of algebraic lightfront holography which uses ideas of algebraic QFT, in particular the modular structure of its associated local operator algebras. In this way the localization properties of LF degrees of freedom including the absence of transverse vacuum fluctuations are confirmed to be stable against interactions. The important universality aspect of lightfront holography is emphasized. Only in this way one is able to extract from the 'split-localization' entropy a split-independent additive entropy-like measure of the entanglement of the vacuum upon restriction to the horizon algebra. (author)
Multiscale permutation entropy analysis of laser beam wandering in isotropic turbulence
Olivares, Felipe; Zunino, Luciano; Gulich, Damián; Pérez, Darío G.; Rosso, Osvaldo A.
2017-10-01
We have experimentally quantified the temporal structural diversity from the coordinate fluctuations of a laser beam propagating through isotropic optical turbulence. The main focus here is on the characterization of the long-range correlations in the wandering of a thin Gaussian laser beam over a screen after propagating through a turbulent medium. To fulfill this goal, a laboratory-controlled experiment was conducted in which coordinate fluctuations of the laser beam were recorded at a sufficiently high sampling rate for a wide range of turbulent conditions. Horizontal and vertical displacements of the laser beam centroid were subsequently analyzed by implementing the symbolic technique based on ordinal patterns to estimate the well-known permutation entropy. We show that the permutation entropy estimations at multiple time scales evidence an interplay between different dynamical behaviors. More specifically, a crossover between two different scaling regimes is observed. We confirm a transition from an integrated stochastic process contaminated with electronic noise to a fractional Brownian motion with a Hurst exponent H =5 /6 as the sampling time increases. Besides, we are able to quantify, from the estimated entropy, the amount of electronic noise as a function of the turbulence strength. We have also demonstrated that these experimental observations are in very good agreement with numerical simulations of noisy fractional Brownian motions with a well-defined crossover between two different scaling regimes.
On the maximum entropy principle in non-extensive thermostatistics
Naudts, Jan
2004-01-01
It is possible to derive the maximum entropy principle from thermodynamic stability requirements. Using as a starting point the equilibrium probability distribution, currently used in non-extensive thermostatistics, it turns out that the relevant entropy function is Renyi's alpha-entropy, and not Tsallis' entropy.
Probability distribution and entropy as a measure of uncertainty
International Nuclear Information System (INIS)
Wang Qiuping A
2008-01-01
The relationship between three probability distributions and their maximizable entropy forms is discussed without postulating entropy property. For this purpose, the entropy I is defined as a measure of uncertainty of the probability distribution of a random variable x by a variational relationship dI = d x-bar - dx-bar, a definition underlying the maximization of entropy for corresponding distribution
Matsubara, Yoshitsugu; Musashi, Yasuo
2017-12-01
The purpose of this study is to explain fluctuations in email size. We have previously investigated the long-term correlations between email send requests and data flow in the system log of the primary staff email server at a university campus, finding that email size frequency follows a power-law distribution with two inflection points, and that the power-law property weakens the correlation of the data flow. However, the mechanism underlying this fluctuation is not completely understood. We collected new log data from both staff and students over six academic years and analyzed the frequency distribution thereof, focusing on the type of content contained in the emails. Furthermore, we obtained permission to collect "Content-Type" log data from the email headers. We therefore collected the staff log data from May 1, 2015 to July 31, 2015, creating two subdistributions. In this paper, we propose a model to explain these subdistributions, which follow log-normal-like distributions. In the log-normal-like model, email senders -consciously or unconsciously- regulate the size of new email sentences according to a normal distribution. The fitting of the model is acceptable for these subdistributions, and the model demonstrates power-law properties for large email sizes. An analysis of the length of new email sentences would be required for further discussion of our model; however, to protect user privacy at the participating organization, we left this analysis for future work. This study provides new knowledge on the properties of email sizes, and our model is expected to contribute to the decision on whether to establish upper size limits in the design of email services.
On the continuity of the entropy
International Nuclear Information System (INIS)
Lassner, G.; Lassner, G.A.
