Apparent and partial molal heat capacities of aqueous rare earth nitrate solutions at 250C
International Nuclear Information System (INIS)
Spedding, F.H.; Baker, J.L.; Walters, J.P.
1979-01-01
Specific heats of aqueous solutions of the trinitrates of La, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu were measured from 0.1 m to saturation at 25 0 C. Apparent molal heat capacities, phi/sub cp/, were calculated for these solutions, and empirical polynomial equations were obtained which expressed phi/sub cp/ as a function of m/sup 1/2/ for each salt. The partial molal heat capacities of the solvent, anti C 1 /sub p/, and solute, anti C 2 /sub p/, were calculated from these equations. Unlike chloride and perchlorate data reported earlier, values of anti C 1 /sub p/ for nitrate solutions across the rare earth series did not show a two series effect. Instead, anti C 1 /sub p/ values at lower concentrations (0.5 and 1.0 m) appear correlated with reported first formation constants for rare earth-nitrate complexes. 31 references, 9 figures, 2 tables
Thermodynamics on the Molality Scale
Canagaratna, Sebastian G.; Maheswaran, M.
2013-01-01
For physical measurements, the compositions of solutions, especially electrolyte solutions, are expressed in terms of molality rather than mole fractions. The development of the necessary thermodynamic equations directly in terms of molality is not common in textbooks, and the treatment in the literature is not very systematic. We develop a…
System Entropy Measurement of Stochastic Partial Differential Systems
Directory of Open Access Journals (Sweden)
Bor-Sen Chen
2016-03-01
Full Text Available System entropy describes the dispersal of a system’s energy and is an indication of the disorder of a physical system. Several system entropy measurement methods have been developed for dynamic systems. However, most real physical systems are always modeled using stochastic partial differential dynamic equations in the spatio-temporal domain. No efficient method currently exists that can calculate the system entropy of stochastic partial differential systems (SPDSs in consideration of the effects of intrinsic random fluctuation and compartment diffusion. In this study, a novel indirect measurement method is proposed for calculating of system entropy of SPDSs using a Hamilton–Jacobi integral inequality (HJII-constrained optimization method. In other words, we solve a nonlinear HJII-constrained optimization problem for measuring the system entropy of nonlinear stochastic partial differential systems (NSPDSs. To simplify the system entropy measurement of NSPDSs, the global linearization technique and finite difference scheme were employed to approximate the nonlinear stochastic spatial state space system. This allows the nonlinear HJII-constrained optimization problem for the system entropy measurement to be transformed to an equivalent linear matrix inequalities (LMIs-constrained optimization problem, which can be easily solved using the MATLAB LMI-toolbox (MATLAB R2014a, version 8.3. Finally, several examples are presented to illustrate the system entropy measurement of SPDSs.
Entropy and convexity for nonlinear partial differential equations.
Ball, John M; Chen, Gui-Qiang G
2013-12-28
Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological and social processes. The concept of entropy originated in thermodynamics and statistical physics during the nineteenth century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the Theme Issue is intended to provide an introduction to entropy, convexity and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this Theme Issue.
Entropy methods for diffusive partial differential equations
Jüngel, Ansgar
2016-01-01
This book presents a range of entropy methods for diffusive PDEs devised by many researchers in the course of the past few decades, which allow us to understand the qualitative behavior of solutions to diffusive equations (and Markov diffusion processes). Applications include the large-time asymptotics of solutions, the derivation of convex Sobolev inequalities, the existence and uniqueness of weak solutions, and the analysis of discrete and geometric structures of the PDEs. The purpose of the book is to provide readers an introduction to selected entropy methods that can be found in the research literature. In order to highlight the core concepts, the results are not stated in the widest generality and most of the arguments are only formal (in the sense that the functional setting is not specified or sufficient regularity is supposed). The text is also suitable for advanced master and PhD students and could serve as a textbook for special courses and seminars.
Uncertainty principle and informational entropy for partially coherent light
Bastiaans, M.J.
1986-01-01
It is shown that, among all partially coherent wave fields having the same informational entropy, the product of the effective widths of the intensity functions in the space and the spatial-frequency domains takes its minimum value for a wave field with a Gaussian-shaped cross-spectral density
International Nuclear Information System (INIS)
Moreno, Nicolás; Malagón, Andrés; Buchner, Richard; Vargas, Edgar F.
2014-01-01
Highlights: • Apparent molal volumes of five isomers of Bu 4 NBr in water have been measured. • The structural effect of branched and linear chains is discussed. • The structural contributions to the ionic volume were calculated. -- Abstract: Apparent molal volumes of a series of differently substituted quaternary ammonium bromides, namely tetra-iso-butyl-, tetra-sec-butyl-, tetra-n-butyl-, di-n-butyl-di-sec-butyl- and di-n-butyl-di-iso-butylammonium bromide have been determined as a function of molal concentration at (298.15, 303.15 and 308.15) K. Partial molar volumes at infinite dilution and ionic molar volumes of these quaternary ammonium cations were determined. Structural volume contributions to the ionic molar volume were also calculated. The symmetric and asymmetric quaternary ammonium cations are “structure making” ions. The contribution of the branched butyl chains predominates over the linear butyl chains in the asymmetric cations
Gravel Image Segmentation in Noisy Background Based on Partial Entropy Method
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Because of wide variation in gray levels and particle dimensions and the presence of many small gravel objects in the background, as well as corrupting the image by noise, it is difficult o segment gravel objects. In this paper, we develop a partial entropy method and succeed to realize gravel objects segmentation. We give entropy principles and fur calculation methods. Moreover, we use minimum entropy error automaticly to select a threshold to segment image. We introduce the filter method using mathematical morphology. The segment experiments are performed by using different window dimensions for a group of gravel image and demonstrates that this method has high segmentation rate and low noise sensitivity.
Entropy generation in Poiseuille flow through a channel partially filled with a porous material
Directory of Open Access Journals (Sweden)
Kumar Vikas
2015-01-01
Full Text Available In the present paper, a theoretical analysis of entropy generation due to fully developed flow and heat transfer through a parallel plate channel partially filled with a porous medium under the effect of transverse magnetic field and radiation is presented. Both horizontal plates of the channel are kept at constant and equal temperature. An exact solution of governing equation for both porous and clear fluid regions has been obtained in closed form. The entropy generation number and the Bejan number are also calculated. The effects of various parameters such as magnetic field parameter, radiation parameter, Brinkman number, permeability parameter, ratios of viscosities and thermal conductivities are examined on velocity, temperature, entropy generation rate.
Quadrupole terms in the Maxwell equations: Born energy, partial molar volume, and entropy of ions.
Slavchov, Radomir I; Ivanov, Tzanko I
2014-02-21
A new equation of state relating the macroscopic quadrupole moment density Q to the gradient of the field ∇E in an isotropic fluid is derived: Q = αQ(∇E - U∇·E/3), where the quadrupolarizability αQ is proportional to the squared molecular quadrupole moment. Using this equation of state, a generalized expression for the Born energy of an ion dissolved in quadrupolar solvent is obtained. It turns out that the potential and the energy of a point charge in a quadrupolar medium are finite. From the obtained Born energy, the partial molar volume and the partial molar entropy of a dissolved ion follow. Both are compared to experimental data for a large number of simple ions in aqueous solutions. From the comparison the value of the quadrupolar length LQ is determined, LQ = (αQ/3ɛ)(1/2) = 1-4 Å. Data for ion transfer from aqueous to polar oil solution are analyzed, which allowed for the determination of the quadrupolarizability of nitrobenzene.
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.
Apparent Molal Volumes of Sodium Fluoride in Mixed Aqueous-Ethanol Solvents
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E. Gomaa
2010-09-01
Full Text Available The densities of different molal concentrations of sodium fluoride at ethanol-water mixtures, as solvent, have been measured over the whole composition range at three different temperatures, 293.15, 303.15 and 313.15oK. From the measured densities, the apparent and limiting molal volumes of the electrolytes have been evaluated. The limiting molal volumes for sodium and fluoride ions were estimated by splitting the ionic contributions as an asymmetric assumption.
Amend, Jan P.; Plyasunov, Andrey V.
2001-11-01
Experimental thermodynamic data for aqueous organic compounds can be combined with the revised Helgeson-Kirkham-Flowers (HKF) equations of state to generate parameters that can be used to estimate standard molal properties as functions of temperature and pressure. In this study, we regressed thermodynamic data for aqueous carbohydrates at temperatures up to 393 K reported in the literature to permit the calculation of the apparent standard molal Gibbs free energies and enthalpies of formation (ΔGo and ΔHo, respectively) and the standard molal entropies (S2o), heat capacities (CP,2o), and volumes (V2o) to 423 K and several hundred MPa of aqueous C5 aldoses (ribose, arabinose, xylose, lyxose) and C5 ketoses (ribulose, xylulose) as well as C6 aldoses (glucose, mannose, galactose) and C6 ketoses (fructose, sorbose). Values of ΔGo for these 11 aqueous carbohydrates are given as a function of temperature at the saturated water vapor pressure (PSAT) and at 50 MPa. Values of ΔGo for aqueous glucose are then combined with those of other aqueous organic and inorganic compounds to calculate values of the standard molal Gibbs free energies of 13 fermentation and respiration reactions (ΔGro) known or likely to be carried out by thermophilic microorganisms. Finally, values of the overall Gibbs free energies of these reactions (ΔGr) are calculated at the temperature, pressure, and chemical composition that obtain in the hydrothermal fluids of Vulcano Island, southern Italy, a site that is widely known for its tremendous diversity of organisms able to live at high temperatures. At likely activities of aqueous glucose, it is shown that thermophiles in the hot springs of Vulcano at 373 K and ∼0.1 MPa can gain between 400 and 3000 kJ per mole of glucose fermented or respired.
International Nuclear Information System (INIS)
De Nicola, Sergio; Fedele, Renato; Man'ko, Margarita A; Man'ko, Vladimir I
2007-01-01
The tomographic-probability description of quantum states is reviewed. The symplectic tomography of quantum states with continuous variables is studied. The symplectic entropy of the states with continuous variables is discussed and its relation to Shannon entropy and information is elucidated. The known entropic uncertainty relations of the probability distribution in position and momentum of a particle are extended and new uncertainty relations for symplectic entropy are obtained. The partial case of symplectic entropy, which is optical entropy of quantum states, is considered. The entropy associated to optical tomogram is shown to satisfy the new entropic uncertainty relation. The example of Gaussian states of harmonic oscillator is studied and the entropic uncertainty relations for optical tomograms of the Gaussian state are shown to minimize the uncertainty relation
Directory of Open Access Journals (Sweden)
J. M. Dick
2006-01-01
Full Text Available Thermodynamic calculations can be used to quantify environmental constraints on the speciation of proteins, such as the pH and temperature dependence of ionization state, and the relative chemical stabilities of proteins in different biogeochemical settings. These calculations depend in part on values of the standard molal Gibbs energies of proteins and their ionization reactions as a function of temperature and pressure. Because these values are not generally available, we calculated values of the standard molal thermodynamic properties at 25°C and 1 bar as well as the revised Helgeson-Kirkham-Flowers equations of state parameters of neutral and charged zwitterionic reference model compounds including aqueous amino acids, polypeptides, and unfolded proteins. The experimental calorimetric and volumetric data for these species taken from the literature were combined with group additivity algorithms to calculate the properties and parameters of neutral and ionized sidechain and backbone groups in unfolded proteins. The resulting set of group contributions enables the calculation of the standard molal Gibbs energy, enthalpy, entropy, isobaric heat capacity, volume, and isothermal compressibility of unfolded proteins in a range of proton ionization states to temperatures and pressures exceeding 100°C and 1000 bar. This approach provides a useful frame of reference for thermodynamic studies of protein folding and complexation reactions. It can also be used to assign provisional values of the net charge and Gibbs energy of ionized proteins as a function of temperature and pH. Using these values, an Eh-pH diagram for a reaction representing the speciation of extracellular proteins from Pyrococcus furiosus and Bacillus subtilis was generated. The predicted predominance limits of these proteins correspond with the different electrochemical conditions of hydrothermal vents and soils. More comprehensive calculations of this kind may reveal pervasive
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...
International Nuclear Information System (INIS)
Clavijo Penagos, J.A.; Blanco, L.H.
2012-01-01
Highlights: ►V φ for HMT and TATD in aqueous solutions around the temperature of maximum density of water are reported. ► V φ is linear in m form m = 0.025 for all the aqueous solutions investigated. ► Variation of V ¯ 2 ∞ with T obeys a second grade polynomial trend. ► The solutes are classified as structure breakers according to Hepler’s criterion. - Abstract: Apparent molal volumes V φ have been determined from density measurements for several aqueous solutions of 1,3,5,7-tetraazatricyclo[3.3.1.1(3,7)]decane (HMT) and 1,3,6,8-tetraazatricyclo[4.4.1.1(3,8)]dodecane (TATD) at T = (275.15, 275.65, 276.15, 276.65, 277.15, 277.65 and 278.15) K as function of composition. The infinite dilution partial molar volumes of solutes in aqueous solution are evaluated through extrapolation. Interactions of the solutes with water are discussed in terms of the effect of the temperature on the volumetric properties and the structure of the solutes. The results are interpreted in terms of water structure-breaking or structure forming character of the solutes.
Absolute entropy of ions in methanol
International Nuclear Information System (INIS)
Abakshin, V.A.; Kobenin, V.A.; Krestov, G.A.
1978-01-01
By measuring the initial thermoelectromotive forces of chains with bromo-silver electrodes in tetraalkylammonium bromide solutions the absolute entropy of bromide-ion in methanol is determined in the 298.15-318.15 K range. The anti Ssub(Brsup(-))sup(0) = 9.8 entropy units value is used for calculation of the absolute partial molar entropy of alkali metal ions and halogenide ions. It has been found that, absolute entropy of Cs + =12.0 entropy units, I - =14.0 entropy units. The obtained ion absolute entropies in methanol at 298.15 K within 1-2 entropy units is in an agreement with published data
Plutonium (IV) complexation by nitrate in acid solutions of ionic strengths from 2 to 19 molal
International Nuclear Information System (INIS)
Berg, J.M.; Veirs, D.K.; Vaughn, R.B.; Cisneros, M.A.; Smith, C.A.
1997-01-01
Titrations of Pu(IV) with HNO 3 in a series of aqueous HClO 4 solutions ranging in ionic strength from 2 to 19 molal were followed using absorption spectrophotometry. The Pu 5f-5f spectra in the visible and near IR range change with complex formation. At each ionic strength, a series of spectra were obtained by varying nitrate concentration. Each series was deconvoluted into spectra f Pu 4+ (aq), Pu(NO 3 ) 3+ and Pu(NO 3 ) 2 2+ complexes, and simultaneously their formation constants were determined. When corrected for the incomplete dissociation of nitric acid, the ionic strength dependence of each formation constant can be described by two parameters, β 0 and Δ var-epsilon using the formulae of specific ion interaction theory. The difficulties with extending this analysis to higher nitrate coordination numbers are discussed
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...
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.
International Nuclear Information System (INIS)
Maes, Christian
2012-01-01
In contrast to the quite unique entropy concept useful for systems in (local) thermodynamic equilibrium, there is a variety of quite distinct nonequilibrium entropies, reflecting different physical points. We disentangle these entropies as they relate to heat, fluctuations, response, time asymmetry, variational principles, monotonicity, volume contraction or statistical forces. However, not all of those extensions yield state quantities as understood thermodynamically. At the end we sketch how aspects of dynamical activity can take over for obtaining an extended Clausius relation.
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.
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 ...
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!
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
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.
Explaining the entropy concept and entropy components
Directory of Open Access Journals (Sweden)
Marko Popovic
2018-04-01
Full Text Available Total entropy of a thermodynamic system consists of two components: thermal entropy due to energy, and residual entropy due to molecular orientation. In this article, a three-step method for explaining entropy is suggested. Step one is to use a classical method to introduce thermal entropy STM as a function of temperature T and heat capacity at constant pressure Cp: STM = ∫(Cp/T dT. Thermal entropy is the entropy due to uncertainty in motion of molecules and vanishes at absolute zero (zero-point energy state. It is also the measure of useless thermal energy that cannot be converted into useful work. The next step is to introduce residual entropy S0 as a function of the number of molecules N and the number of distinct orientations available to them in a crystal m: S0 = N kB ln m, where kB is the Boltzmann constant. Residual entropy quantifies the uncertainty in molecular orientation. Residual entropy, unlike thermal entropy, is independent of temperature and remains present at absolute zero. The third step is to show that thermal entropy and residual entropy add up to the total entropy of a thermodynamic system S: S = S0 + STM. This method of explanation should result in a better comprehension of residual entropy and thermal entropy, as well as of their similarities and differences. The new method was tested in teaching at Faculty of Chemistry University of Belgrade, Serbia. The results of the test show that the new method has a potential to improve the quality of teaching.
SpatEntropy: Spatial Entropy Measures in R
Altieri, Linda; Cocchi, Daniela; Roli, Giulia
2018-01-01
This article illustrates how to measure the heterogeneity of spatial data presenting a finite number of categories via computation of spatial entropy. The R package SpatEntropy contains functions for the computation of entropy and spatial entropy measures. The extension to spatial entropy measures is a unique feature of SpatEntropy. In addition to the traditional version of Shannon's entropy, the package includes Batty's spatial entropy, O'Neill's entropy, Li and Reynolds' contagion index, Ka...
Entanglement generation and entropy growth due to intrinsic decoherence in the Jaynes-Cummings model
International Nuclear Information System (INIS)
Obada, A.-S.F.; Hessian, Hosny A.
2004-01-01
We study how intrinsic decoherence leads to growing entropy and a strong degradation of the maximal generated entanglement in the multiquanta Jaynes-Cummings model. We find an exact solution of the Milburn equation in multiquanta precesses and calculate the partial entropy of the particle (atom or trapped ion) and field subsystem as well as total entropy. As the total entropy is not conserved, and it is shown to increase as time develops, one cannot use the partial field or atomic entropy as a direct measure of particle-field entanglement. For a good entropy measure, we also calculate the negativity of the eigenvalues of the partially transposed density matrix. We find that, at least qualitatively, the difference of the total entropy to the sum of field and atom partial entropies can be also used as an entanglement measure. Our results show that the degree of entanglement is very sensitive to any change in the intrinsic decoherence parameter
Quantum dynamical entropy revisited
International Nuclear Information System (INIS)
Hudetz, T.
1996-10-01
We define a new quantum dynamical entropy, which is a 'hybrid' of the closely related, physically oriented entropy introduced by Alicki and Fannes in 1994, and of the mathematically well-developed, single-argument entropy introduced by Connes, Narnhofer and Thirring in 1987. We show that this new quantum dynamical entropy has many properties similar to the ones of the Alicki-Fannes entropy, and also inherits some additional properties from the CNT entropy. In particular, the 'hybrid' entropy interpolates between the two different ways in which both the AF and the CNT entropy of the shift automorphism on the quantum spin chain agree with the usual quantum entropy density, resulting in even better agreement. Also, the new quantum dynamical entropy generalizes the classical dynamical entropy of Kolmogorov and Sinai in the same way as does the AF entropy. Finally, we estimate the 'hybrid' entropy both for the Powers-Price shift systems and for the noncommutative Arnold map on the irrational rotation C * -algebra, leaving some interesting open problems. (author)
Directory of Open Access Journals (Sweden)
Urban Kordes
2005-10-01
Full Text Available The paper tries to tackle the question of connection between entropy and the living. Definitions of life as the phenomenon that defies entropy are overviewed and the conclusion is reached that life is in a way dependant on entropy - it couldn't exist without it. Entropy is a sort of medium, a fertile soil, that gives life possibility to blossom. Paper ends with presenting some consequences for the field of artificial intelligence.