1977-01-01
It is shown for a quantum-mechanical system with finite degree of freedom taking into account also unbounded observables one gets physical topologies on the state-observable system with respect to which the entropy becomes a continuous function
The entropy of a hole in spacetime
Balasubramanian, V.; Chowdhury, B.D.; Czech, B.; de Boer, J.
2013-01-01
We compute the gravitational entropy of "spherical Rindler space", a timedependent, 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
Topological entropy for induced hyperspace maps
Energy Technology Data Exchange (ETDEWEB)
Canovas Pena, Jose S. [Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, 30203 Cartagena, Murcia (Spain)]. E-mail: Jose.canovas@upct.es; Lopez, Gabriel Soler [Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, 30203 Cartagena, Murcia (Spain)]. E-mail: Gabriel.soler@upct.es
2006-05-15
Let (X,d) be a compact metric space and let f:X->X be continuous. Let K(X) be the family of compact subsets of X endowed with the Hausdorff metric and define the extension f-bar :K(X)->K(X) by f-bar (K)=f(K) for any K-bar K(X). We prove that the topological entropy of f-bar is greater or equal than the topological entropy of f, and this inequality can be strict. On the other hand, we prove that the topological entropy of f is positive if and only if the topological entropy of f-bar is also positive.
Independent Component Analysis by Entropy Maximization (INFOMAX)
National Research Council Canada - National Science Library
Garvey, Jennie H
2007-01-01
... (BSS). The Infomax method separates unknown source signals from a number of signal mixtures by maximizing the entropy of a transformed set of signal mixtures and is accomplished by performing gradient ascent in MATLAB...
Thermoeconomic diagnosis and entropy generation paradox
DEFF Research Database (Denmark)
Sigthorsson, Oskar; Ommen, Torben Schmidt; Elmegaard, Brian
2017-01-01
In the entropy generation paradox, the entropy generation number, as a function of heat exchanger effectiveness, counter-intuitively approaches zero in two limits symmetrically from a single maximum. In thermoeconomic diagnosis, namely in the characteristic curve method, the exergy destruction...... to the entropy generation paradox, as a decreased heat exchanger effectiveness (as in the case of an operation anomaly in the component) can counter-intuitively result in decreased exergy destruction rate of the component. Therefore, along with an improper selection of independent variables, the heat exchanger...... increases in case of an operation anomaly in a component. The normalised exergy destruction rate as the dependent variable therefore resolves the relation of the characteristic curve method with the entropy generation paradox....
Two-dimensional maximum entropy image restoration
International Nuclear Information System (INIS)
Brolley, J.E.; Lazarus, R.B.; Suydam, B.R.; Trussell, H.J.
1977-07-01
An optical check problem was constructed to test P LOG P maximum entropy restoration of an extremely distorted image. Useful recovery of the original image was obtained. Comparison with maximum a posteriori restoration is made. 7 figures
Entanglement entropy of magnetic electron stars
Energy Technology Data Exchange (ETDEWEB)
Albash, Tameem; Johnson, Clifford V.; MacDonald, Scott [Department of Physics and Astronomy, University of Southern California,920 Bloom Walk, Los Angeles, CA (United States)
2015-09-24
We study the behavior of the entanglement entropy in (2+1)-dimensional strongly coupled theories via the AdS/CFT correspondence. We consider theories at a finite charge density with a magnetic field, with their holographic dual being Einstein-Maxwell-Dilaton theory in four dimensional anti-de Sitter gravity. Restricting to black hole and electron star solutions at zero temperature in the presence of a background magnetic field, we compute their holographic entanglement entropy using the Ryu-Takayanagi prescription for both strip and disk geometries. In the case of the electric or magnetic zero temperature black holes, we are able to confirm that the entanglement entropy is invariant under electric-magnetic duality. In the case of the electron star with a finite magnetic field, for the strip geometry, we find a discontinuity in the first derivative of the entanglement entropy as the strip width is increased.
Fused Entropy Algorithm in Optical Computed Tomography
Directory of Open Access Journals (Sweden)
Xiong Wan
2014-02-01
Full Text Available In most applications of optical computed tomography (OpCT, limited-view problems are often encountered, which can be solved to a certain extent with typical OpCT reconstructive algorithms. The concept of entropy first emerged in information theory has been introduced into OpCT algorithms, such as maximum entropy (ME algorithms and cross entropy (CE algorithms, which have demonstrated their superiority over traditional OpCT algorithms, yet have their own limitations. A fused entropy (FE algorithm, which follows an optimized criterion combining self-adaptively ME with CE, is proposed and investigated by comparisons with ME, CE and some traditional OpCT algorithms. Reconstructed results of several physical models show this FE algorithm has a good convergence and can achieve better precision than other algorithms, which verifies the feasibility of FE as an approach of optimizing computation, not only for OpCT, but also for other image processing applications.
Minimal entropy approximation for cellular automata
International Nuclear Information System (INIS)
Fukś, Henryk
2014-01-01
We present a method for the construction of approximate orbits of measures under the action of cellular automata which is complementary to the local structure theory. The local structure theory is based on the idea of Bayesian extension, that is, construction of a probability measure consistent with given block probabilities and maximizing entropy. If instead of maximizing entropy one minimizes it, one can develop another method for the construction of approximate orbits, at the heart of which is the iteration of finite-dimensional maps, called minimal entropy maps. We present numerical evidence that the minimal entropy approximation sometimes outperforms the local structure theory in characterizing the properties of cellular automata. The density response curve for elementary CA rule 26 is used to illustrate this claim. (paper)
A dual method for maximum entropy restoration
Smith, C. B.
1979-01-01
A simple iterative dual algorithm for maximum entropy image restoration is presented. The dual algorithm involves fewer parameters than conventional minimization in the image space. Minicomputer test results for Fourier synthesis with inadequate phantom data are given.
Entropy for theories with indefinite causal structure
International Nuclear Information System (INIS)
Markes, Sonia; Hardy, Lucien
2011-01-01
Any theory with definite causal structure has a defined past and future, be it defined by light cones or an absolute time scale. Entropy is a concept that has traditionally been reliant on a definite notion of causality. However, without a definite notion of causality, the concept of entropy is not all lost. Indefinite causal structure results from combining probabilistic predictions and dynamical space-time. The causaloid framework lays the mathematical groundwork to be able to treat indefinite causal structure. In this paper, we build on the causaloid mathematics and define a causally-unbiased entropy for an indefinite causal structure. In defining a causally-unbiased entropy, there comes about an emergent idea of causality in the form of a measure of causal connectedness, termed the Q factor.
Entropy Generation Analysis of Wildfire Propagation
Directory of Open Access Journals (Sweden)
Elisa Guelpa
2017-08-01
Full Text Available Entropy generation is commonly applied to describe the evolution of irreversible processes, such as heat transfer and turbulence. These are both dominating phenomena in fire propagation. In this paper, entropy generation analysis is applied to a grassland fire event, with the aim of finding possible links between entropy generation and propagation directions. The ultimate goal of such analysis consists in helping one to overcome possible limitations of the models usually applied to the prediction of wildfire propagation. These models are based on the application of the superimposition of the effects due to wind and slope, which has proven to fail in various cases. The analysis presented here shows that entropy generation allows a detailed analysis of the landscape propagation of a fire and can be thus applied to its quantitative description.
Applications of quantum entropy to statistics
International Nuclear Information System (INIS)
Silver, R.N.; Martz, H.F.
1994-01-01
This paper develops two generalizations of the maximum entropy (ME) principle. First, Shannon classical entropy is replaced by von Neumann quantum entropy to yield a broader class of information divergences (or penalty functions) for statistics applications. Negative relative quantum entropy enforces convexity, positivity, non-local extensivity and prior correlations such as smoothness. This enables the extension of ME methods from their traditional domain of ill-posed in-verse problems to new applications such as non-parametric density estimation. Second, given a choice of information divergence, a combination of ME and Bayes rule is used to assign both prior and posterior probabilities. Hyperparameters are interpreted as Lagrange multipliers enforcing constraints. Conservation principles are proposed to act statistical regularization and other hyperparameters, such as conservation of information and smoothness. ME provides an alternative to heirarchical Bayes methods
Entropy Evaluation Based on Value Validity
Directory of Open Access Journals (Sweden)
Tarald O. Kvålseth
2014-09-01
Full Text Available Besides its importance in statistical physics and information theory, the Boltzmann-Shannon entropy S has become one of the most widely used and misused summary measures of various attributes (characteristics in diverse fields of study. It has also been the subject of extensive and perhaps excessive generalizations. This paper introduces the concept and criteria for value validity as a means of determining if an entropy takes on values that reasonably reflect the attribute being measured and that permit different types of comparisons to be made for different probability distributions. While neither S nor its relative entropy equivalent S* meet the value-validity conditions, certain power functions of S and S* do to a considerable extent. No parametric generalization offers any advantage over S in this regard. A measure based on Euclidean distances between probability distributions is introduced as a potential entropy that does comply fully with the value-validity requirements and its statistical inference procedure is discussed.