Entropy of Baker's Transformation
Institute of Scientific and Technical Information of China (English)
栾长福
2003-01-01
Four theorems about four different kinds of entropies for Baker's transformation are presented. The Kolmogorov entropy of Baker's transformation is sensitive to the initial flips by the time. The topological entropy of Baker's transformation is found to be log k. The conditions for the state of Baker's transformation to be forbidden are also derived. The relations among the Shanonn, Kolmogorov, topological and Boltzmann entropies are discussed in details.
Physical entropy, information entropy and their evolution equations
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Inspired by the evolution equation of nonequilibrium statistical physics entropy and the concise statistical formula of the entropy production rate, we develop a theory of the dynamic information entropy and build a nonlinear evolution equation of the information entropy density changing in time and state variable space. Its mathematical form and physical meaning are similar to the evolution equation of the physical entropy: The time rate of change of information entropy density originates together from drift, diffusion and production. The concise statistical formula of information entropy production rate is similar to that of physical entropy also. Furthermore, we study the similarity and difference between physical entropy and information entropy and the possible unification of the two statistical entropies, and discuss the relationship among the principle of entropy increase, the principle of equilibrium maximum entropy and the principle of maximum information entropy as well as the connection between them and the entropy evolution equation.
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.)
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)
Volkenstein, Mikhail V
2009-01-01
The book "Entropy and Information" deals with the thermodynamical concept of entropy and its relationship to information theory. It is successful in explaining the universality of the term "Entropy" not only as a physical phenomenon, but reveals its existence also in other domains. E.g., Volkenstein discusses the "meaning" of entropy in a biological context and shows how entropy is related to artistic activities. Written by the renowned Russian bio-physicist Mikhail V. Volkenstein, this book on "Entropy and Information" surely serves as a timely introduction to understand entropy from a thermodynamic perspective and is definitely an inspiring and thought-provoking book that should be read by every physicist, information-theorist, biologist, and even artist.
Czech Academy of Sciences Publication Activity Database
Heyrovská, Raji
2007-01-01
Roč. 436, č. 1-3 (2007), s. 287-293 ISSN 0009-2614 R&D Projects: GA MŠk(CZ) LC06035 Institutional research plan: CEZ:AV0Z50040702 Keywords : alkali halides * ionic hydration * golden ratio Subject RIV: BO - Biophysics Impact factor: 2.207, year: 2007
RNA Thermodynamic Structural Entropy.
Garcia-Martin, Juan Antonio; Clote, Peter
2015-01-01
Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe the first two accurate and efficient algorithms to compute the conformational entropy for RNA secondary structures, with respect to the Turner energy model, where free energy parameters are determined from UV absorption experiments. An algorithm to compute the derivational entropy for RNA secondary structures had previously been introduced, using stochastic context free grammars (SCFGs). However, the numerical value of derivational entropy depends heavily on the chosen context free grammar and on the training set used to estimate rule probabilities. Using data from the Rfam database, we determine that both of our thermodynamic methods, which agree in numerical value, are substantially faster than the SCFG method. Thermodynamic structural entropy is much smaller than derivational entropy, and the correlation between length-normalized thermodynamic entropy and derivational entropy is moderately weak to poor. In applications, we plot the structural entropy as a function of temperature for known thermoswitches, such as the repression of heat shock gene expression (ROSE) element, we determine that the correlation between hammerhead ribozyme cleavage activity and total free energy is improved by including an additional free energy term arising from conformational entropy, and we plot the structural entropy of windows of the HIV-1 genome. Our software RNAentropy can compute structural entropy for any user-specified temperature, and supports both the Turner'99 and Turner'04 energy parameters. It follows that RNAentropy is state-of-the-art software to compute RNA secondary structure conformational entropy. Source code is available at https://github.com/clotelab/RNAentropy/; a full web server is available at http
RNA Thermodynamic Structural Entropy.
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
Entropy Exchange in Coupled Field-Superconducting Charge Qubit System with Intrinsic Decoherence
Institute of Scientific and Technical Information of China (English)
SHAO Bin; ZHANG Jian; ZOU Jian
2006-01-01
Based on the intrinsic decoherence effect, partial entropy properties of a super conducting charge qubitinside a single-mode cavity field is investigated, and entropy exchange which is recently regarded as a kind of anti-correlated behavior of the entropy between subsystems is explored. Our results show that although the intrinsic decoherenceleads to an effective irreversible evolution of the interacting system due to a suppression of coherent quantum features through the decay of off-diagonal matrix elements of the density operator and has an apparently influence on the partial entropy of two individual subsystems, it does not effect the entropy exchange between the two subsystems.
Maximum Quantum Entropy Method
Sim, Jae-Hoon; Han, Myung Joon
2018-01-01
Maximum entropy method for analytic continuation is extended by introducing quantum relative entropy. This new method is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input matrix. As a result, the continuation of off-diagonal elements becomes straightforward. Without introducing any further ambiguity, the Bayesian probabilistic interpretation is maintained just as in the conventional maximum entropy method. The applications o...
Transplanckian entanglement entropy
International Nuclear Information System (INIS)
Chang, Darwin; Chu, C.-S.; Lin Fengli
2004-01-01
The entanglement entropy of the event horizon is known to be plagued by the UV divergence due to the infinitely blue-shifted near horizon modes. In this Letter we calculate the entanglement entropy using the transplanckian dispersion relation, which has been proposed to model the quantum gravity effects. We show that, very generally, the entropy is rendered UV finite due to the suppression of high energy modes effected by the transplanckian dispersion relation
2015-09-29
antiferroelectrics. Phys. Rev. Lett. 110, 017603 (2013). 22. Cantor , B., Chang, I., Knight, P. & Vincent, A. Microstructural development in equiatomic...Science 345, 1153–1158 (2014). 24. Gali, A. & George , E. Tensile properties of high- and medium-entropy alloys. Intermetallics 39, 74–78 (2013). 25...148–153 (2014). 26. Otto, F., Yang, Y., Bei, H. & George , E. Relative effects of enthalpy and entropy on the phase stability of equiatomic high-entropy
International Nuclear Information System (INIS)
Kolb, E.W.; Lindley, D.; Seckel, D.
1984-01-01
For a cosmological model with d noncompact and D compact spatial dimensions and symmetry R 1 x S/sup d/ x S/sup D/, we calculate the entropy produced in d dimensions due to the compactification of D dimensions and show it too small to be of cosmological interest. Although insufficient entropy is produced in the model we study, the contraction of extra dimensions does lead to entropy production. We discuss modifications of our assumptions, including changing our condition for decoupling of the extra dimensions, which may lead to a large entropy production and change our conclusions
ENTROPY FUNCTIONAL FOR CONTINUOUS SYSTEMS OF FINITE ENTROPY
Institute of Scientific and Technical Information of China (English)
M. Rahimi A. Riazi
2012-01-01
In this article,we introduce the concept of entropy functional for continuous systems on compact metric spaces,and prove some of its properties.We also extract the Kolmogorov entropy from the entropy functional.
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 ...
Indian Academy of Sciences (India)
During the process of ageing, the balance shifts in the direction of anarchy. Death is ... tion of life and the laws of statistieal physics and entropy, both of which ... capable of doing work. ... defined by Ludwig Boltzmann in 1877, the entropy of the.
Energy Technology Data Exchange (ETDEWEB)
Bao, Ning [Institute for Quantum Information and Matter, California Institute of Technology,Pasadena, CA 91125 (United States); Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Nezami, Sepehr [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States); Ooguri, Hirosi [Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo,Kashiwa 277-8583 (Japan); Stoica, Bogdan [Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Sully, James [Theory Group, SLAC National Accelerator Laboratory, Stanford University,Menlo Park, CA 94025 (United States); Walter, Michael [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States)
2015-09-21
We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.
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.
Entropy and Digital Installation
Directory of Open Access Journals (Sweden)
Susan Ballard
2005-01-01
Full Text Available This paper examines entropy as a process which introduces ideas of distributed materiality to digital installation. Beginning from an analysis of entropy as both force and probability measure within information theory and it’s extension in Ruldof Arnheim’s text ‘Entropy and Art” it develops an argument for the positive rather thannegative forces of entropy. The paper centres on a discussion of two recent works by New Zealand artists Ronnie van Hout (“On the Run”, Wellington City Gallery, NZ, 2004 and Alex Monteith (“Invisible Cities”, Physics Room Contemporary Art Space, Christchurch, NZ, 2004. Ballard suggests that entropy, rather than being a hindrance to understanding or a random chaotic force, discloses a necessary and material politics of noise present in digital installation.
Nonsymmetric entropy I: basic concepts and results
Liu, Chengshi
2006-01-01
A new concept named nonsymmetric entropy which generalizes the concepts of Boltzman's entropy and shannon's entropy, was introduced. Maximal nonsymmetric entropy principle was proven. Some important distribution laws were derived naturally from maximal nonsymmetric entropy principle.
Entropy 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, Roger; Stadje, M.A.
2010-01-01
We introduce entropy coherent and entropy convex measures of risk and prove a collection of axiomatic characterization and duality results. We show in particular that entropy coherent and entropy convex measures of risk emerge as negative certainty equivalents in (the regular and a generalized
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
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,
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)
Black hole thermodynamical entropy
International Nuclear Information System (INIS)
Tsallis, Constantino; Cirto, Leonardo J.L.
2013-01-01
As early as 1902, Gibbs pointed out that systems whose partition function diverges, e.g. gravitation, lie outside the validity of the Boltzmann-Gibbs (BG) theory. Consistently, since the pioneering Bekenstein-Hawking results, physically meaningful evidence (e.g., the holographic principle) has accumulated that the BG entropy S BG of a (3+1) black hole is proportional to its area L 2 (L being a characteristic linear length), and not to its volume L 3 . Similarly it exists the area law, so named because, for a wide class of strongly quantum-entangled d-dimensional systems, S BG is proportional to lnL if d=1, and to L d-1 if d>1, instead of being proportional to L d (d ≥ 1). These results violate the extensivity of the thermodynamical entropy of a d-dimensional system. This thermodynamical inconsistency disappears if we realize that the thermodynamical entropy of such nonstandard systems is not to be identified with the BG additive entropy but with appropriately generalized nonadditive entropies. Indeed, the celebrated usefulness of the BG entropy is founded on hypothesis such as relatively weak probabilistic correlations (and their connections to ergodicity, which by no means can be assumed as a general rule of nature). Here we introduce a generalized entropy which, for the Schwarzschild black hole and the area law, can solve the thermodynamic puzzle. (orig.)
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.
The constraint rule of the maximum entropy principle
Uffink, J.
1995-01-01
The principle of maximum entropy is a method for assigning values to probability distributions on the basis of partial information. In usual formulations of this and related methods of inference one assumes that this partial information takes the form of a constraint on allowed probability
Some remarks on conditional entropy
Nijst, A.G.P.M.
1969-01-01
Using a definition of conditional entropy given by Hanen and Neveu [5, 10, 11] we discuss in this paper some properties of conditional entropy and mean entropy, in particular an integral representation of conditional entropy (§ 2), and the decomposition theorem of the KolmogorovSina¯i invariant (§
Zhong, X.; Galvez, M. E.
2017-12-01
Metamorphic fluids are a crucial ingredient of geodynamic evolution, i.e. heat transfer, rock mechanics and metamorphic/metasomatic reactions. During crustal evolution at elevated P and T, rock forming components can be effectively fractionated from the reactive rock system by at least two processes: 1. extraction from porous rocks by liquid phases such as solute-bearing (e.g. Na+, Mg2+) aqueous fluids or partial melts. 2. isolation from effective bulk rock composition due to slow intragranular diffusion in high-P refractory phases such as garnet. The effect of phase fractionation (garnet, partial melt and aqueous species) on fluid - rock composition and properties remain unclear, mainly due to a high demand in quantitative computations of the thermodynamic interactions between rocks and fluids over a wide P-T range. To investigate this problem, we build our work on an approach initially introduced by Galvez et al., (2015) with new functionalities added in a MATLAB code (Rubisco). The fluxes of fractionated components in fluid, melt and garnet are monitored along a typical prograde P-T path for a model crustal pelite. Some preliminary results suggest a marginal effect of fractionated aqueous species on fluid and rock properties (e.g. pH, composition), but the corresponding fluxes are significant in the context of mantle wedge metasomatism. Our work provides insight into the role of high-P phase fractionation on mass redistribution between the surface and deep Earth in subduction zones. Existing limitations relevant to our liquid/mineral speciation/fractionation model will be discussed as well. ReferencesGalvez, M.E., Manning, C.E., Connolly, J.A.D., Rumble, D., 2015. The solubility of rocks in metamorphic fluids: A model for rock-dominated conditions to upper mantle pressure and temperature. Earth Planet. Sci. Lett. 430, 486-498.
Entropy of international trades
Oh, Chang-Young; Lee, D.-S.
2017-05-01
The organization of international trades is highly complex under the collective efforts towards economic profits of participating countries given inhomogeneous resources for production. Considering the trade flux as the probability of exporting a product from a country to another, we evaluate the entropy of the world trades in the period 1950-2000. The trade entropy has increased with time, and we show that it is mainly due to the extension of trade partnership. For a given number of trade partners, the mean trade entropy is about 60% of the maximum possible entropy, independent of time, which can be regarded as a characteristic of the trade fluxes' heterogeneity and is shown to be derived from the scaling and functional behaviors of the universal trade-flux distribution. The correlation and time evolution of the individual countries' gross-domestic products and the number of trade partners show that most countries achieved their economic growth partly by extending their trade relationship.
International Nuclear Information System (INIS)
Estes, John; Jensen, Kristan; O’Bannon, Andy; Tsatis, Efstratios; Wrase, Timm
2014-01-01
We study a number of (3+1)- and (2+1)-dimensional defect and boundary conformal field theories holographically dual to supergravity theories. In all cases the defects or boundaries are planar, and the defects are codimension-one. Using holography, we compute the entanglement entropy of a (hemi-)spherical region centered on the defect (boundary). We define defect and boundary entropies from the entanglement entropy by an appropriate background subtraction. For some (3+1)-dimensional theories we find evidence that the defect/boundary entropy changes monotonically under certain renormalization group flows triggered by operators localized at the defect or boundary. This provides evidence that the g-theorem of (1+1)-dimensional field theories generalizes to higher dimensions
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
Katan, Claudine; Mohite, Aditya D.; Even, Jacky
2018-05-01
Claudine Katan, Aditya D. Mohite and Jacky Even discuss the possible impact of various entropy contributions (stochastic structural fluctuations, anharmonicity and lattice softness) on the optoelectronic properties of halide perovskite materials and devices.
Directory of Open Access Journals (Sweden)
F. S. Zhang
2016-01-01
Full Text Available The spatial mapping of losses attributable to such disasters is now well established as a means of describing the spatial patterns of disaster risk, and it has been shown to be suitable for many types of major meteorological disasters. However, few studies have been carried out by developing a regression model to estimate the effects of the spatial distribution of meteorological factors on losses associated with meteorological disasters. In this study, the proposed approach is capable of the following: (a estimating the spatial distributions of seven meteorological factors using Bayesian maximum entropy, (b identifying the four mapping methods used in this research with the best performance based on the cross validation, and (c establishing a fitted model between the PLS components and disaster losses information using partial least squares regression within a specific research area. The results showed the following: (a best mapping results were produced by multivariate Bayesian maximum entropy with probabilistic soft data; (b the regression model using three PLS components, extracted from seven meteorological factors by PLS method, was the most predictive by means of PRESS/SS test; (c northern Hunan Province sustains the most damage, and southeastern Gansu Province and western Guizhou Province sustained the least.
Sze, Vivienne; Marpe, Detlev
2014-01-01
Context-Based Adaptive Binary Arithmetic Coding (CABAC) is a method of entropy coding first introduced in H.264/AVC and now used in the latest High Efficiency Video Coding (HEVC) standard. While it provides high coding efficiency, the data dependencies in H.264/AVC CABAC make it challenging to parallelize and thus limit its throughput. Accordingly, during the standardization of entropy coding for HEVC, both aspects of coding efficiency and throughput were considered. This chapter describes th...
Manfredi; Feix
2000-10-01
The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such a definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of entanglement of a quantum state. It is shown that smoothing of the Wigner function induces an increase in entropy. This fact is used to derive some simple rules to construct positive-definite probability distributions which are also admissible Wigner functions.
Manfredi, G.; Feix, M. R.
2002-01-01
The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of entanglement of a quantum state. It is shown that smoothing of the Wigner function induces an increase in entropy. This fact is used to derive some simple rules to construct positive definite probability distributions which are also admissible Wigner functions
Feasible Histories, Maximum Entropy
International Nuclear Information System (INIS)
Pitowsky, I.
1999-01-01
We consider the broadest possible consistency condition for a family of histories, which extends all previous proposals. A family that satisfies this condition is called feasible. On each feasible family of histories we choose a probability measure by maximizing entropy, while keeping the probabilities of commuting histories to their quantum mechanical values. This procedure is justified by the assumption that decoherence increases entropy. Finally, a criterion for identifying the nearly classical families is proposed
Gulamsarwar, Syazwani; Salleh, Zabidin
2017-08-01
The purpose of this paper is to generalize the notions of Adler's topological entropy along with their several fundamental properties. A function f : X → Y is said to be R-map if f-1 (V) is regular open in X for every regular open set V in Y. Thus, we initiated a notion of topological nearly entropy for topological R-dynamical systems which is based on nearly compact relative to the space by using R-map.
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.
Entropy, matter, and cosmology.
Prigogine, I; Géhéniau, J
1986-09-01
The role of irreversible processes corresponding to creation of matter in general relativity is investigated. The use of Landau-Lifshitz pseudotensors together with conformal (Minkowski) coordinates suggests that this creation took place in the early universe at the stage of the variation of the conformal factor. The entropy production in this creation process is calculated. It is shown that these dissipative processes lead to the possibility of cosmological models that start from empty conditions and gradually build up matter and entropy. Gravitational entropy takes a simple meaning as associated to the entropy that is necessary to produce matter. This leads to an extension of the third law of thermodynamics, as now the zero point of entropy becomes the space-time structure out of which matter is generated. The theory can be put into a convenient form using a supplementary "C" field in Einstein's field equations. The role of the C field is to express the coupling between gravitation and matter leading to irreversible entropy production.