Effects of quantum entropy on bag constant
International Nuclear Information System (INIS)
Miller, D.E.; Tawfik, A.
2012-01-01
The effects of quantum entropy on the bag constant are studied at low temperatures and for small chemical potentials. The inclusion of the quantum entropy of the quarks in the equation of state provides the hadronic bag with an additional heat which causes a decrease in the effective latent heat inside the bag. We have considered two types of baryonic bags, Δ and Ω - . In both cases we have found that the bag constant without the quantum entropy almost does not change with temperature and quark chemical potential. The contribution from the quantum entropy to the equation of state clearly decreases the value of the bag constant. Furthermore, we construct states densities for quarks using the 'Thomas Fermi model' and take into consideration a thermal potential for the interaction. (author)
Big Bang or vacuum fluctuation
International Nuclear Information System (INIS)
Zel'dovich, Ya.B.
1980-01-01
Some general properties of vacuum fluctuations in quantum field theory are described. The connection between the ''energy dominance'' of the energy density of vacuum fluctuations in curved space-time and the presence of singularity is discussed. It is pointed out that a de-Sitter space-time (with the energy density of the vacuum fluctuations in the Einstein equations) that matches the expanding Friedman solution may describe the history of the Universe before the Big Bang. (P.L.)
Fluctuations in high-energy particle collisions
International Nuclear Information System (INIS)
Gronqvist, Hanna
2016-01-01
We study fluctuations that are omnipresent in high-energy particle collisions. These fluctuations can be either of either classical or quantum origin and we will study both. Firstly, we consider the type of quantum fluctuations that arise in proton-proton collisions. These are computable perturbatively in quantum field theory and we will focus on a specific class of diagrams in this set-up. Secondly, we will consider the fluctuations that are present in collisions between nuclei that can be heavier than protons. These are the quantum laws of nature that describe the positions of nucleons within a nucleus, but also the hydrodynamic fluctuations of classical, thermal origin that affect the evolution of the medium produced in heavy-ion collisions. The fluctuations arising in proton-proton collisions can be computed analytically up to a certain order in perturbative quantum field theory. We will focus on one-loop diagrams of a fixed topology. Loop diagrams give rise to integrals that typically are hard to evaluate. We show how modern mathematical methods can be used to ease their computation. We will study the relations among unitarity cuts of a diagram, the discontinuity across the corresponding branch cut and the coproduct. We show how the original integral corresponding to a given diagram can be reconstructed from the information contained in the coproduct. We expect that these methods can be applied to solve more complicated topologies and help in the computation of new amplitudes in the future. Finally, we study the two types of fluctuations arising in heavy-ion collisions. These are related either to the initial state or the intermediate state of matter produced in such collisions. The initial state fluctuations are experimentally observed to give rise to non-Gaussianities in the final-state spectra. We show how these non-Gaussianities can be explained by the random position and interaction energy of 'sources' in the colliding nuclei. Furthermore, we
Inverse scattering problem in turbulent magnetic fluctuations
Directory of Open Access Journals (Sweden)
R. A. Treumann
2016-08-01
Full Text Available We apply a particular form of the inverse scattering theory to turbulent magnetic fluctuations in a plasma. In the present note we develop the theory, formulate the magnetic fluctuation problem in terms of its electrodynamic turbulent response function, and reduce it to the solution of a special form of the famous Gelfand–Levitan–Marchenko equation of quantum mechanical scattering theory. The last of these applies to transmission and reflection in an active medium. The theory of turbulent magnetic fluctuations does not refer to such quantities. It requires a somewhat different formulation. We reduce the theory to the measurement of the low-frequency electromagnetic fluctuation spectrum, which is not the turbulent spectral energy density. The inverse theory in this form enables obtaining information about the turbulent response function of the medium. The dynamic causes of the electromagnetic fluctuations are implicit to it. Thus, it is of vital