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
EEG entropy measures in anesthesia
Directory of Open Access Journals (Sweden)
Zhenhu eLiang
2015-02-01
Full Text Available Objective: Entropy algorithms have been widely used in analyzing EEG signals during anesthesia. However, a systematic comparison of these entropy algorithms in assessing anesthesia drugs’ effect is lacking. In this study, we compare the capability of twelve entropy indices for monitoring depth of anesthesia (DoA and detecting the burst suppression pattern (BSP, in anesthesia induced by GA-BAergic agents.Methods: Twelve indices were investigated, namely Response Entropy (RE and State entropy (SE, three wavelet entropy (WE measures (Shannon WE (SWE, Tsallis WE (TWE and Renyi WE (RWE, Hilbert-Huang spectral entropy (HHSE, approximate entropy (ApEn, sample entropy (SampEn, Fuzzy entropy, and three permutation entropy (PE measures (Shannon PE (SPE, Tsallis PE (TPE and Renyi PE (RPE. Two EEG data sets from sevoflurane-induced and isoflu-rane-induced anesthesia respectively were selected to assess the capability of each entropy index in DoA monitoring and BSP detection. To validate the effectiveness of these entropy algorithms, phar-macokinetic / pharmacodynamic (PK/PD modeling and prediction probability analysis were applied. The multifractal detrended fluctuation analysis (MDFA as a non-entropy measure was compared.Results: All the entropy and MDFA indices could track the changes in EEG pattern during different anesthesia states. Three PE measures outperformed the other entropy indices, with less baseline vari-ability, higher coefficient of determination and prediction probability, and RPE performed best; ApEn and SampEn discriminated BSP best. Additionally, these entropy measures showed an ad-vantage in computation efficiency compared with MDFA.Conclusion: Each entropy index has its advantages and disadvantages in estimating DoA. Overall, it is suggested that the RPE index was a superior measure.Significance: Investigating the advantages and disadvantages of these entropy indices could help improve current clinical indices for monitoring DoA.
Bianconi, Ginestra
2009-03-01
In this paper we generalize the concept of random networks to describe network ensembles with nontrivial features by a statistical mechanics approach. This framework is able to describe undirected and directed network ensembles as well as weighted network ensembles. These networks might have nontrivial community structure or, in the case of networks embedded in a given space, they might have a link probability with a nontrivial dependence on the distance between the nodes. These ensembles are characterized by their entropy, which evaluates the cardinality of networks in the ensemble. In particular, in this paper we define and evaluate the structural entropy, i.e., the entropy of the ensembles of undirected uncorrelated simple networks with given degree sequence. We stress the apparent paradox that scale-free degree distributions are characterized by having small structural entropy while they are so widely encountered in natural, social, and technological complex systems. We propose a solution to the paradox by proving that scale-free degree distributions are the most likely degree distribution with the corresponding value of the structural entropy. Finally, the general framework we present in this paper is able to describe microcanonical ensembles of networks as well as canonical or hidden-variable network ensembles with significant implications for the formulation of network-constructing algorithms.
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.
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)
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
Parametric Bayesian Estimation of Differential Entropy and Relative Entropy
Gupta; Srivastava
2010-01-01
Given iid samples drawn from a distribution with known parametric form, we propose the minimization of expected Bregman divergence to form Bayesian estimates of differential entropy and relative entropy, and derive such estimators for the uniform, Gaussian, Wishart, and inverse Wishart distributions. Additionally, formulas are given for a log gamma Bregman divergence and the differential entropy and relative entropy for the Wishart and inverse Wishart. The results, as always with Bayesian est...
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
Energy Technology Data Exchange (ETDEWEB)
Gruszkiewicz, Miroslaw S. [Oak Ridge National Laboratory, Chemical Sciences Division, P.O. Box 2008, Building 4500S MS-6110, Oak Ridge, TN 37831-6110 (United States)]. E-mail: gruszkiewicz@ornl.gov; Simonson, John M. [Oak Ridge National Laboratory, Chemical Sciences Division, P.O. Box 2008, Building 4500S MS-6110, Oak Ridge, TN 37831-6110 (United States)]. E-mail: simonsonjm@ornl.gov
2005-09-15
The Oak Ridge National Laboratory high-temperature isopiestic apparatus was outfitted with precise pressure gauges to allow for direct vapor pressure measurements. Vapor pressures over concentrated solutions of CaCl{sub 2}(aq), and CaBr{sub 2}(aq) were measured at temperatures between (380.15 and 523.15) K in the range of water activities between 0.2 and 0.85. Isopiestic molalities were used to determine osmotic coefficients at the conditions where NaCl reference standard solutions remained undersaturated. The main goal of this work was to improve the accuracy of isopiestic comparisons based on the calcium chloride reference standard. Osmotic coefficients for CaCl{sub 2}(aq) and CaBr{sub 2}(aq) calculated from both isopiestic and direct vapor pressure results were combined with the literature data and used to build general thermodynamic models based on a variant of extended Pitzer ion-interaction equations and valid at the saturation pressure of water. While these empirical models approach the accuracy of the experimental data in a wider range of concentrations and temperatures than any previously published equations, considerable amounts of accurate data and a substantial effort are required in order to obtain a satisfactory representation using power series-based virial equations. The effect of experimental uncertainties on the accuracy of the direct vapor pressure results is discussed, including in particular the error caused by the presence in the apparatus of a small amount of CO{sub 2}. The substantial decrease of the solubility product of CaCO{sub 3} in concentrated chloride solutions at temperatures above 423 K is a serious defect of calcium chloride as a water activity reference standard.
International Nuclear Information System (INIS)
Gruszkiewicz, Miroslaw S.; Simonson, John M.
2005-01-01
The Oak Ridge National Laboratory high-temperature isopiestic apparatus was outfitted with precise pressure gauges to allow for direct vapor pressure measurements. Vapor pressures over concentrated solutions of CaCl 2 (aq), and CaBr 2 (aq) were measured at temperatures between (380.15 and 523.15) K in the range of water activities between 0.2 and 0.85. Isopiestic molalities were used to determine osmotic coefficients at the conditions where NaCl reference standard solutions remained undersaturated. The main goal of this work was to improve the accuracy of isopiestic comparisons based on the calcium chloride reference standard. Osmotic coefficients for CaCl 2 (aq) and CaBr 2 (aq) calculated from both isopiestic and direct vapor pressure results were combined with the literature data and used to build general thermodynamic models based on a variant of extended Pitzer ion-interaction equations and valid at the saturation pressure of water. While these empirical models approach the accuracy of the experimental data in a wider range of concentrations and temperatures than any previously published equations, considerable amounts of accurate data and a substantial effort are required in order to obtain a satisfactory representation using power series-based virial equations. The effect of experimental uncertainties on the accuracy of the direct vapor pressure results is discussed, including in particular the error caused by the presence in the apparatus of a small amount of CO 2 . The substantial decrease of the solubility product of CaCO 3 in concentrated chloride solutions at temperatures above 423 K is a serious defect of calcium chloride as a water activity reference standard
International Nuclear Information System (INIS)
Hudetz, T.
1989-01-01
As a 'by-product' of the Connes-Narnhofer-Thirring theory of dynamical entropy for (originally non-Abelian) nuclear C * -algebras, the well-known variational principle for topological entropy is eqivalently reformulated in purly algebraically defined terms for (separable) Abelian C * -algebras. This 'algebraic variational principle' should not only nicely illustrate the 'feed-back' of methods developed for quantum dynamical systems to the classical theory, but it could also be proved directly by 'algebraic' methods and could thus further simplify the original proof of the variational principle (at least 'in principle'). 23 refs. (Author)
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....
Directory of Open Access Journals (Sweden)
F. TopsÃƒÂ¸e
2001-09-01
Full Text Available Abstract: In its modern formulation, the Maximum Entropy Principle was promoted by E.T. Jaynes, starting in the mid-fifties. The principle dictates that one should look for a distribution, consistent with available information, which maximizes the entropy. However, this principle focuses only on distributions and it appears advantageous to bring information theoretical thinking more prominently into play by also focusing on the "observer" and on coding. This view was brought forward by the second named author in the late seventies and is the view we will follow-up on here. It leads to the consideration of a certain game, the Code Length Game and, via standard game theoretical thinking, to a principle of Game Theoretical Equilibrium. This principle is more basic than the Maximum Entropy Principle in the sense that the search for one type of optimal strategies in the Code Length Game translates directly into the search for distributions with maximum entropy. In the present paper we offer a self-contained and comprehensive treatment of fundamentals of both principles mentioned, based on a study of the Code Length Game. Though new concepts and results are presented, the reading should be instructional and accessible to a rather wide audience, at least if certain mathematical details are left aside at a rst reading. The most frequently studied instance of entropy maximization pertains to the Mean Energy Model which involves a moment constraint related to a given function, here taken to represent "energy". This type of application is very well known from the literature with hundreds of applications pertaining to several different elds and will also here serve as important illustration of the theory. But our approach reaches further, especially regarding the study of continuity properties of the entropy function, and this leads to new results which allow a discussion of models with so-called entropy loss. These results have tempted us to speculate over
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.)
Entanglement entropy and duality
Energy Technology Data Exchange (ETDEWEB)
Radičević, Ðorđe [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA 94305-4060 (United States)
2016-11-22
Using the algebraic approach to entanglement entropy, we study several dual pairs of lattice theories and show how the entropy is completely preserved across each duality. Our main result is that a maximal algebra of observables in a region typically dualizes to a non-maximal algebra in a dual region. In particular, we show how the usual notion of tracing out external degrees of freedom dualizes to a tracing out coupled to an additional summation over superselection sectors. We briefly comment on possible extensions of our results to more intricate dualities, including holographic ones.
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)
Algebraic entropy for algebraic maps
International Nuclear Information System (INIS)
Hone, A N W; Ragnisco, Orlando; Zullo, Federico
2016-01-01
We propose an extension of the concept of algebraic entropy, as introduced by Bellon and Viallet for rational maps, to algebraic maps (or correspondences) of a certain kind. The corresponding entropy is an index of the complexity of the map. The definition inherits the basic properties from the definition of entropy for rational maps. We give an example with positive entropy, as well as two examples taken from the theory of Bäcklund transformations. (letter)
International Nuclear Information System (INIS)
Hansen, Frank
2016-01-01
Incremental information, as measured by the quantum entropy, is increasing when two ensembles are united. This result was proved by Lieb and Ruskai, and it is the foundation for the proof of strong subadditivity of quantum entropy. We present a truly elementary proof of this fact in the context of the broader family of matrix entropies introduced by Chen and Tropp.
Energy Technology Data Exchange (ETDEWEB)
Hansen, Frank, E-mail: frank.hansen@m.tohoku.ac.jp [Tohoku University, Institute for Excellence in Higher Education (Japan)
2016-06-15
Incremental information, as measured by the quantum entropy, is increasing when two ensembles are united. This result was proved by Lieb and Ruskai, and it is the foundation for the proof of strong subadditivity of quantum entropy. We present a truly elementary proof of this fact in the context of the broader family of matrix entropies introduced by Chen and Tropp.
Partial differential equations
Evans, Lawrence C
2010-01-01
This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...
Relations Among Some Fuzzy Entropy Formulae
Institute of Scientific and Technical Information of China (English)
卿铭
2004-01-01
Fuzzy entropy has been widely used to analyze and design fuzzy systems, and many fuzzy entropy formulae have been proposed. For further in-deepth analysis of fuzzy entropy, the axioms and some important formulae of fuzzy entropy are introduced. Some equivalence results among these fuzzy entropy formulae are proved, and it is shown that fuzzy entropy is a special distance measurement.
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 ...
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 ...
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.
Rescaling Temperature and Entropy
Olmsted, John, III
2010-01-01
Temperature and entropy traditionally are expressed in units of kelvin and joule/kelvin. These units obscure some important aspects of the natures of these thermodynamic quantities. Defining a rescaled temperature using the Boltzmann constant, T' = k[subscript B]T, expresses temperature in energy units, thereby emphasizing the close relationship…
Optimized Kernel Entropy Components.
Izquierdo-Verdiguier, Emma; Laparra, Valero; Jenssen, Robert; Gomez-Chova, Luis; Camps-Valls, Gustau
2017-06-01
This brief addresses two main issues of the standard kernel entropy component analysis (KECA) algorithm: the optimization of the kernel decomposition and the optimization of the Gaussian kernel parameter. KECA roughly reduces to a sorting of the importance of kernel eigenvectors by entropy instead of variance, as in the kernel principal components analysis. In this brief, we propose an extension of the KECA method, named optimized KECA (OKECA), that directly extracts the optimal features retaining most of the data entropy by means of compacting the information in very few features (often in just one or two). The proposed method produces features which have higher expressive power. In particular, it is based on the independent component analysis framework, and introduces an extra rotation to the eigen decomposition, which is optimized via gradient-ascent search. This maximum entropy preservation suggests that OKECA features are more efficient than KECA features for density estimation. In addition, a critical issue in both the methods is the selection of the kernel parameter, since it critically affects the resulting performance. Here, we analyze the most common kernel length-scale selection criteria. The results of both the methods are illustrated in different synthetic and real problems. Results show that OKECA returns projections with more expressive power than KECA, the most successful rule for estimating the kernel parameter is based on maximum likelihood, and OKECA is more robust to the selection of the length-scale parameter in kernel density estimation.
Zucker, M. H.
This paper is a critical analysis and reassessment of entropic functioning as it applies to the question of whether the ultimate fate of the universe will be determined in the future to be "open" (expanding forever to expire in a big chill), "closed" (collapsing to a big crunch), or "flat" (balanced forever between the two). The second law of thermodynamics declares that entropy can only increase and that this principle extends, inevitably, to the universe as a whole. This paper takes the position that this extension is an unwarranted projection based neither on experience nonfact - an extrapolation that ignores the powerful effect of a gravitational force acting within a closed system. Since it was originally presented by Clausius, the thermodynamic concept of entropy has been redefined in terms of "order" and "disorder" - order being equated with a low degree of entropy and disorder with a high degree. This revised terminology more subjective than precise, has generated considerable confusion in cosmology in several critical instances. For example - the chaotic fireball of the big bang, interpreted by Stephen Hawking as a state of disorder (high entropy), is infinitely hot and, thermally, represents zero entropy (order). Hawking, apparently focusing on the disorderly "chaotic" aspect, equated it with a high degree of entropy - overlooking the fact that the universe is a thermodynamic system and that the key factor in evaluating the big-bang phenomenon is the infinitely high temperature at the early universe, which can only be equated with zero entropy. This analysis resolves this confusion and reestablishes entropy as a cosmological function integrally linked to temperature. The paper goes on to show that, while all subsystems contained within the universe require external sources of energization to have their temperatures raised, this requirement does not apply to the universe as a whole. The universe is the only system that, by itself can raise its own
Entropy equilibrium equation and dynamic entropy production in environment liquid
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The entropy equilibrium equation is the basis of the nonequilibrium state thermodynamics. But the internal energy implies the kinetic energy of the fluid micelle relative to mass center in the classical entropy equilibrium equation at present. This internal energy is not the mean kinetic energy of molecular movement in thermodynamics. Here a modified entropy equilibrium equation is deduced, based on the concept that the internal energy is just the mean kinetic energy of the molecular movement. A dynamic entropy production is introduced into the entropy equilibrium equation to describe the dynamic process distinctly. This modified entropy equilibrium equation can describe not only the entropy variation of the irreversible processes but also the reversible processes in a thermodynamic system. It is more reasonable and suitable for wider applications.
Entropy, neutro-entropy and anti-entropy for neutrosophic information
Vasile Patrascu
2017-01-01
This approach presents a multi-valued representation of the neutrosophic information. It highlights the link between the bifuzzy information and neutrosophic one. The constructed deca-valued structure shows the neutrosophic information complexity. This deca-valued structure led to construction of two new concepts for the neutrosophic information: neutro-entropy and anti-entropy. These two concepts are added to the two existing: entropy and non-entropy. Thus, we obtained the following triad: e...
Twinning of Polymer Crystals Suppressed by Entropy
Directory of Open Access Journals (Sweden)
Nikos Ch. Karayiannis
2014-09-01
Full Text Available We propose an entropic argument as partial explanation of the observed scarcity of twinned structures in crystalline samples of synthetic organic polymeric materials. Polymeric molecules possess a much larger number of conformational degrees of freedom than low molecular weight substances. The preferred conformations of polymer chains in the bulk of a single crystal are often incompatible with the conformations imposed by the symmetry of a growth twin, both at the composition surfaces and in the twin axis. We calculate the differences in conformational entropy between chains in single crystals and chains in twinned crystals, and find that the reduction in chain conformational entropy in the twin is sufficient to make the single crystal the stable thermodynamic phase. The formation of cyclic twins in molecular dynamics simulations of chains of hard spheres must thus be attributed to kinetic factors. In more realistic polymers this entropic contribution to the free energy can be canceled or dominated by nonbonded and torsional energetics.
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.
The different paths to entropy
International Nuclear Information System (INIS)
Benguigui, L
2013-01-01
In order to understand how the complex concept of entropy emerged, we propose a trip into the past, reviewing the works of Clausius, Boltzmann, Gibbs and Planck. In particular, since Gibbs's work is not very well known we present a detailed analysis, recalling the three definitions of entropy that Gibbs gives. The introduction of entropy in quantum mechanics gives in a compact form all the classical definitions of entropy. Perhaps one of the most important aspects of entropy is to see it as a thermodynamic potential like the others proposed by Callen. The calculation of fluctuations in thermodynamic quantities is thus naturally related to entropy. We close with some remarks on entropy and irreversibility. (paper)
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...
Nonlinear radiative heat flux and heat source/sink on entropy generation minimization rate
Hayat, T.; Khan, M. Waleed Ahmed; Khan, M. Ijaz; Alsaedi, A.
2018-06-01
Entropy generation minimization in nonlinear radiative mixed convective flow towards a variable thicked surface is addressed. Entropy generation for momentum and temperature is carried out. The source for this flow analysis is stretching velocity of sheet. Transformations are used to reduce system of partial differential equations into ordinary ones. Total entropy generation rate is determined. Series solutions for the zeroth and mth order deformation systems are computed. Domain of convergence for obtained solutions is identified. Velocity, temperature and concentration fields are plotted and interpreted. Entropy equation is studied through nonlinear mixed convection and radiative heat flux. Velocity and temperature gradients are discussed through graphs. Meaningful results are concluded in the final remarks.
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
Hyperspherical entanglement entropy
International Nuclear Information System (INIS)
Dowker, J S
2010-01-01
The coefficient of the log term in the entanglement entropy associated with hyperspherical surfaces in flat spacetime is shown to equal the conformal anomaly by conformally transforming Euclideanized spacetime to a sphere and using already existing formulae for the relevant heat-kernel coefficients after cyclic factoring. The result follows from the fact that the conformal anomaly on this lune has an extremum at the ordinary sphere limit. A proof is given. Agreement with a recent evaluation of the coefficient is found.
Hyperspherical entanglement entropy
Energy Technology Data Exchange (ETDEWEB)
Dowker, J S, E-mail: dowker@man.ac.u [Theory Group, School of Physics and Astronomy, University of Manchester, Manchester (United Kingdom)
2010-11-05
The coefficient of the log term in the entanglement entropy associated with hyperspherical surfaces in flat spacetime is shown to equal the conformal anomaly by conformally transforming Euclideanized spacetime to a sphere and using already existing formulae for the relevant heat-kernel coefficients after cyclic factoring. The result follows from the fact that the conformal anomaly on this lune has an extremum at the ordinary sphere limit. A proof is given. Agreement with a recent evaluation of the coefficient is found.
Entropy for Mechanically Vibrating Systems
Tufano, Dante
The research contained within this thesis deals with the subject of entropy as defined for and applied to mechanically vibrating systems. This work begins with an overview of entropy as it is understood in the fields of classical thermodynamics, information theory, statistical mechanics, and statistical vibroacoustics. Khinchin's definition of entropy, which is the primary definition used for the work contained in this thesis, is introduced in the context of vibroacoustic systems. The main goal of this research is to to establish a mathematical framework for the application of Khinchin's entropy in the field of statistical vibroacoustics by examining the entropy context of mechanically vibrating systems. The introduction of this thesis provides an overview of statistical energy analysis (SEA), a modeling approach to vibroacoustics that motivates this work on entropy. The objective of this thesis is given, and followed by a discussion of the intellectual merit of this work as well as a literature review of relevant material. Following the introduction, an entropy analysis of systems of coupled oscillators is performed utilizing Khinchin's definition of entropy. This analysis develops upon the mathematical theory relating to mixing entropy, which is generated by the coupling of vibroacoustic systems. The mixing entropy is shown to provide insight into the qualitative behavior of such systems. Additionally, it is shown that the entropy inequality property of Khinchin's entropy can be reduced to an equality using the mixing entropy concept. This equality can be interpreted as a facet of the second law of thermodynamics for vibroacoustic systems. Following this analysis, an investigation of continuous systems is performed using Khinchin's entropy. It is shown that entropy analyses using Khinchin's entropy are valid for continuous systems that can be decomposed into a finite number of modes. The results are shown to be analogous to those obtained for simple oscillators
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...
Caticha, Ariel
2007-11-01
What is information? Is it physical? We argue that in a Bayesian theory the notion of information must be defined in terms of its effects on the beliefs of rational agents. Information is whatever constrains rational beliefs and therefore it is the force that induces us to change our minds. This problem of updating from a prior to a posterior probability distribution is tackled through an eliminative induction process that singles out the logarithmic relative entropy as the unique tool for inference. The resulting method of Maximum relative Entropy (ME), which is designed for updating from arbitrary priors given information in the form of arbitrary constraints, includes as special cases both MaxEnt (which allows arbitrary constraints) and Bayes' rule (which allows arbitrary priors). Thus, ME unifies the two themes of these workshops—the Maximum Entropy and the Bayesian methods—into a single general inference scheme that allows us to handle problems that lie beyond the reach of either of the two methods separately. I conclude with a couple of simple illustrative examples.
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.
Numerical investigation into entropy generation in a transient ...
Indian Academy of Sciences (India)
This work investigates the effects of convective cooling on entropy generation in a transient generalized Couette flow of water-based nanofluids containing Copper (Cu) and Alumina (Al2O3) as nanoparticles. Both First and Second Laws of thermodynamics are utilised to analyse the problem. The model partial differential ...
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.
Logarithmic black hole entropy corrections and holographic Renyi entropy
Energy Technology Data Exchange (ETDEWEB)
Mahapatra, Subhash [The Institute of Mathematical Sciences, Chennai (India); KU Leuven - KULAK, Department of Physics, Kortrijk (Belgium)
2018-01-15
The entanglement and Renyi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Renyi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order G{sub D}{sup 0}. The entropic c-function and the inequalities of the Renyi entropy are also satisfied even with the correction terms. (orig.)
Parametric Bayesian Estimation of Differential Entropy and Relative Entropy
Directory of Open Access Journals (Sweden)
Maya Gupta
2010-04-01
Full Text Available Given iid samples drawn from a distribution with known parametric form, we propose the minimization of expected Bregman divergence to form Bayesian estimates of differential entropy and relative entropy, and derive such estimators for the uniform, Gaussian, Wishart, and inverse Wishart distributions. Additionally, formulas are given for a log gamma Bregman divergence and the differential entropy and relative entropy for the Wishart and inverse Wishart. The results, as always with Bayesian estimates, depend on the accuracy of the prior parameters, but example simulations show that the performance can be substantially improved compared to maximum likelihood or state-of-the-art nonparametric estimators.
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.)
Calculation of von Neumann entropy for hydrogen and positronium negative ions
International Nuclear Information System (INIS)
Lin, Chien-Hao; Ho, Yew Kam
2014-01-01
In the present work, we carry out calculations of von Neumann entropies and linear entropies for the hydrogen negative ion and the positronium negative ion. We concentrate on the spatial (electron–electron orbital) entanglement in these ions by using highly correlated Hylleraas functions to represent their ground states, and to take care of correlation effects. We apply the Schmidt decomposition method on the partial-wave expanded two-electron wave functions, and from which the one-particle reduced density matrix can be obtained, leading to the quantifications of linear entropy and von Neumann entropy in the H − and Ps − ions. - Highlights: • We calculate von Neumann entropies and linear entropies for hydrogen and positronium negative ions. • We employ highly correlated Hylleraas functions to take into account of correlation effects. • Spatial (electron–electron orbital) entanglement is quantified using the Schmidt decomposition method. • The eigenvalues of the one-particle reduced density matrix are calculated
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.
Credal Networks under Maximum Entropy
Lukasiewicz, Thomas
2013-01-01
We apply the principle of maximum entropy to select a unique joint probability distribution from the set of all joint probability distributions specified by a credal network. In detail, we start by showing that the unique joint distribution of a Bayesian tree coincides with the maximum entropy model of its conditional distributions. This result, however, does not hold anymore for general Bayesian networks. We thus present a new kind of maximum entropy models, which are computed sequentially. ...
Editorial: Entropy in Landscape Ecology
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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.
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
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.
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.
Information Entropy Measures for Stand Structural Diversity:Joint Entropy
Institute of Scientific and Technical Information of China (English)
Lei Xiangdong; Lu Yuanchang
2004-01-01
Structural diversity is the key attribute of a stand. A set of biodiversity measures in ecology was introduced in forest management for describing stand structure, of which Shannon information entropy (Shannon index) has been the most widely used measure of species diversity. It is generally thought that tree size diversity could serve as a good proxy for height diversity. However, tree size diversity and height diversity for stand structure is not completely consistent. Stand diameter cannot reflect height information completely. Either tree size diversity or height diversity is one-dimensional information entropy measure. This paper discussed the method of multiple-dimensional information entropy measure with the concept of joint entropy. It is suggested that joint entropy is a good measure for describing overall stand structural diversity.
Relative Entropy, Interaction Energy and the Nature of Dissipation
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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.
Weak entropy inequalities and entropic convergence
Institute of Scientific and Technical Information of China (English)
2008-01-01
A criterion for algebraic convergence of the entropy is presented and an algebraic convergence result for the entropy of an exclusion process is improved. A weak entropy inequality is considered and its relationship to entropic convergence is discussed.
Entropy concentration and the empirical coding game
Grünwald, P.D.
2008-01-01
We give a characterization of maximum entropy/minimum relative entropy inference by providing two 'strong entropy concentration' theorems. These theorems unify and generalize Jaynes''concentration phenomenon' and Van Campenhout and Cover's 'conditional limit theorem'. The theorems characterize
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.
International Nuclear Information System (INIS)
Steinmeyer, D.
1992-01-01
When we talk about saving energy what we usually mean is not wasting work. What we try to do when we design a process, is to use work as effectively as possible. It's hard to do that if we can't see it clearly. This paper illustrates how work can be seen (or calculated) without imposing entropy as a screen in front of it. We've all heard that the second law tells us that the entropy of the universe is increasing, and we are left with the feeling that the universe is ultimately headed for chaos, but receive little other information from this statement. A slightly more useful statement of the second law is the work potential of the universe is decreasing. However, this statement carries a needlessly negative ring. A simplified definition of the second law is: It takes work to change things. With these two corollaries: We can calculate the theoretical minimum work needed for a given change; and We can express the value of all changes in terms of work
Possible extended forms of thermodynamic entropy
International Nuclear Information System (INIS)
Sasa, Shin-ichi
2014-01-01
Thermodynamic entropy is determined by a heat measurement through the Clausius equality. The entropy then formalizes a fundamental limitation of operations by the second law of thermodynamics. The entropy is also expressed as the Shannon entropy of the microscopic degrees of freedom. Whenever an extension of thermodynamic entropy is attempted, we must pay special attention to how its three different aspects just mentioned are altered. In this paper, we discuss possible extensions of the thermodynamic entropy. (paper)
Configurational entropy of glueball states
Energy Technology Data Exchange (ETDEWEB)
Bernardini, Alex E., E-mail: alexeb@ufscar.br [Departamento de Física, Universidade Federal de São Carlos, PO Box 676, 13565-905, São Carlos, SP (Brazil); Braga, Nelson R.F., E-mail: braga@if.ufrj.br [Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, RJ 21941-972 (Brazil); Rocha, Roldão da, E-mail: roldao.rocha@ufabc.edu.br [CMCC, Universidade Federal do ABC, UFABC, 09210-580, Santo André (Brazil)
2017-02-10
The configurational entropy of glueball states is calculated using a holographic description. Glueball states are represented by a supergravity dual picture, consisting of a 5-dimensional graviton–dilaton action of a dynamical holographic AdS/QCD model. The configurational entropy is studied as a function of the glueball spin and of the mass, providing information about the stability of the glueball states.
Thermostatistical aspects of generalized entropies
International Nuclear Information System (INIS)
Fa, K.S.; Lenzi, E.K.
2004-01-01
We investigate the properties concerning a class of generalized entropies given by S q,r =k{1-[Σ i p i q ] r }/[r(q-1)] which include Tsallis' entropy (r=1), the usual Boltzmann-Gibbs entropy (q=1), Renyi's entropy (r=0) and normalized Tsallis' entropy (r=-1). In order to obtain the generalized thermodynamic relations we use the laws of thermodynamics and considering the hypothesis that the joint probability of two independent systems is given by p ij A c upB =p i A p j B . We show that the transmutation which occurs from Tsallis' entropy to Renyi's entropy also occur with S q,r . In this scenario, we also analyze the generalized variance, covariance and correlation coefficient of a non-interacting system by using extended optimal Lagrange multiplier approach. We show that the correlation coefficient tends to zero in the thermodynamic limit. However, Renyi's entropy related to this non-interacting system presents a certain degree of non-extensivity
Entropy statistics and information theory
Frenken, K.; Hanusch, H.; Pyka, A.
2007-01-01
Entropy measures provide important tools to indicate variety in distributions at particular moments in time (e.g., market shares) and to analyse evolutionary processes over time (e.g., technical change). Importantly, entropy statistics are suitable to decomposition analysis, which renders the
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
Black brane entropy and hydrodynamics
Booth, I.; Heller, M.P.; Spaliński, M.
2011-01-01
A generalization of entropy to near-equilibrium phenomena is provided by the notion of a hydrodynamic entropy current. Recent advances in holography have lead to the formulation of fluid-gravity duality, a remarkable connection between the hydrodynamics of certain strongly coupled media and dynamics
High Entropy Random Selection Protocols
H. Buhrman (Harry); M. Christandl (Matthias); M. Koucky (Michal); Z. Lotker (Zvi); B. Patt-Shamir; M. Charikar; K. Jansen; O. Reingold; J. Rolim
2007-01-01
textabstractIn this paper, we construct protocols for two parties that do not trust each other, to generate random variables with high Shannon entropy. We improve known bounds for the trade off between the number of rounds, length of communication and the entropy of the outcome.
Entropy and equilibrium via games of complexity
Topsøe, Flemming
2004-09-01
It is suggested that thermodynamical equilibrium equals game theoretical equilibrium. Aspects of this thesis are discussed. The philosophy is consistent with maximum entropy thinking of Jaynes, but goes one step deeper by deriving the maximum entropy principle from an underlying game theoretical principle. The games introduced are based on measures of complexity. Entropy is viewed as minimal complexity. It is demonstrated that Tsallis entropy ( q-entropy) and Kaniadakis entropy ( κ-entropy) can be obtained in this way, based on suitable complexity measures. A certain unifying effect is obtained by embedding these measures in a two-parameter family of entropy functions.
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
Entropy Budget for Hawking Evaporation
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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.
Zero entropy continuous interval maps and MMLS-MMA property
Jiang, Yunping
2018-06-01
We prove that the flow generated by any continuous interval map with zero topological entropy is minimally mean-attractable and minimally mean-L-stable. One of the consequences is that any oscillating sequence is linearly disjoint from all flows generated by all continuous interval maps with zero topological entropy. In particular, the Möbius function is linearly disjoint from all flows generated by all continuous interval maps with zero topological entropy (Sarnak’s conjecture for continuous interval maps). Another consequence is a non-trivial example of a flow having discrete spectrum. We also define a log-uniform oscillating sequence and show a result in ergodic theory for comparison. This material is based upon work supported by the National Science Foundation. It is also partially supported by a collaboration grant from the Simons Foundation (grant number 523341) and PSC-CUNY awards and a grant from NSFC (grant number 11571122).
Entropy exchange and entanglement in the Jaynes-Cummings model
International Nuclear Information System (INIS)
Boukobza, E.; Tannor, D.J.
2005-01-01
The Jaynes-Cummings model (JCM) is the simplest fully quantum model that describes the interaction between light and matter. We extend a previous analysis by Phoenix and Knight [Ann. Phys. 186, 381 (1988)] of the JCM by considering mixed states of both the light and matter. We present examples of qualitatively different entropic correlations. In particular, we explore the regime of entropy exchange between light and matter, i.e., where the rate of change of the two are anticorrelated. This behavior contrasts with the case of pure light-matter states in which the rate of change of the two entropies are positively correlated and in fact identical. We give an analytical derivation of the anticorrelation phenomenon and discuss the regime of its validity. Finally, we show a strong correlation between the region of the Bloch sphere characterized by entropy exchange and that characterized by minimal entanglement as measured by the negative eigenvalues of the partially transposed density matrix
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
Introduction to maximum entropy
International Nuclear Information System (INIS)
Sivia, D.S.
1988-01-01
The maximum entropy (MaxEnt) principle has been successfully used in image reconstruction in a wide variety of fields. We review the need for such methods in data analysis and show, by use of a very simple example, why MaxEnt is to be preferred over other regularizing functions. This leads to a more general interpretation of the MaxEnt method, and its use is illustrated with several different examples. Practical difficulties with non-linear problems still remain, this being highlighted by the notorious phase problem in crystallography. We conclude with an example from neutron scattering, using data from a filter difference spectrometer to contrast MaxEnt with a conventional deconvolution. 12 refs., 8 figs., 1 tab
Introduction to maximum entropy
International Nuclear Information System (INIS)
Sivia, D.S.
1989-01-01
The maximum entropy (MaxEnt) principle has been successfully used in image reconstruction in a wide variety of fields. The author reviews the need for such methods in data analysis and shows, by use of a very simple example, why MaxEnt is to be preferred over other regularizing functions. This leads to a more general interpretation of the MaxEnt method, and its use is illustrated with several different examples. Practical difficulties with non-linear problems still remain, this being highlighted by the notorious phase problem in crystallography. He concludes with an example from neutron scattering, using data from a filter difference spectrometer to contrast MaxEnt with a conventional deconvolution. 12 refs., 8 figs., 1 tab
International Nuclear Information System (INIS)
Kandrup, H.E.
1988-01-01
The notion of a p-particle entropy Sp introduced by Kandrup (1987) is applied here to a Newtonian cosmology modeled as an expanding system of identical point masses studying the time dependence of S1 and S2 in the framework of the linearized theory considered by Fall and Saslaw (1976). It is found that if, at some initial time t0, the galaxy-galaxy correlation function vanished, then S1(t0) = S2(t0). At least for short times t - t0 thereafter, S1 and Delta S = S1 - S2 increase on a characteristic time scale. For all times t after t0, S1(t) = S2(t) or greater. 13 references
Directory of Open Access Journals (Sweden)
Jikai Chen
2016-12-01
Full Text Available In a power system, the analysis of transient signals is the theoretical basis of fault diagnosis and transient protection theory. Shannon wavelet entropy (SWE and Shannon wavelet packet entropy (SWPE are powerful mathematics tools for transient signal analysis. Combined with the recent achievements regarding SWE and SWPE, their applications are summarized in feature extraction of transient signals and transient fault recognition. For wavelet aliasing at adjacent scale of wavelet decomposition, the impact of wavelet aliasing is analyzed for feature extraction accuracy of SWE and SWPE, and their differences are compared. Meanwhile, the analyses mentioned are verified by partial discharge (PD feature extraction of power cable. Finally, some new ideas and further researches are proposed in the wavelet entropy mechanism, operation speed and how to overcome wavelet aliasing.
Entropy flow and generation in radiative transfer between surfaces
Energy Technology Data Exchange (ETDEWEB)
Zhang, Z.M.; Basu, S. [Georgia Institute of Technolgy, Atlanta, GA (United States). George W. Woodruff School of Mechanical Engineering
2007-02-15
Entropy of radiation has been used to derive the laws of blackbody radiation and determine the maximum efficiency of solar energy conversion. Along with the advancement in thermophotovoltaic technologies and nanoscale heat radiation, there is an urgent need to determine the entropy flow and generation in radiative transfer between nonideal surfaces when multiple reflections are significant. This paper investigates entropy flow and generation when incoherent multiple reflections are included, without considering the effects of interference and photon tunneling. The concept of partial equilibrium is applied to interpret the monochromatic radiation temperature of thermal radiation, T{sub l}(l,{omega}), which is dependent on both wavelength l and direction {omega}. The entropy flux and generation can thus be evaluated for nonideal surfaces. It is shown that several approximate expressions found in the literature can result in significant errors in entropy analysis even for diffuse-gray surfaces. The present study advances the thermodynamics of nonequilibrium thermal radiation and will have a significant impact on the future development of thermophotovoltaic and other radiative energy conversion devices. (author)
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.
Zero modes and entanglement entropy
Energy Technology Data Exchange (ETDEWEB)
Yazdi, Yasaman K. [Perimeter Institute for Theoretical Physics,31 Caroline St. N., Waterloo, ON, N2L 2Y5 (Canada); Department of Physics and Astronomy, University of Waterloo,200 University Avenue West, Waterloo, ON, N2L 3G1 (Canada)
2017-04-26
Ultraviolet divergences are widely discussed in studies of entanglement entropy. Also present, but much less understood, are infrared divergences due to zero modes in the field theory. In this note, we discuss the importance of carefully handling zero modes in entanglement entropy. We give an explicit example for a chain of harmonic oscillators in 1D, where a mass regulator is necessary to avoid an infrared divergence due to a zero mode. We also comment on a surprising contribution of the zero mode to the UV-scaling of the entanglement entropy.
Shannon's information is not entropy
International Nuclear Information System (INIS)
Schiffer, M.