interest in low-frequency magnetic turbulence. The theory is developed until presentation of the equations in applicable form to observations of turbulent electromagnetic fluctuations as input from measurements. Solution of the final integral equation should be done by standard numerical methods based on iteration. We point to the possibility of treating power law fluctuation spectra as an example. Formulation of the problem to include observations of spectral power densities in turbulence is not attempted. This leads to severe mathematical problems and requires a reformulation of inverse scattering theory. One particular aspect of the present inverse theory of turbulent fluctuations is that its structure naturally leads to spatial information which is obtained from the temporal information that is inherent to the observation of time series. The Taylor assumption is not needed here. This is a consequence of Maxwell's equations, which couple space and time evolution. The inversion procedure takes
Directory of Open Access Journals (Sweden)
John McCamley
2017-01-01
Full Text Available The aim of this investigation was to compare and contrast the use of cross sample entropy (xSE and cross recurrence quantification analysis (cRQA measures for the assessment of coupling of rhythmical patterns. Measures were assessed using simulated signals with regular, chaotic, and random fluctuations in frequency, amplitude, and a combination of both. Biological data were studied as models of normal and abnormal locomotor-respiratory coupling. Nine signal types were generated for seven frequency ratios. Fifteen patients with COPD (abnormal coupling and twenty-one healthy controls (normal coupling walked on a treadmill at three speeds while breathing and walking were recorded. xSE and the cRQA measures of percent determinism, maximum line, mean line, and entropy were quantified for both the simulated and experimental data. In the simulated data, xSE, percent determinism, and entropy were influenced by the frequency manipulation. The 1 : 1 frequency ratio was different than other frequency ratios for almost all measures and/or manipulations. The patients with COPD used a 2 : 3 ratio more often and xSE, percent determinism, maximum line, mean line, and cRQA entropy were able to discriminate between the groups. Analysis of the effects of walking speed indicated that all measures were able to discriminate between speeds.
State-Space Geometry, Statistical Fluctuations, and Black Holes in String Theory
Directory of Open Access Journals (Sweden)
Stefano Bellucci
2014-01-01
Full Text Available We study the state-space geometry of various extremal and nonextremal black holes in string theory. From the notion of the intrinsic geometry, we offer a state-space perspective to the black hole vacuum fluctuations. For a given black hole entropy, we explicate the intrinsic geometric meaning of the statistical fluctuations, local and global stability conditions, and long range statistical correlations. We provide a set of physical motivations pertaining to the extremal and nonextremal black holes, namely, the meaning of the chemical geometry and physics of correlation. We illustrate the state-space configurations for general charge extremal black holes. In sequel, we extend our analysis for various possible charge and anticharge nonextremal black holes. From the perspective of statistical fluctuation theory, we offer general remarks, future directions, and open issues towards the intrinsic geometric understanding of the vacuum fluctuations and black holes in string theory.
State-space Geometry, Statistical Fluctuations and Black Holes in String Theory
Bellucci, Stefano
2011-01-01
We study the state-space geometry of various extremal and nonextremal black holes in string theory. From the notion of the intrinsic geometry, we offer a new perspective of black hole vacuum fluctuations. For a given black hole entropy, we explicate the intrinsic state-space geometric meaning of the statistical fluctuations, local and global stability conditions and long range statistical correlations. We provide a set of physical motivations pertaining to the extremal and nonextremal black holes, \\textit{viz.}, the meaning of the chemical geometry and physics of correlation. We illustrate the state-space configurations for general charge extremal black holes. In sequel, we extend our analysis for various possible charge and anticharge nonextremal black holes. From the perspective of statistical fluctuation theory, we offer general remarks, future directions and open issues towards the intrinsic geometric understanding of the vacuum fluctuations and black holes in string theory. Keywords: Intrinsic Geometry; ...