1990-01-01
In this letter we clear up the long-standing misidentification of Shannon's Information with Entropy. We show that Information, in contrast to Entropy, is not invariant under unitary transformations and that these quantities are only equivalent for representations consisting of Hamiltonian eigenstates. We illustrate this fact through a toy system consisting of a harmonic oscillator in a coherent state. It is further proved that the representations which maximize the information are those which are energy-eigenstates. This fact sets the entropy as an upper bound for Shannon's Information. (author)
Entropy Learning in Neural Network
Directory of Open Access Journals (Sweden)
Geok See Ng
2017-12-01
Full Text Available In this paper, entropy term is used in the learning phase of a neural network. As learning progresses, more hidden nodes get into saturation. The early creation of such hidden nodes may impair generalisation. Hence entropy approach is proposed to dampen the early creation of such nodes. The entropy learning also helps to increase the importance of relevant nodes while dampening the less important nodes. At the end of learning, the less important nodes can then be eliminated to reduce the memory requirements of the neural network.
DEFF Research Database (Denmark)
Müller-Lennert, Martin; Dupont-Dupuis, Fréderic; Szehr, Oleg
2013-01-01
The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies, or mutual information, and have found many applications in in...
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)
Parameters Tuning of Model Free Adaptive Control Based on Minimum Entropy
Institute of Scientific and Technical Information of China (English)
Chao Ji; Jing Wang; Liulin Cao; Qibing Jin
2014-01-01
Dynamic linearization based model free adaptive control(MFAC) algorithm has been widely used in practical systems, in which some parameters should be tuned before it is successfully applied to process industries. Considering the random noise existing in real processes, a parameter tuning method based on minimum entropy optimization is proposed,and the feature of entropy is used to accurately describe the system uncertainty. For cases of Gaussian stochastic noise and non-Gaussian stochastic noise, an entropy recursive optimization algorithm is derived based on approximate model or identified model. The extensive simulation results show the effectiveness of the minimum entropy optimization for the partial form dynamic linearization based MFAC. The parameters tuned by the minimum entropy optimization index shows stronger stability and more robustness than these tuned by other traditional index,such as integral of the squared error(ISE) or integral of timeweighted absolute error(ITAE), when the system stochastic noise exists.
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
Renyi entropy and conformal defects
Energy Technology Data Exchange (ETDEWEB)
Bianchi, Lorenzo [Humboldt-Univ. Berlin (Germany). Inst. fuer Physik; Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; Meineri, Marco [Scuola Normale Superiore, Pisa (Italy); Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); Istituto Nazionale di Fisica Nucleare, Pisa (Italy); Myers, Robert C. [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); Smolkin, Michael [California Univ., Berkely, CA (United States). Center for Theoretical Physics and Department of Physics
2016-04-18
We propose a field theoretic framework for calculating the dependence of Renyi entropies on the shape of the entangling surface in a conformal field theory. Our approach rests on regarding the corresponding twist operator as a conformal defect and in particular, we define the displacement operator which implements small local deformations of the entangling surface. We identify a simple constraint between the coefficient defining the two-point function of the displacement operator and the conformal weight of the twist operator, which consolidates a number of distinct conjectures on the shape dependence of the Renyi entropy. As an example, using this approach, we examine a conjecture regarding the universal coefficient associated with a conical singularity in the entangling surface for CFTs in any number of spacetime dimensions. We also provide a general formula for the second order variation of the Renyi entropy arising from small deformations of a spherical entangling surface, extending Mezei's results for the entanglement entropy.
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.
Renyi entropy and conformal defects
International Nuclear Information System (INIS)
Bianchi, Lorenzo; Myers, Robert C.; Smolkin, Michael
2016-01-01
We propose a field theoretic framework for calculating the dependence of Renyi entropies on the shape of the entangling surface in a conformal field theory. Our approach rests on regarding the corresponding twist operator as a conformal defect and in particular, we define the displacement operator which implements small local deformations of the entangling surface. We identify a simple constraint between the coefficient defining the two-point function of the displacement operator and the conformal weight of the twist operator, which consolidates a number of distinct conjectures on the shape dependence of the Renyi entropy. As an example, using this approach, we examine a conjecture regarding the universal coefficient associated with a conical singularity in the entangling surface for CFTs in any number of spacetime dimensions. We also provide a general formula for the second order variation of the Renyi entropy arising from small deformations of a spherical entangling surface, extending Mezei's results for the entanglement entropy.
Entropy of adsorption of mixed surfactants from solutions onto the air/water interface
Chen, L.-W.; Chen, J.-H.; Zhou, N.-F.
1995-01-01
The partial molar entropy change for mixed surfactant molecules adsorbed from solution at the air/water interface has been investigated by surface thermodynamics based upon the experimental surface tension isotherms at various temperatures. Results for different surfactant mixtures of sodium dodecyl sulfate and sodium tetradecyl sulfate, decylpyridinium chloride and sodium alkylsulfonates have shown that the partial molar entropy changes for adsorption of the mixed surfactants were generally negative and decreased with increasing adsorption to a minimum near the maximum adsorption and then increased abruptly. The entropy decrease can be explained by the adsorption-orientation of surfactant molecules in the adsorbed monolayer and the abrupt entropy increase at the maximum adsorption is possible due to the strong repulsion between the adsorbed molecules.
Algorithmic randomness and physical entropy
International Nuclear Information System (INIS)
Zurek, W.H.
1989-01-01
Algorithmic randomness provides a rigorous, entropylike measure of disorder of an individual, microscopic, definite state of a physical system. It is defined by the size (in binary digits) of the shortest message specifying the microstate uniquely up to the assumed resolution. Equivalently, algorithmic randomness can be expressed as the number of bits in the smallest program for a universal computer that can reproduce the state in question (for instance, by plotting it with the assumed accuracy). In contrast to the traditional definitions of entropy, algorithmic randomness can be used to measure disorder without any recourse to probabilities. Algorithmic randomness is typically very difficult to calculate exactly but relatively easy to estimate. In large systems, probabilistic ensemble definitions of entropy (e.g., coarse-grained entropy of Gibbs and Boltzmann's entropy H=lnW, as well as Shannon's information-theoretic entropy) provide accurate estimates of the algorithmic entropy of an individual system or its average value for an ensemble. One is thus able to rederive much of thermodynamics and statistical mechanics in a setting very different from the usual. Physical entropy, I suggest, is a sum of (i) the missing information measured by Shannon's formula and (ii) of the algorithmic information content---algorithmic randomness---present in the available data about the system. This definition of entropy is essential in describing the operation of thermodynamic engines from the viewpoint of information gathering and using systems. These Maxwell demon-type entities are capable of acquiring and processing information and therefore can ''decide'' on the basis of the results of their measurements and computations the best strategy for extracting energy from their surroundings. From their internal point of view the outcome of each measurement is definite
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.
Spontaneous entropy decrease and its statistical formula
Xing, Xiu-San
2007-01-01
Why can the world resist the law of entropy increase and produce self-organizing structure? Does the entropy of an isolated system always only increase and never decrease? Can be thermodymamic degradation and self-organizing evolution united? How to unite? In this paper starting out from nonequilibrium entropy evolution equation we proved that a new entropy decrease could spontaneously emerge in nonequilibrium system with internal attractive interaction. This new entropy decrease coexists wit...
Arithmetic of quantum entropy function
International Nuclear Information System (INIS)
Sen, Ashoke
2009-01-01
Quantum entropy function is a proposal for computing the entropy associated with the horizon of a black hole in the extremal limit, and is related via AdS/CFT correspondence to the dimension of the Hilbert space in a dual quantum mechanics. We show that in N = 4 supersymmetric string theories, quantum entropy function formalism naturally explains the origin of the subtle differences between the microscopic degeneracies of quarter BPS dyons carrying different torsion, i.e. different arithmetical properties. These arise from additional saddle points in the path integral - whose existence depends on the arithmetical properties of the black hole charges - constructed as freely acting orbifolds of the original AdS 2 x S 2 near horizon geometry. During this analysis we demonstrate that the quantum entropy function is insensitive to the details of the infrared cutoff used in the computation, and the details of the boundary terms added to the action. We also discuss the role of the asymptotic symmetries of AdS 2 in carrying out the path integral in the definition of quantum entropy function. Finally we show that even though quantum entropy function is expected to compute the absolute degeneracy in a given charge and angular momentum sector, it can also be used to compute the index. This can then be compared with the microscopic computation of the index.
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)
Partial Transposition on Bipartite System
International Nuclear Information System (INIS)
Xi-Jun, Ren; Yong-Jian, Han; Yu-Chun, Wu; Guang-Can, Guo
2008-01-01
Many properties of partial transposition are unclear as yet. Here we carefully consider the number of the negative eigenvalues of ρ T (ρ's partial transposition) when ρ is a two-partite state. There is strong evidence to show that the number of negative eigenvalues of ρ T is N(N − 1)/2 at most when ρ is a state in Hilbert space C N C N . For the special case, the 2 × 2 system, we use this result to give a partial proof of the conjecture |ρ T | T ≥ 0. We find that this conjecture is strongly connected with the entanglement of the state corresponding to the negative eigenvalue of ρ T or the negative entropy of ρ
Quantum key distribution with finite resources: Smooth Min entropy vs. Smooth Renyi entropy
Energy Technology Data Exchange (ETDEWEB)
Mertz, Markus; Abruzzo, Silvestre; Bratzik, Sylvia; Kampermann, Hermann; Bruss, Dagmar [Institut fuer Theoretische Physik III, Duesseldorf (Germany)
2010-07-01
We consider different entropy measures that play an important role in the analysis of the security of QKD with finite resources. The smooth min entropy leads to an optimal bound for the length of a secure key. Another bound on the secure key length was derived by using Renyi entropies. Unfortunately, it is very hard or even impossible to calculate these entropies for realistic QKD scenarios. To estimate the security rate it becomes important to find computable bounds on these entropies. Here, we compare a lower bound for the smooth min entropy with a bound using Renyi entropies. We compare these entropies for the six-state protocol with symmetric attacks.
Entanglement entropy and the colored Jones polynomial
Balasubramanian, Vijay; DeCross, Matthew; Fliss, Jackson; Kar, Arjun; Leigh, Robert G.; Parrikar, Onkar
2018-05-01
We study the multi-party entanglement structure of states in Chern-Simons theory created by performing the path integral on 3-manifolds with linked torus boundaries, called link complements. For gauge group SU(2), the wavefunctions of these states (in a particular basis) are the colored Jones polynomials of the corresponding links. We first review the case of U(1) Chern-Simons theory where these are stabilizer states, a fact we use to re-derive an explicit formula for the entanglement entropy across a general link bipartition. We then present the following results for SU(2) Chern-Simons theory: (i) The entanglement entropy for a bipartition of a link gives a lower bound on the genus of surfaces in the ambient S 3 separating the two sublinks. (ii) All torus links (namely, links which can be drawn on the surface of a torus) have a GHZ-like entanglement structure — i.e., partial traces leave a separable state. By contrast, through explicit computation, we test in many examples that hyperbolic links (namely, links whose complements admit hyperbolic structures) have W-like entanglement — i.e., partial traces leave a non-separable state. (iii) Finally, we consider hyperbolic links in the complexified SL(2,C) Chern-Simons theory, which is closely related to 3d Einstein gravity with a negative cosmological constant. In the limit of small Newton constant, we discuss how the entanglement structure is controlled by the Neumann-Zagier potential on the moduli space of hyperbolic structures on the link complement.
Does horizon entropy satisfy a quantum null energy conjecture?
Fu, Zicao; Marolf, Donald
2016-12-01
A modern version of the idea that the area of event horizons gives 4G times an entropy is the Hubeny-Rangamani causal holographic information (CHI) proposal for holographic field theories. Given a region R of a holographic QFTs, CHI computes A/4G on a certain cut of an event horizon in the gravitational dual. The result is naturally interpreted as a coarse-grained entropy for the QFT. CHI is known to be finitely greater than the fine-grained Hubeny-Rangamani-Takayanagi (HRT) entropy when \\partial R lies on a Killing horizon of the QFT spacetime, and in this context satisfies other non-trivial properties expected of an entropy. Here we present evidence that it also satisfies the quantum null energy condition (QNEC), which bounds the second derivative of the entropy of a quantum field theory on one side of a non-expanding null surface by the flux of stress-energy across the surface. In particular, we show CHI to satisfy the QNEC in 1 + 1 holographic CFTs when evaluated in states dual to conical defects in AdS3. This surprising result further supports the idea that CHI defines a useful notion of coarse-grained holographic entropy, and suggests unprecedented bounds on the rate at which bulk horizon generators emerge from a caustic. To supplement our motivation, we include an appendix deriving a corresponding coarse-grained generalized second law for 1 + 1 holographic CFTs perturbatively coupled to dilaton gravity.
Maximum Entropy in Drug Discovery
Directory of Open Access Journals (Sweden)
Chih-Yuan Tseng
2014-07-01
Full Text Available Drug discovery applies multidisciplinary approaches either experimentally, computationally or both ways to identify lead compounds to treat various diseases. While conventional approaches have yielded many US Food and Drug Administration (FDA-approved drugs, researchers continue investigating and designing better approaches to increase the success rate in the discovery process. In this article, we provide an overview of the current strategies and point out where and how the method of maximum entropy has been introduced in this area. The maximum entropy principle has its root in thermodynamics, yet since Jaynes’ pioneering work in the 1950s, the maximum entropy principle has not only been used as a physics law, but also as a reasoning tool that allows us to process information in hand with the least bias. Its applicability in various disciplines has been abundantly demonstrated. We give several examples of applications of maximum entropy in different stages of drug discovery. Finally, we discuss a promising new direction in drug discovery that is likely to hinge on the ways of utilizing maximum entropy.
International Nuclear Information System (INIS)
Partanen, Jaakko I.
2013-01-01
Highlights: • This work reports new equations for thermodynamic activity quantities in aqueous MgCl 2 solutions. • The new equations are functionally the same as those obtained previously solutions of CaCl 2 and uni-univalent electrolytes. • The new activity and osmotic coefficients are fully traceable and transparent. • These new values were tested thoroughly with existing literature data. -- Abstract: The Hückel equation used in this study for the thermodynamic activity quantities in dilute MgCl 2 solutions up to an ionic strength (=I m ) of 1.5 mol · kg −1 contains two parameters being dependent on the electrolyte, i.e., those of B and b 1 . The former is linearly related to the ion-size parameter in the Debye–Hückel equation and the latter is the coefficient of the linear correction term with respect to the molality. For more concentrated solutions up to I m of 9.0 mol · kg −1 , an extended Hückel equation was used. For it, the Hückel equation was extended with a quadratic term in molality, and the coefficient of this term is the third parameter b 2 . Parameters B and b 1 for dilute MgCl 2 solutions were obtained from the isopiestic data of Robinson and Stokes for solutions of this salt and KCl [Trans. Faraday Soc. 36 (1940) 733] by using the previous Hückel parameters for dilute KCl solutions [J. Chem. Eng. Data 54 (2009) 208]. The resulting parameters for MgCl 2 solutions were successfully tested with all isopiestic data available in the literature for dilute solutions of this salt. For less dilute solutions, new values for parameters b 1 and b 2 were determined for the extended version of the Hückel equation of MgCl 2 solutions from the isopiestic data of Rard and Miller [J. Chem. Eng. Data 26 (1981) 38] for NaCl and MgCl 2 solutions but the dilute-solution value for parameter B was used. The previous extended Hückel equation for concentrated NaCl solutions was used in this estimation (see the KCl citation above). In the tests of the
Lemons, Don S
2013-01-01
Striving to explore the subject in as simple a manner as possible, this book helps readers understand the elusive concept of entropy. Innovative aspects of the book include the construction of statistical entropy, the derivation of the entropy of classical systems from purely classical assumptions, and a statistical thermodynamics approach to the ideal Fermi and ideal Bose gases. Derivations are worked through step-by-step and important applications are highlighted in over 20 worked examples. Nearly 50 end-of-chapter exercises test readers' understanding. The book also features a glossary giving definitions for all essential terms, a time line showing important developments, and list of books for further study. It is an ideal supplement to undergraduate courses in physics, engineering, chemistry and mathematics.
Shannon entropy and particle decays
Carrasco Millán, Pedro; García-Ferrero, M. Ángeles; Llanes-Estrada, Felipe J.; Porras Riojano, Ana; Sánchez García, Esteban M.
2018-05-01
We deploy Shannon's information entropy to the distribution of branching fractions in a particle decay. This serves to quantify how important a given new reported decay channel is, from the point of view of the information that it adds to the already known ones. Because the entropy is additive, one can subdivide the set of channels and discuss, for example, how much information the discovery of a new decay branching would add; or subdivide the decay distribution down to the level of individual quantum states (which can be quickly counted by the phase space). We illustrate the concept with some examples of experimentally known particle decay distributions.
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.
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
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 ...
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.
Multivariate refined composite multiscale entropy analysis
International Nuclear Information System (INIS)
Humeau-Heurtier, Anne
2016-01-01
Multiscale entropy (MSE) has become a prevailing method to quantify signals complexity. MSE relies on sample entropy. However, MSE may yield imprecise complexity estimation at large scales, because sample entropy does not give precise estimation of entropy when short signals are processed. A refined composite multiscale entropy (RCMSE) has therefore recently been proposed. Nevertheless, RCMSE is for univariate signals only. The simultaneous analysis of multi-channel (multivariate) data often over-performs studies based on univariate signals. We therefore introduce an extension of RCMSE to multivariate data. Applications of multivariate RCMSE to simulated processes reveal its better performances over the standard multivariate MSE. - Highlights: • Multiscale entropy quantifies data complexity but may be inaccurate at large scale. • A refined composite multiscale entropy (RCMSE) has therefore recently been proposed. • Nevertheless, RCMSE is adapted to univariate time series only. • We herein introduce an extension of RCMSE to multivariate data. • It shows better performances than the standard multivariate multiscale entropy.
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.
A brief introduction to sofic entropy theory
Bowen, Lewis
2017-01-01
Sofic entropy theory is a generalization of the classical Kolmogorov-Sinai entropy theory to actions of large class of non-amenable groups called sofic groups. This is a short introduction with a guide to the literature.
Notes on entanglement entropy in string theory
International Nuclear Information System (INIS)
He, Song; Numasawa, Tokiro; Takayanagi, Tadashi; Watanabe, Kento
2015-01-01
In this paper, we study the conical entropy in string theory in the simplest setup of dividing the nine dimensional space into two halves. This corresponds to the leading quantum correction to the horizon entropy in string theory on the Rindler space. This entropy is also called the conical entropy and includes surface term contributions. We first derive a new simple formula of the conical entropy for any free higher spin fields. Then we apply this formula to computations of conical entropy in open and closed superstring. In our analysis of closed string, we study the twisted conical entropy defined by making use of string theory on Melvin backgrounds. This quantity is easier to calculate owing to the folding trick. Our analysis shows that the conical entropy in closed superstring is UV finite owing to the string scale cutoff.
Definition of Nonequilibrium Entropy of General Systems
Mei, Xiaochun
1999-01-01
The definition of nonequilibrium entropy is provided for the general nonequilibrium processes by connecting thermodynamics with statistical physics, and the principle of entropy increment in the nonequilibrium processes is also proved in the paper. The result shows that the definition of nonequilibrium entropy is not unique.
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.
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.
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.
Regularities of changes of metal melting entropy
International Nuclear Information System (INIS)
Kats, S.A.; Chekhovskoj, V.Ya.
1980-01-01
Most trustworthy data on temperatures, heats and entropies of fusion of metals have been used as a basis to throw light on the laws governing variations of the entropy of metals fusion. The elaborated procedure is used to predict the entropies of the metals fusion whose thermodynamic properties under high temperatures have not yet been investigated
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
The dynamical entropy of quantum systems
International Nuclear Information System (INIS)
Connes, A.; Narnhofer, H.; Thirring, W.
1987-01-01
The definition of the dynamical entropy for automorphisms of C * - algebras is represented. Several properties are discussed; especially it is argued that the entropy of the shift can be shown in special cases to be equal with the entropy density. (Author)
Entropy-driven phase transitions
Frenkel, D.
1999-01-01
Increase in visible order can be associated with an increase in microscopic disorder. This phenomenon leads to many counter-intuitive phenomena such as entropy driven crystallization and phase separation. I devote special attention to the entropic depletion interaction as a means to tune the range
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 ...
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 ...
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.
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
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
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
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.
Relation Entropy and Transferable Entropy Think of Aggregation on Group Decision Making
Institute of Scientific and Technical Information of China (English)
CHENG Qi-yue; QIU Wan-hua; LIU Xiao-feng
2002-01-01
In this paper, aggregation question based on group decision making and a single decision making is studied. The theory of entropy is applied to the sets pair analysis. The system of relation entropy and the transferable entropy notion are put. The character is studied. An potential by the relation entropy and transferable entropy are defined. It is the consistency measure on the group between a single decision making. We gained a new aggregation effective definition on the group misjudge.
Indian Academy of Sciences (India)
First page Back Continue Last page Overview Graphics. Partial Cancellation. Full Cancellation is desirable. But complexity requirements are enormous. 4000 tones, 100 Users billions of flops !!! Main Idea: Challenge: To determine which cross-talker to cancel on what “tone” for a given victim. Constraint: Total complexity is ...
Entropy generation in a mixed convection Poiseulle flow of molybdenum disulphide Jeffrey nanofluid
Gul, Aaiza; Khan, Ilyas; Makhanov, Stanislav S.
2018-06-01
Entropy analysis in a mixed convection Poiseulle flow of a Molybdenum Disulphide Jeffrey Nanofluid (MDJN) is presented. Mixed convection is caused due to buoyancy force and external pressure gradient. The problem is formulated in terms of a boundary value problem for a system of partial differential equations. An analytical solution for the velocity and the temperature is obtained using the perturbation technique. Entropy generation has been derived as a function of the velocity and temperature gradients. The solutions are displayed graphically and the relevant importance of the input parameters is discussed. A Jeffrey nanofluid (JN) has been compared with a second grade nanofluid (SGN) and Newtonian nanofluid (NN). It is found that the entropy generation decreases when the temperature increases whereas increasing the Brickman number increases entropy generation.
Entropy-power uncertainty relations: towards a tight inequality for all Gaussian pure states
International Nuclear Information System (INIS)
Hertz, Anaelle; Jabbour, Michael G; Cerf, Nicolas J
2017-01-01
We show that a proper expression of the uncertainty relation for a pair of canonically-conjugate continuous variables relies on entropy power, a standard notion in Shannon information theory for real-valued signals. The resulting entropy-power uncertainty relation is equivalent to the entropic formulation of the uncertainty relation due to Bialynicki-Birula and Mycielski, but can be further extended to rotated variables. Hence, based on a reasonable assumption, we give a partial proof of a tighter form of the entropy-power uncertainty relation taking correlations into account and provide extensive numerical evidence of its validity. Interestingly, it implies the generalized (rotation-invariant) Schrödinger–Robertson uncertainty relation exactly as the original entropy-power uncertainty relation implies Heisenberg relation. It is saturated for all Gaussian pure states, in contrast with hitherto known entropic formulations of the uncertainty principle. (paper)
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.
Entropy Generation on Nanofluid Flow through a Horizontal Riga Plate
Directory of Open Access Journals (Sweden)
Tehseen Abbas
2016-06-01
Full Text Available In this article, entropy generation on viscous nanofluid through a horizontal Riga plate has been examined. The present flow problem consists of continuity, linear momentum, thermal energy, and nanoparticle concentration equation which are simplified with the help of Oberbeck-Boussinesq approximation. The resulting highly nonlinear coupled partial differential equations are solved numerically by means of the shooting method (SM. The expression of local Nusselt number and local Sherwood number are also taken into account and discussed with the help of table. The physical influence of all the emerging parameters such as Brownian motion parameter, thermophoresis parameter, Brinkmann number, Richardson number, nanoparticle flux parameter, Lewis number and suction parameter are demonstrated graphically. In particular, we conferred their influence on velocity profile, temperature profile, nanoparticle concentration profile and Entropy profile.
Enthalpy-entropy compensation in protein unfolding
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Enthalpy-entropy compensation was found to be a universal law in protein unfolding based on over 3 000 experimental data. Water molecular reorganization accompanying the protein unfolding was suggested as the origin of the enthalpy-entropy compensation in protein unfolding. It is indicated that the enthalpy-entropy compensation constitutes the physical foundation that satisfies the biological need of the small free energy changes in protein unfolding, without the sacrifice of the bio-diversity of proteins. The enthalpy-entropy compensation theory proposed herein also provides valuable insights into the Privalov's puzzle of enthalpy and entropy convergence in protein unfolding.
Receiver function estimated by maximum entropy deconvolution
Institute of Scientific and Technical Information of China (English)
吴庆举; 田小波; 张乃铃; 李卫平; 曾融生
2003-01-01
Maximum entropy deconvolution is presented to estimate receiver function, with the maximum entropy as the rule to determine auto-correlation and cross-correlation functions. The Toeplitz equation and Levinson algorithm are used to calculate the iterative formula of error-predicting filter, and receiver function is then estimated. During extrapolation, reflective coefficient is always less than 1, which keeps maximum entropy deconvolution stable. The maximum entropy of the data outside window increases the resolution of receiver function. Both synthetic and real seismograms show that maximum entropy deconvolution is an effective method to measure receiver function in time-domain.
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
q-entropy for symbolic dynamical systems
International Nuclear Information System (INIS)
Zhao, Yun; Pesin, Yakov
2015-01-01
For symbolic dynamical systems we use the Carathéodory construction as described in (Pesin 1997 Dimension Theory in Dynamical Systems, ConTemporary Views and Applications (Chicago: University of Chicago Press)) to introduce the notions of q-topological and q-metric entropies. We describe some basic properties of these entropies and in particular, discuss relations between q-metric entropy and local metric entropy. Both q-topological and q-metric entropies are new invariants respectively under homeomorphisms and metric isomorphisms of dynamical systems. (paper)
Holographic charged Rényi entropies
Belin, Alexandre; Hung, Ling-Yan; Maloney, Alexander; Matsuura, Shunji; Myers, Robert C.; Sierens, Todd
2013-12-01
We construct a new class of entanglement measures by extending the usual definition of Rényi entropy to include a chemical potential. These charged Rényi entropies measure the degree of entanglement in different charge sectors of the theory and are given by Euclidean path integrals with the insertion of a Wilson line encircling the entangling surface. We compute these entropies for a spherical entangling surface in CFT's with holographic duals, where they are related to entropies of charged black holes with hyperbolic horizons. We also compute charged Rényi entropies in free field theories.
Controlling the Shannon Entropy of Quantum Systems
Directory of Open Access Journals (Sweden)
Yifan Xing
2013-01-01
Full Text Available This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking.
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)
Minimization of entropy production in separate and connected process units
Energy Technology Data Exchange (ETDEWEB)
Roesjorde, Audun
2004-08-01
reducing the recycle stream, increasing the pressure of the separation section, and increasing the conversion and selectivity of the reactor, a large reduction in the entropy production of the process was obtained. The results showed that the most inefficient units were the reactor, partial condenser and the two distillation columns, even after the optimization was carried out. This may motivate further work along these lines in the chemical process industry. (author)
Entropy-based financial asset pricing.
Directory of Open Access Journals (Sweden)
Mihály Ormos
Full Text Available We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing model. For asset pricing we define the continuous entropy as an alternative measure of risk. Our results show that entropy decreases in the function of the number of securities involved in a portfolio in a similar way to the standard deviation, and that efficient portfolios are situated on a hyperbola in the expected return-entropy system. For empirical investigation we use daily returns of 150 randomly selected securities for a period of 27 years. Our regression results show that entropy has a higher explanatory power for the expected return than the capital asset pricing model beta. Furthermore we show the time varying behavior of the beta along with entropy.
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.
Wavelet entropy characterization of elevated intracranial pressure.
Xu, Peng; Scalzo, Fabien; Bergsneider, Marvin; Vespa, Paul; Chad, Miller; Hu, Xiao
2008-01-01
Intracranial Hypertension (ICH) often occurs for those patients with traumatic brain injury (TBI), stroke, tumor, etc. Pathology of ICH is still controversial. In this work, we used wavelet entropy and relative wavelet entropy to study the difference existed between normal and hypertension states of ICP for the first time. The wavelet entropy revealed the similar findings as the approximation entropy that entropy during ICH state is smaller than that in normal state. Moreover, with wavelet entropy, we can see that ICH state has the more focused energy in the low wavelet frequency band (0-3.1 Hz) than the normal state. The relative wavelet entropy shows that the energy distribution in the wavelet bands between these two states is actually different. Based on these results, we suggest that ICH may be formed by the re-allocation of oscillation energy within brain.
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.
International Nuclear Information System (INIS)
1978-11-01
This discussion paper considers the possibility of applying to the recycle of plutonium in thermal reactors a particular method of partial processing based on the PUREX process but named CIVEX to emphasise the differences. The CIVEX process is based primarily on the retention of short-lived fission products. The paper suggests: (1) the recycle of fission products with uranium and plutonium in thermal reactor fuel would be technically feasible; (2) it would, however, take ten years or more to develop the CIVEX process to the point where it could be launched on a commercial scale; (3) since the majority of spent fuel to be reprocessed this century will have been in storage for ten years or more, the recycling of short-lived fission products with the U-Pu would not provide an effective means of making refabrication fuel ''inaccessible'' because the radioactivity associated with the fission products would have decayed. There would therefore be no advantage in partial processing
Directory of Open Access Journals (Sweden)
М.М. Karimova
2017-05-01
Full Text Available A girl with partial gigantism (the increased I and II fingers of the left foot is being examined. This condition is a rare and unresolved problem, as the definite reason of its development is not determined. Wait-and-see strategy is recommended, as well as correcting operations after closing of growth zones, and forming of data pool for generalization and development of schemes of drug and radial therapeutic methods.
Entropy and Entropy Production: Old Misconceptions and New Breakthroughs
Directory of Open Access Journals (Sweden)
Leonid M. Martyushev
2013-03-01
Full Text Available Persistent misconceptions existing for dozens of years and influencing progress in various fields of science are sometimes encountered in the scientific and especially, the popular-science literature. The present brief review deals with two such interrelated misconceptions (misunderstandings. The first misunderstanding: entropy is a measure of disorder. This is an old and very common opinion. The second misconception is that the entropy production minimizes in the evolution of nonequilibrium systems. However, as it has recently become clear, evolution (progress in Nature demonstrates the opposite, i.e., maximization of the entropy production. The principal questions connected with this maximization are considered herein. The two misconceptions mentioned above can lead to the apparent contradiction between the conclusions of modern thermodynamics and the basic conceptions of evolution existing in biology. In this regard, the analysis of these issues seems extremely important and timely as it contributes to the deeper understanding of the laws of development of the surrounding World and the place of humans in it.
Conditional quantum entropy power inequality for d-level quantum systems
Jeong, Kabgyun; Lee, Soojoon; Jeong, Hyunseok
2018-04-01
We propose an extension of the quantum entropy power inequality for finite dimensional quantum systems, and prove a conditional quantum entropy power inequality by using the majorization relation as well as the concavity of entropic functions also given by Audenaert et al (2016 J. Math. Phys. 57 052202). Here, we make particular use of the fact that a specific local measurement after a partial swap operation (or partial swap quantum channel) acting only on finite dimensional bipartite subsystems does not affect the majorization relation for the conditional output states when a separable ancillary subsystem is involved. We expect our conditional quantum entropy power inequality to be useful, and applicable in bounding and analyzing several capacity problems for quantum channels.
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.
On Maximum Entropy and Inference
Directory of Open Access Journals (Sweden)
Luigi Gresele
2017-11-01
Full Text Available Maximum entropy is a powerful concept that entails a sharp separation between relevant and irrelevant variables. It is typically invoked in inference, once an assumption is made on what the relevant variables are, in order to estimate a model from data, that affords predictions on all other (dependent variables. Conversely, maximum entropy can be invoked to retrieve the relevant variables (sufficient statistics directly from the data, once a model is identified by Bayesian model selection. We explore this approach in the case of spin models with interactions of arbitrary order, and we discuss how relevant interactions can be inferred. In this perspective, the dimensionality of the inference problem is not set by the number of parameters in the model, but by the frequency distribution of the data. We illustrate the method showing its ability to recover the correct model in a few prototype cases and discuss its application on a real dataset.
Entropy favours open colloidal lattices
Mao, Xiaoming; Chen, Qian; Granick, Steve
2013-03-01
Burgeoning experimental and simulation activity seeks to understand the existence of self-assembled colloidal structures that are not close-packed. Here we describe an analytical theory based on lattice dynamics and supported by experiments that reveals the fundamental role entropy can play in stabilizing open lattices. The entropy we consider is associated with the rotational and vibrational modes unique to colloids interacting through extended attractive patches. The theory makes predictions of the implied temperature, pressure and patch-size dependence of the phase diagram of open and close-packed structures. More generally, it provides guidance for the conditions at which targeted patchy colloidal assemblies in two and three dimensions are stable, thus overcoming the difficulty in exploring by experiment or simulation the full range of conceivable parameters.
Maximizing Entropy over Markov Processes
DEFF Research Database (Denmark)
Biondi, Fabrizio; Legay, Axel; Nielsen, Bo Friis
2013-01-01
The channel capacity of a deterministic system with confidential data is an upper bound on the amount of bits of data an attacker can learn from the system. We encode all possible attacks to a system using a probabilistic specification, an Interval Markov Chain. Then the channel capacity...... as a reward function, a polynomial algorithm to verify the existence of an system maximizing entropy among those respecting a specification, a procedure for the maximization of reward functions over Interval Markov Chains and its application to synthesize an implementation maximizing entropy. We show how...... to use Interval Markov Chains to model abstractions of deterministic systems with confidential data, and use the above results to compute their channel capacity. These results are a foundation for ongoing work on computing channel capacity for abstractions of programs derived from code....
Maximizing entropy over Markov processes
DEFF Research Database (Denmark)
Biondi, Fabrizio; Legay, Axel; Nielsen, Bo Friis
2014-01-01
The channel capacity of a deterministic system with confidential data is an upper bound on the amount of bits of data an attacker can learn from the system. We encode all possible attacks to a system using a probabilistic specification, an Interval Markov Chain. Then the channel capacity...... as a reward function, a polynomial algorithm to verify the existence of a system maximizing entropy among those respecting a specification, a procedure for the maximization of reward functions over Interval Markov Chains and its application to synthesize an implementation maximizing entropy. We show how...... to use Interval Markov Chains to model abstractions of deterministic systems with confidential data, and use the above results to compute their channel capacity. These results are a foundation for ongoing work on computing channel capacity for abstractions of programs derived from code. © 2014 Elsevier...
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.
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.
Multivariate Generalized Multiscale Entropy Analysis
Directory of Open Access Journals (Sweden)
Anne Humeau-Heurtier
2016-11-01
Full Text Available Multiscale entropy (MSE was introduced in the 2000s to quantify systems’ complexity. MSE relies on (i a coarse-graining procedure to derive a set of time series representing the system dynamics on different time scales; (ii the computation of the sample entropy for each coarse-grained time series. A refined composite MSE (rcMSE—based on the same steps as MSE—also exists. Compared to MSE, rcMSE increases the accuracy of entropy estimation and reduces the probability of inducing undefined entropy for short time series. The multivariate versions of MSE (MMSE and rcMSE (MrcMSE have also been introduced. In the coarse-graining step used in MSE, rcMSE, MMSE, and MrcMSE, the mean value is used to derive representations of the original data at different resolutions. A generalization of MSE was recently published, using the computation of different moments in the coarse-graining procedure. However, so far, this generalization only exists for univariate signals. We therefore herein propose an extension of this generalized MSE to multivariate data. The multivariate generalized algorithms of MMSE and MrcMSE presented herein (MGMSE and MGrcMSE, respectively are first analyzed through the processing of synthetic signals. We reveal that MGrcMSE shows better performance than MGMSE for short multivariate data. We then study the performance of MGrcMSE on two sets of short multivariate electroencephalograms (EEG available in the public domain. We report that MGrcMSE may show better performance than MrcMSE in distinguishing different types of multivariate EEG data. MGrcMSE could therefore supplement MMSE or MrcMSE in the processing of multivariate datasets.
Entropy in an expanding universe
International Nuclear Information System (INIS)
Frautschi, S.
1982-01-01
The question of how the observed evolution of organized structures from initial chaos in the expanding universe can be reconciled with the laws of statistical mechanics is studied, with emphasis on effects of the expansion and gravity. Some major sources of entropy increase are listed. An expanding causal region is defined in which the entropy, though increasing, tends to fall further and further behind its maximum possible value, thus allowing for the development of order. The related questions of whether entropy will continue increasing without limit in the future, and whether such increase in the form of Hawking radiation or radiation from positronium might enable life to maintain itself permanently, are considered. Attempts to find a scheme for preserving life based on solid structures fail because events such as quantum tunneling recurrently disorganize matter on a very long but fixed time scale, whereas all energy sources slow down progressively in an expanding universe. However, there remains hope that other modes of life capable of maintaining themselves permanently can be found
Resonance transport and kinetic entropy
International Nuclear Information System (INIS)
Ivanov, Yu.B.; Knoll, J.; Voskresensky, D.N.
2000-01-01
We continue the description of the dynamics of unstable particles within the real-time formulation of nonequilibrium field theory initiated in a previous paper . There we suggest to use Baym's PHI-functional method in order to achieve approximation schemes with 'built in' consistency with respect to conservation laws and thermodynamics even in the case of particles with finite damping width. Starting from Kadanoff-Baym equations we discuss a consistent first order gradient approach to transport which preserves the PHI-derivable properties. The validity conditions for the resulting quantum four-phase-space kinetic theory are discussed under the perspective to treat particles with broad damping widths. This non-equilibrium dynamics naturally includes all those quantum features already inherent in the corresponding equilibrium limit (e.g. Matsubara formalism) at the same level of PHI-derivable approximation. Various collision-term diagrams are discussed including those of higher order which lead to memory effects. As an important novel part we derive a generalized nonequilibrium expression for the kinetic entropy flow, which includes contributions from fluctuations and mass-width effects. In special cases an H-theorem is derived implying that the entropy can only increase with time. Memory effects in the kinetic terms provide contributions to the kinetic entropy flow that in the equilibrium limit recover the famous bosonic type T 3 lnT correction to the specific heat in the case of Fermi liquids like Helium-3
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.
The density process of the minimal entropy Martingale measure in a ...
African Journals Online (AJOL)
In a stochastic volatility market the Radon-Nikodym density of the minimal entropy martingale measure can be expressed in terms of the solution of a semilinear partial differential equation (PDE). This fact has been explored and illustrated for the time-homogeneous case in a recent paper by Benth and Karlsen [3]. However ...
Can the maximum entropy principle be explained as a consistency requirement?
Uffink, J.
1997-01-01
The principle of maximum entropy is a general method to assign values to probability distributions on the basis of partial information. This principle, introduced by Jaynes in 1957, forms an extension of the classical principle of insufficient reason. It has been further generalized, both in
Statistical mechanical theory of liquid entropy
International Nuclear Information System (INIS)
Wallace, D.C.
1993-01-01
The multiparticle correlation expansion for the entropy of a classical monatomic liquid is presented. This entropy expresses the physical picture in which there is no free particle motion, but rather, each atom moves within a cage formed by its neighbors. The liquid expansion, including only pair correlations, gives an excellent account of the experimental entropy of most liquid metals, of liquid argon, and the hard sphere liquid. The pair correlation entropy is well approximated by a universal function of temperature. Higher order correlation entropy, due to n-particle irreducible correlations for n≥3, is significant in only a few liquid metals, and its occurrence suggests the presence of n-body forces. When the liquid theory is applied to the study of melting, the author discovers the important classification of normal and anomalous melting, according to whether there is not or is a significant change in the electronic structure upon melting, and he discovers the universal disordering entropy for melting of a monatomic crystal. Interesting directions for future research are: extension to include orientational correlations of molecules, theoretical calculation of the entropy of water, application to the entropy of the amorphous state, and correlational entropy of compressed argon. The author clarifies the relation among different entropy expansions in the recent literature
Entropy in molecular recognition by proteins.
Caro, José A; Harpole, Kyle W; Kasinath, Vignesh; Lim, Jackwee; Granja, Jeffrey; Valentine, Kathleen G; Sharp, Kim A; Wand, A Joshua
2017-06-20
Molecular recognition by proteins is fundamental to molecular biology. Dissection of the thermodynamic energy terms governing protein-ligand interactions has proven difficult, with determination of entropic contributions being particularly elusive. NMR relaxation measurements have suggested that changes in protein conformational entropy can be quantitatively obtained through a dynamical proxy, but the generality of this relationship has not been shown. Twenty-eight protein-ligand complexes are used to show a quantitative relationship between measures of fast side-chain motion and the underlying conformational entropy. We find that the contribution of conformational entropy can range from favorable to unfavorable, which demonstrates the potential of this thermodynamic variable to modulate protein-ligand interactions. For about one-quarter of these complexes, the absence of conformational entropy would render the resulting affinity biologically meaningless. The dynamical proxy for conformational entropy or "entropy meter" also allows for refinement of the contributions of solvent entropy and the loss in rotational-translational entropy accompanying formation of high-affinity complexes. Furthermore, structure-based application of the approach can also provide insight into long-lived specific water-protein interactions that escape the generic treatments of solvent entropy based simply on changes in accessible surface area. These results provide a comprehensive and unified view of the general role of entropy in high-affinity molecular recognition by proteins.
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.
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
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....
Entropy type complexity of quantum processes
International Nuclear Information System (INIS)
Watanabe, Noboru
2014-01-01
von Neumann entropy represents the amount of information in the quantum state, and this was extended by Ohya for general quantum systems [10]. Umegaki first defined the quantum relative entropy for σ-finite von Neumann algebras, which was extended by Araki, and Uhlmann, for general von Neumann algebras and *-algebras, respectively. In 1983 Ohya introduced the quantum mutual entropy by using compound states; this describes the amount of information correctly transmitted through the quantum channel, which was also extended by Ohya for general quantum systems. In this paper, we briefly explain Ohya's S-mixing entropy and the quantum mutual entropy for general quantum systems. By using structure equivalent class, we will introduce entropy type functionals based on quantum information theory to improve treatment for the Gaussian communication process. (paper)
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.
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.
Black hole versus cosmological horizon entropy
International Nuclear Information System (INIS)
Davis, Tamara M; Davies, P C W; Lineweaver, Charles H
2003-01-01
The generalized second law of thermodynamics states that entropy always increases when all event horizons are attributed with an entropy proportional to their area. We test the generalized second law by investigating the change in entropy when dust, radiation and black holes cross a cosmological event horizon. We generalize for flat, open and closed Friedmann-Robertson-Walker universes by using numerical calculations to determine the cosmological horizon evolution. In most cases, the loss of entropy from within the cosmological horizon is more than balanced by an increase in cosmological event horizon entropy, maintaining the validity of the generalized second law of thermodynamics. However, an intriguing set of open universe models shows an apparent entropy decrease when black holes disappear over the cosmological event horizon. We anticipate that this apparent violation of the generalized second law will disappear when solutions are available for black holes embedded in arbitrary backgrounds
The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems
Di Francesco, M.
2008-12-08
We study the long-time asymptotics of reaction-diffusion-type systems that feature a monotone decaying entropy (Lyapunov, free energy) functional. We consider both bounded domains and confining potentials on the whole space for arbitrary space dimensions. Our aim is to derive quantitative expressions for (or estimates of) the rates of convergence towards an (entropy minimizing) equilibrium state in terms of the constants of diffusion and reaction and with respect to conserved quantities. Our method, the so-called entropy approach, seeks to quantify convergence to equilibrium by using functional inequalities, which relate quantitatively the entropy and its dissipation in time. The entropy approach is well suited to nonlinear problems and known to be quite robust with respect to model variations. It has already been widely applied to scalar diffusion-convection equations, and the main goal of this paper is to study its generalization to systems of partial differential equations that contain diffusion and reaction terms and admit fewer conservation laws than the size of the system. In particular, we successfully apply the entropy approach to general linear systems and to a nonlinear example of a reaction-diffusion-convection system arising in solid-state physics as a paradigm for general nonlinear systems. © 2008 The Royal Society.
Entropy jump across an inviscid shock wave
Salas, Manuel D.; Iollo, Angelo
1995-01-01
The shock jump conditions for the Euler equations in their primitive form are derived by using generalized functions. The shock profiles for specific volume, speed, and pressure are shown to be the same, however density has a different shock profile. Careful study of the equations that govern the entropy shows that the inviscid entropy profile has a local maximum within the shock layer. We demonstrate that because of this phenomenon, the entropy, propagation equation cannot be used as a conservation law.
New Definition and Properties of Fuzzy Entropy
Institute of Scientific and Technical Information of China (English)
Qing Ming; Qin Yingbing
2006-01-01
Let X = (x1,x2 ,…,xn ) and F(X) be a fuzzy set on a universal set X. A new definition of fuzzy entropy about a fuzzy set A on F(X), e*, is defined based on the order relation "≤" on [0,1/2] n. It is proved that e* is a σ-entropy under an additional requirement. Besides, some entropy formulas are presented and related properties are discussed.
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.
Entropy In the Universe: A New Approach
Directory of Open Access Journals (Sweden)
Antonio Alfonso-Faus
2000-09-01
Full Text Available Abstract: We propose a new definition of entropy for any mass m, based on gravitation and through the concept of a gravitational cross section. It turns out to be proportional to mass, and therefore extensive, and to the age of the Universe. It is a Machian approach. It is also the number of gravity quanta the mass has emitted through its age. The entropy of the Uni-verse is so determined and the cosmological entropy problem solved.
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...
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.
Entropy as a measure of diffusion
International Nuclear Information System (INIS)
Aghamohammadi, Amir; Fatollahi, Amir H.; Khorrami, Mohammad; Shariati, Ahmad
2013-01-01
The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large times the entropy tends exponentially to a constant. For systems with no stationary density, at large times the entropy is logarithmic with a coefficient specifying the speed of the diffusion. As an example, the large-time behaviors of the entropy and the variance are compared for various types of fractional-derivative diffusions.
Entropy as a measure of diffusion
Energy Technology Data Exchange (ETDEWEB)
Aghamohammadi, Amir, E-mail: mohamadi@alzahra.ac.ir; Fatollahi, Amir H., E-mail: fath@alzahra.ac.ir; Khorrami, Mohammad, E-mail: mamwad@mailaps.org; Shariati, Ahmad, E-mail: shariati@mailaps.org
2013-10-15
The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large times the entropy tends exponentially to a constant. For systems with no stationary density, at large times the entropy is logarithmic with a coefficient specifying the speed of the diffusion. As an example, the large-time behaviors of the entropy and the variance are compared for various types of fractional-derivative diffusions.
Holographic entanglement entropy and cyclic cosmology
Frampton, Paul H.
2018-06-01
We discuss a cyclic cosmology in which the visible universe, or introverse, is all that is accessible to an observer while the extroverse represents the total spacetime originating from the time when the dark energy began to dominate. It is argued that entanglement entropy of the introverse is the more appropriate quantity to render infinitely cyclic, rather than the entropy of the total universe. Since vanishing entanglement entropy implies disconnected spacetimes, at the turnaround when the introverse entropy is zero the disconnected extroverse can be jettisoned with impunity.
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.
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 ...
Towse, Clare-Louise; Akke, Mikael; Daggett, Valerie
2017-04-27
Molecular dynamics (MD) simulations contain considerable information with regard to the motions and fluctuations of a protein, the magnitude of which can be used to estimate conformational entropy. Here we survey conformational entropy across protein fold space using the Dynameomics database, which represents the largest existing data set of protein MD simulations for representatives of essentially all known protein folds. We provide an overview of MD-derived entropies accounting for all possible degrees of dihedral freedom on an unprecedented scale. Although different side chains might be expected to impose varying restrictions on the conformational space that the backbone can sample, we found that the backbone entropy and side chain size are not strictly coupled. An outcome of these analyses is the Dynameomics Entropy Dictionary, the contents of which have been compared with entropies derived by other theoretical approaches and experiment. As might be expected, the conformational entropies scale linearly with the number of residues, demonstrating that conformational entropy is an extensive property of proteins. The calculated conformational entropies of folding agree well with previous estimates. Detailed analysis of specific cases identifies deviations in conformational entropy from the average values that highlight how conformational entropy varies with sequence, secondary structure, and tertiary fold. Notably, α-helices have lower entropy on average than do β-sheets, and both are lower than coil regions.
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.
Entanglement entropy of excited states
International Nuclear Information System (INIS)
Alba, Vincenzo; Fagotti, Maurizio; Calabrese, Pasquale
2009-01-01
We study the entanglement entropy of a block of contiguous spins in excited states of spin chains. We consider the XY model in a transverse field and the XXZ Heisenberg spin chain. For the latter, we developed a numerical application of the algebraic Bethe ansatz. We find two main classes of states with logarithmic and extensive behavior in the dimension of the block, characterized by the properties of excitations of the state. This behavior can be related to the locality properties of the Hamiltonian having a given state as the ground state. We also provide several details of the finite size scaling
International Nuclear Information System (INIS)
Kim, Jongkwang; Kim, Sowun; Lee, Kunsang; Kwon, Younghun
2009-01-01
In this article, we investigate the language structure in yeast 16 chromosomes. In order to find it, we use the entropy analysis for codons (or amino acids) of yeast 16 chromosomes, developed in analysis of natural language by Montemurro et al. From the analysis, we can see that there exists a language structure in codons (or amino acids) of yeast 16 chromosomes. Also we find that the grammar structure of amino acids of yeast 16 chromosomes has a deep relationship with secondary structure of protein.
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.
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)
Gravitational entropies in LTB dust models
International Nuclear Information System (INIS)
Sussman, Roberto A; Larena, Julien
2014-01-01
We consider generic Lemaître–Tolman–Bondi (LTB) dust models to probe the gravitational entropy proposals of Clifton, Ellis and Tavakol (CET) and of Hosoya and Buchert (HB). We also consider a variant of the HB proposal based on a suitable quasi-local scalar weighted average. We show that the conditions for entropy growth for all proposals are directly related to a negative correlation of similar fluctuations of the energy density and Hubble scalar. While this correlation is evaluated locally for the CET proposal, it must be evaluated in a non-local domain dependent manner for the two HB proposals. By looking at the fulfilment of these conditions at the relevant asymptotic limits we are able to provide a well grounded qualitative description of the full time evolution and radial asymptotic scaling of the three entropies in generic models. The following rigorous analytic results are obtained for the three proposals: (i) entropy grows when the density growing mode is dominant, (ii) all ever-expanding hyperbolic models reach a stable terminal equilibrium characterized by an inhomogeneous entropy maximum in their late time evolution; (iii) regions with decaying modes and collapsing elliptic models exhibit unstable equilibria associated with an entropy minimum (iv) near singularities the CET entropy diverges while the HB entropies converge; (v) the CET entropy converges for all models in the radial asymptotic range, whereas the HB entropies only converge for models asymptotic to a Friedmann–Lemaître–Robertson–Walker background. The fact that different independent proposals yield fairly similar conditions for entropy production, time evolution and radial scaling in generic LTB models seems to suggest that their common notion of a ‘gravitational entropy’ may be a theoretically robust concept applicable to more general spacetimes. (paper)
Conditional maximum-entropy method for selecting prior distributions in Bayesian statistics
Abe, Sumiyoshi
2014-11-01
The conditional maximum-entropy method (abbreviated here as C-MaxEnt) is formulated for selecting prior probability distributions in Bayesian statistics for parameter estimation. This method is inspired by a statistical-mechanical approach to systems governed by dynamics with largely separated time scales and is based on three key concepts: conjugate pairs of variables, dimensionless integration measures with coarse-graining factors and partial maximization of the joint entropy. The method enables one to calculate a prior purely from a likelihood in a simple way. It is shown, in particular, how it not only yields Jeffreys's rules but also reveals new structures hidden behind them.
Exergy of partially coherent thermal radiation
International Nuclear Information System (INIS)
Wijewardane, S.; Goswami, Yogi
2012-01-01
Exergy of electromagnetic radiation has been studied by a number of researchers for well over four decades in order to estimate the maximum conversion efficiencies of thermal radiation. As these researchers primarily dealt with solar and blackbody radiation, which have a low degree of coherence, they did not consider the partial coherence properties of thermal radiation. With the recent development of surface structures, which can emit radiation with high degree of coherence, the importance of considering the partial coherent properties in exergy calculation has become a necessity as the coherence properties directly influence the entropy of the wave field. Here in this paper we derive an expression for the exergy of quasi-monochromatic radiation using statistical thermodynamics and show that it is identical with the expressions derived using classical thermodynamics. We also present a method to calculate the entropy, thereby the exergy of partially coherent radiation using statistical thermodynamics and a method called matrix treatment of wave field. -- Highlights: ► Considered partial coherence of radiation for the first time to calculate exergy. ► The importance of this method is emphasized with energy conversion examples. ► Derived an expression for the exergy of radiation using statistical thermodynamics. ► Adopted a method to calculate intensity of statistically independent principle wave.
Some relations between entropy and approximation numbers
Institute of Scientific and Technical Information of China (English)
郑志明
1999-01-01
A general result is obtained which relates the entropy numbers of compact maps on Hilbert space to its approximation numbers. Compared with previous works in this area, it is particularly convenient for dealing with the cases where the approximation numbers decay rapidly. A nice estimation between entropy and approximation numbers for noncompact maps is given.
Length scale for configurational entropy in microemulsions
Reiss, H.; Kegel, W.K.; Groenewold, J.
1996-01-01
In this paper we study the length scale that must be used in evaluating the mixing entropy in a microemulsion. The central idea involves the choice of a length scale in configuration space that is consistent with the physical definition of entropy in phase space. We show that this scale may be
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…
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
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…
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
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…
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)
On the Conditional Entropy of Wireless Networks
DEFF Research Database (Denmark)
Coon, Justin P.; Badiu, Mihai Alin; Gündüz, Deniz
2018-01-01
The characterization of topological uncertainty in wireless networks using the formalism of graph entropy has received interest in the spatial networks community. In this paper, we develop lower bounds on the entropy of a wireless network by conditioning on potential network observables. Two appr...... a homogeneous binomial point process in this work) and the network topology....
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)
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 ...
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…
The Thermal Entropy Density of Spacetime
Directory of Open Access Journals (Sweden)
Rongjia Yang
2013-01-01
Full Text Available Introducing the notion of thermal entropy density via the first law of thermodynamics and assuming the Einstein equation as an equation of thermal state, we obtain the thermal entropy density of any arbitrary spacetime without assuming a temperature or a horizon. The results confirm that there is a profound connection between gravity and thermodynamics.
Holographic entanglement entropy in Lovelock gravities
de Boer, J.; Kulaxizi, M.; Parnachev, A.
2011-01-01
We study entanglement entropies of simply connected surfaces in field theories dual to Lovelock gravities. We consider Gauss-Bonnet and cubic Lovelock gravities in detail. In the conformal case the logarithmic terms in the entanglement entropy are governed by the conformal anomalies of the CFT; we
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
The improvement of Clausius entropy and its application in entropy analysis
Institute of Scientific and Technical Information of China (English)
WU Jing; GUO ZengYuan
2008-01-01
The defects of Cleusius entropy which Include s premise of reversible process and a process quantlty of heat in Its definition are discussed in this paper. Moreover, the heat temperature quotient under reversible conditions, i.e. (δQ/T)rev, is essentially a process quantity although it is numerically equal to the entropy change. The sum of internal energy temperature quotient and work temperature quotient is defined as the improved form of Clausius entropy and it can be further proved to be a state funcllon. Unlike Clausius entropy, the improved deflnltion consists of system properties wlthout premise just like other state functions, for example, pressure p and enthalpy h, etc. it is unnecessary to invent reversible paths when calculating entropy change for irreversible processes based on the improved form of entropy since it is independent of process. Furthermore, entropy balance equations for internally and externally irreversible processes are deduced respectively based on the concepts of thermal reservoir entropy transfer and system entropy transfer. Finally, some examples are presented to show that the improved deflnitlon of Clausius entropy provides a clear concept as well as a convenient method for en-tropy change calculation.
Analysis of complex time series using refined composite multiscale entropy
International Nuclear Information System (INIS)
Wu, Shuen-De; Wu, Chiu-Wen; Lin, Shiou-Gwo; Lee, Kung-Yen; Peng, Chung-Kang
2014-01-01
Multiscale entropy (MSE) is an effective algorithm for measuring the complexity of a time series that has been applied in many fields successfully. However, MSE may yield an inaccurate estimation of entropy or induce undefined entropy because the coarse-graining procedure reduces the length of a time series considerably at large scales. Composite multiscale entropy (CMSE) was recently proposed to improve the accuracy of MSE, but it does not resolve undefined entropy. Here we propose a refined composite multiscale entropy (RCMSE) to improve CMSE. For short time series analyses, we demonstrate that RCMSE increases the accuracy of entropy estimation and reduces the probability of inducing undefined entropy.
On S-mixing entropy of quantum channels
Mukhamedov, Farrukh; Watanabe, Noboru
2018-06-01
In this paper, an S-mixing entropy of quantum channels is introduced as a generalization of Ohya's S-mixing entropy. We investigate several properties of the introduced entropy. Moreover, certain relations between the S-mixing entropy and the existing map and output entropies of quantum channels are investigated as well. These relations allowed us to find certain connections between separable states and the introduced entropy. Hence, there is a sufficient condition to detect entangled states. Moreover, several properties of the introduced entropy are investigated. Besides, entropies of qubit and phase-damping channels are calculated.
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
On the way towards a generalized entropy maximization procedure
International Nuclear Information System (INIS)
Bagci, G. Baris; Tirnakli, Ugur
2009-01-01
We propose a generalized entropy maximization procedure, which takes into account the generalized averaging procedures and information gain definitions underlying the generalized entropies. This novel generalized procedure is then applied to Renyi and Tsallis entropies. The generalized entropy maximization procedure for Renyi entropies results in the exponential stationary distribution asymptotically for q element of (0,1] in contrast to the stationary distribution of the inverse power law obtained through the ordinary entropy maximization procedure. Another result of the generalized entropy maximization procedure is that one can naturally obtain all the possible stationary distributions associated with the Tsallis entropies by employing either ordinary or q-generalized Fourier transforms in the averaging procedure.
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.
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
Directory of Open Access Journals (Sweden)
Yun He
2018-05-01
Full Text Available We examine the entropy of black holes in de Sitter space and black holes surrounded by quintessence. These black holes have multiple horizons, including at least the black hole event horizon and a horizon outside it (cosmological horizon for de Sitter black holes and “quintessence horizon” for the black holes surrounded by quintessence. Based on the consideration that the two horizons are not independent each other, we conjecture that the total entropy of these black holes should not be simply the sum of entropies of the two horizons, but should have an extra term coming from the correlations between the two horizons. Different from our previous works, in this paper we consider the cosmological constant as the variable and employ an effective method to derive the explicit form of the entropy. We also try to discuss the thermodynamic stabilities of these black holes according to the entropy and the effective temperature.
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
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)
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.
Entanglement entropy in top-down models
Energy Technology Data Exchange (ETDEWEB)
Jones, Peter A.R.; Taylor, Marika [Mathematical Sciences and STAG Research Centre, University of Southampton,Highfield, Southampton, SO17 1BJ (United Kingdom)
2016-08-26
We explore holographic entanglement entropy in ten-dimensional supergravity solutions. It has been proposed that entanglement entropy can be computed in such top-down models using minimal surfaces which asymptotically wrap the compact part of the geometry. We show explicitly in a wide range of examples that the holographic entanglement entropy thus computed agrees with the entanglement entropy computed using the Ryu-Takayanagi formula from the lower-dimensional Einstein metric obtained from reduction over the compact space. Our examples include not only consistent truncations but also cases in which no consistent truncation exists and Kaluza-Klein holography is used to identify the lower-dimensional Einstein metric. We then give a general proof, based on the Lewkowycz-Maldacena approach, of the top-down entanglement entropy formula.
Entanglement entropy in top-down models
International Nuclear Information System (INIS)
Jones, Peter A.R.; Taylor, Marika
2016-01-01
We explore holographic entanglement entropy in ten-dimensional supergravity solutions. It has been proposed that entanglement entropy can be computed in such top-down models using minimal surfaces which asymptotically wrap the compact part of the geometry. We show explicitly in a wide range of examples that the holographic entanglement entropy thus computed agrees with the entanglement entropy computed using the Ryu-Takayanagi formula from the lower-dimensional Einstein metric obtained from reduction over the compact space. Our examples include not only consistent truncations but also cases in which no consistent truncation exists and Kaluza-Klein holography is used to identify the lower-dimensional Einstein metric. We then give a general proof, based on the Lewkowycz-Maldacena approach, of the top-down entanglement entropy formula.
Low Streamflow Forcasting using Minimum Relative Entropy
Cui, H.; Singh, V. P.
2013-12-01
Minimum relative entropy spectral analysis is derived in this study, and applied to forecast streamflow time series. Proposed method extends the autocorrelation in the manner that the relative entropy of underlying process is minimized so that time series data can be forecasted. Different prior estimation, such as uniform, exponential and Gaussian assumption, is taken to estimate the spectral density depending on the autocorrelation structure. Seasonal and nonseasonal low streamflow series obtained from Colorado River (Texas) under draught condition is successfully forecasted using proposed method. Minimum relative entropy determines spectral of low streamflow series with higher resolution than conventional method. Forecasted streamflow is compared to the prediction using Burg's maximum entropy spectral analysis (MESA) and Configurational entropy. The advantage and disadvantage of each method in forecasting low streamflow is discussed.
Entropy of uremia and dialysis technology.
Ronco, Claudio
2013-01-01
The second law of thermodynamics applies with local exceptions to patient history and therapy interventions. Living things preserve their low level of entropy throughout time because they receive energy from their surroundings in the form of food. They gain their order at the expense of disordering the nutrients they consume. Death is the thermodynamically favored state: it represents a large increase in entropy as molecular structure yields to chaos. The kidney is an organ dissipating large amounts of energy to maintain the level of entropy of the organism as low as possible. Diseases, and in particular uremia, represent conditions of rapid increase in entropy. Therapeutic strategies are oriented towards a reduction in entropy or at least a decrease in the speed of entropy increase. Uremia is a process accelerating the trend towards randomness and disorder (increase in entropy). Dialysis is a factor external to the patient that tends to reduce the level of entropy caused by kidney disease. Since entropy can only increase in closed systems, energy and work must be spent to limit the entropy of uremia. This energy should be adapted to the system (patient) and be specifically oriented and personalized. This includes a multidimensional effort to achieve an adequate dialysis that goes beyond small molecular weight solute clearance. It includes a biological plan for recovery of homeostasis and a strategy towards long-term rehabilitation of the patient. Such objectives can be achieved with a combination of technology and innovation to answer specific questions that are still present after 60 years of dialysis history. This change in the individual bioentropy may represent a local exception to natural trends as the patient could be considered an isolated universe responding to the classic laws of thermodynamics. Copyright © 2013 S. Karger AG, Basel.
Zhu, C
2003-01-01
This paper is concerned with the existence and uniqueness of the entropy solution to the initial boundary value problem for the inviscid Burgers equation. To apply the method of vanishing viscosity to study the existence of the entropy solution, we first introduce the initial boundary value problem for the viscous Burgers equation, and as in Evans (1998 Partial Differential Equations (Providence, RI: American Mathematical Society) and Hopf (1950 Commun. Pure Appl. Math. 3 201-30), give the formula of the corresponding viscosity solutions by Hopf-Cole transformation. Secondly, we prove the convergence of the viscosity solution sequences and verify that the limiting function is an entropy solution. Finally, we give an example to show how our main result can be applied to solve the initial boundary value problem for the Burgers equation.
Maximum-entropy networks pattern detection, network reconstruction and graph combinatorics
Squartini, Tiziano
2017-01-01
This book is an introduction to maximum-entropy models of random graphs with given topological properties and their applications. Its original contribution is the reformulation of many seemingly different problems in the study of both real networks and graph theory within the unified framework of maximum entropy. Particular emphasis is put on the detection of structural patterns in real networks, on the reconstruction of the properties of networks from partial information, and on the enumeration and sampling of graphs with given properties. After a first introductory chapter explaining the motivation, focus, aim and message of the book, chapter 2 introduces the formal construction of maximum-entropy ensembles of graphs with local topological constraints. Chapter 3 focuses on the problem of pattern detection in real networks and provides a powerful way to disentangle nontrivial higher-order structural features from those that can be traced back to simpler local constraints. Chapter 4 focuses on the problem o...
International Nuclear Information System (INIS)
Zhu, Changjiang; Duan, Renjun
2003-01-01
This paper is concerned with the existence and uniqueness of the entropy solution to the initial boundary value problem for the inviscid Burgers equation. To apply the method of vanishing viscosity to study the existence of the entropy solution, we first introduce the initial boundary value problem for the viscous Burgers equation, and as in Evans (1998 Partial Differential Equations (Providence, RI: American Mathematical Society) and Hopf (1950 Commun. Pure Appl. Math. 3 201-30), give the formula of the corresponding viscosity solutions by Hopf-Cole transformation. Secondly, we prove the convergence of the viscosity solution sequences and verify that the limiting function is an entropy solution. Finally, we give an example to show how our main result can be applied to solve the initial boundary value problem for the Burgers equation
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)
Maximum Entropy: Clearing up Mysteries
Directory of Open Access Journals (Sweden)
Marian GrendÃƒÂ¡r
2001-04-01
Full Text Available Abstract: There are several mystifications and a couple of mysteries pertinent to MaxEnt. The mystifications, pitfalls and traps are set up mainly by an unfortunate formulation of Jaynes' die problem, the cause cÃƒÂ©lÃƒÂ¨bre of MaxEnt. After discussing the mystifications a new formulation of the problem is proposed. Then we turn to the mysteries. An answer to the recurring question 'Just what are we accomplishing when we maximize entropy?' [8], based on MaxProb rationale of MaxEnt [6], is recalled. A brief view on the other mystery: 'What is the relation between MaxEnt and the Bayesian method?' [9], in light of the MaxProb rationale of MaxEnt suggests that there is not and cannot be a conflict between MaxEnt and Bayes Theorem.
International Nuclear Information System (INIS)
Dowker, J S
2013-01-01
I give some scalar field theory calculations on a d-dimensional lune of arbitrary angle, evaluating, numerically, the effective action which is expressed as a simple quadrature, for conformal coupling. Using this, the entanglement and Rényi entropies are computed. Massive fields are also considered and a renormalization to make the (one-loop) effective action vanish for infinite mass is suggested and used, not entirely successfully. However a universal coefficient is derived from the large mass expansion. From the deformation of the corresponding lune result, I conjecture that the effective action on all odd manifolds with a simple conical singularity has an extremum when the singularity disappears. For the round sphere, I show how to convert the quadrature form of the conformal Laplacian determinant into the more usual sum of Riemann ζ-functions (and log 2). (paper)
The improvement of Clausius entropy and its application in entropy analysis
Institute of Scientific and Technical Information of China (English)
2008-01-01
The defects of Clausius entropy which include a premise of reversible process and a process quantity of heat in its definition are discussed in this paper. Moreover, the heat temperature quotient under reversible conditions, i.e. (δQ/T)rev, is essentially a process quantity although it is numerically equal to the entropy change. The sum of internal energy temperature quotient and work temperature quotient is defined as the improved form of Clausius entropy and it can be further proved to be a state function. Unlike Clausius entropy, the improved definition consists of system properties without premise just like other state functions, for example, pressure p and enthalpy h, etc. It is unnecessary to invent reversible paths when calculating entropy change for irreversible processes based on the improved form of entropy since it is independent of process. Furthermore, entropy balance equations for internally and externally irreversible processes are deduced respectively based on the concepts of thermal reservoir entropy transfer and system entropy transfer. Finally, some examples are presented to show that the improved definition of Clausius entropy provides a clear concept as well as a convenient method for en- tropy change calculation.
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 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)
Towards operational interpretations of generalized entropies
Topsøe, Flemming
2010-12-01
The driving force behind our study has been to overcome the difficulties you encounter when you try to extend the clear and convincing operational interpretations of classical Boltzmann-Gibbs-Shannon entropy to other notions, especially to generalized entropies as proposed by Tsallis. Our approach is philosophical, based on speculations regarding the interplay between truth, belief and knowledge. The main result demonstrates that, accepting philosophically motivated assumptions, the only possible measures of entropy are those suggested by Tsallis - which, as we know, include classical entropy. This result constitutes, so it seems, a more transparent interpretation of entropy than previously available. However, further research to clarify the assumptions is still needed. Our study points to the thesis that one should never consider the notion of entropy in isolation - in order to enable a rich and technically smooth study, further concepts, such as divergence, score functions and descriptors or controls should be included in the discussion. This will clarify the distinction between Nature and Observer and facilitate a game theoretical discussion. The usefulness of this distinction and the subsequent exploitation of game theoretical results - such as those connected with the notion of Nash equilibrium - is demonstrated by a discussion of the Maximum Entropy Principle.
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.
Entropy Generation Analysis of Desalination Technologies
Directory of Open Access Journals (Sweden)
John H. Lienhard V
2011-09-01
Full Text Available Increasing global demand for fresh water is driving the development and implementation of a wide variety of seawater desalination technologies. Entropy generation analysis, and specifically, Second Law efficiency, is an important tool for illustrating the influence of irreversibilities within a system on the required energy input. When defining Second Law efficiency, the useful exergy output of the system must be properly defined. For desalination systems, this is the minimum least work of separation required to extract a unit of water from a feed stream of a given salinity. In order to evaluate the Second Law efficiency, entropy generation mechanisms present in a wide range of desalination processes are analyzed. In particular, entropy generated in the run down to equilibrium of discharge streams must be considered. Physical models are applied to estimate the magnitude of entropy generation by component and individual processes. These formulations are applied to calculate the total entropy generation in several desalination systems including multiple effect distillation, multistage flash, membrane distillation, mechanical vapor compression, reverse osmosis, and humidification-dehumidification. Within each technology, the relative importance of each source of entropy generation is discussed in order to determine which should be the target of entropy generation minimization. As given here, the correct application of Second Law efficiency shows which systems operate closest to the reversible limit and helps to indicate which systems have the greatest potential for improvement.
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
The covariant entropy bound in gravitational collapse
International Nuclear Information System (INIS)
Gao, Sijie; Lemos, Jose P. S.
2004-01-01
We study the covariant entropy bound in the context of gravitational collapse. First, we discuss critically the heuristic arguments advanced by Bousso. Then we solve the problem through an exact model: a Tolman-Bondi dust shell collapsing into a Schwarzschild black hole. After the collapse, a new black hole with a larger mass is formed. The horizon, L, of the old black hole then terminates at the singularity. We show that the entropy crossing L does not exceed a quarter of the area of the old horizon. Therefore, the covariant entropy bound is satisfied in this process. (author)
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...
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.
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.
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...
Entropy viscosity method for nonlinear conservation laws
Guermond, Jean-Luc; Pasquetti, Richard; Popov, Bojan
2011-01-01
A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.
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.
Density estimation by maximum quantum entropy
International Nuclear Information System (INIS)
Silver, R.N.; Wallstrom, T.; Martz, H.F.
1993-01-01
A new Bayesian method for non-parametric density estimation is proposed, based on a mathematical analogy to quantum statistical physics. The mathematical procedure is related to maximum entropy methods for inverse problems and image reconstruction. The information divergence enforces global smoothing toward default models, convexity, positivity, extensivity and normalization. The novel feature is the replacement of classical entropy by quantum entropy, so that local smoothing is enforced by constraints on differential operators. The linear response of the estimate is proportional to the covariance. The hyperparameters are estimated by type-II maximum likelihood (evidence). The method is demonstrated on textbook data sets
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.
Minimizing the entropy production in a chemical process for dehydrogenation of propane
International Nuclear Information System (INIS)
Rosjorde, A.; Kjelstrup, S.; Johannessen, E.; Hansen, R.
2007-01-01
We minimize the total entropy production of a process designed for dehydrogenation of propane. The process consists of 21 units, including a plug-flow reactor, a partial condenser, two tray distillation columns and a handful of heat exchangers and compressors. The units were modeled in a manner that made them relatively insensitive to changes in the molar flow rates, to make the optimization more flexible. The operating conditions, as well as to some degree the design of selected units, which minimized the total entropy production of the process, were found. The most important variables were the amount of recycled propane and propylene, conversion and selectivity in the reactor, as well as the number of tubes in the reactor. The optimal conversion, selectivity and recycle flows were results of a very clear trade-off among the entropy produced in the reactor, the partial condenser and the two distillation columns. Although several simplifying assumptions were made for computational reasons, this shows for the first time that it is also meaningful to use the entropy production as an objective function in chemical engineering process optimization studies
Entropies of the automata networks with additive rule
Institute of Scientific and Technical Information of China (English)
Guo－qingGU; GeCHEN; 等
1996-01-01
The matrix presentation for automata networks with additive rule are described.A set of entropy theorems of additive automata network are proved and an analytic formula of its entropy is built.For example,we proved that the topological entropy is identically equal to metric entropy for an additive antomata network.
Directory of Open Access Journals (Sweden)
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.
International Nuclear Information System (INIS)
Banach, Zbigniew; Larecki, Wieslaw
2013-01-01
The spectral formulation of the nine-moment radiation hydrodynamics resulting from using the Boltzmann entropy maximization procedure is considered. The analysis is restricted to the one-dimensional flows of a gas of massless fermions. The objective of the paper is to demonstrate that, for such flows, the spectral nine-moment maximum entropy hydrodynamics of fermionic radiation is not a purely formal theory. We first determine the domains of admissible values of the spectral moments and of the Lagrange multipliers corresponding to them. We then prove the existence of a solution to the constrained entropy optimization problem. Due to the strict concavity of the entropy functional defined on the space of distribution functions, there exists a one-to-one correspondence between the Lagrange multipliers and the moments. The maximum entropy closure of moment equations results in the symmetric conservative system of first-order partial differential equations for the Lagrange multipliers. However, this system can be transformed into the equivalent system of conservation equations for the moments. These two systems are consistent with the additional conservation equation interpreted as the balance of entropy. Exploiting the above facts, we arrive at the differential relations satisfied by the entropy function and the additional function required to close the system of moment equations. We refer to this additional function as the moment closure function. In general, the moment closure and entropy–entropy flux functions cannot be explicitly calculated in terms of the moments determining the state of a gas. Therefore, we develop a perturbation method of calculating these functions. Some additional analytical (and also numerical) results are obtained, assuming that the maximum entropy distribution function tends to the Maxwell–Boltzmann limit. (paper)
On the entropy variation in the scenario of entropic gravity
Xiao, Yong; Bai, Shi-Yang
2018-05-01
In the scenario of entropic gravity, entropy varies as a function of the location of the matter, while the tendency to increase entropy appears as gravity. We concentrate on studying the entropy variation of a typical gravitational system with different relative positions between the mass and the gravitational source. The result is that the entropy of the system doesn't increase when the mass is displaced closer to the gravitational source. In this way it disproves the proposal of entropic gravity from thermodynamic entropy. It doesn't exclude the possibility that gravity originates from non-thermodynamic entropy like entanglement entropy.
Energy Technology Data Exchange (ETDEWEB)
Lewis, Derek
1969-07-01
A method is described for the estimation of equilibrium constants for aqueous systems at temperatures up to 374 deg C from entropy and free energy data for 25 deg C and data on the variation of heat capacity with temperature. Partial molal heat capacities of aqueous ions are estimated on the basis of the principle that, with suitably chosen standard states, the partial molal entropies of ions of a particular class at any given temperature are linearly related to the corresponding entropies at some reference temperature. The method suggested is compared with other methods, based on the Van't Hoff isobar and on an extension of the conventional scale of ionic free energy at 25 deg C, and the general dependence of aqueous equilibria on ionic heat capacity is considered.
Entropy production in a cell and reversal of entropy flow as an anticancer therapy
Institute of Scientific and Technical Information of China (English)
Liao-fu LUO
2009-01-01
The entropy production rate of cancer cells is always higher than healthy cells in the case where no external field is applied. Different entropy production between two kinds of cells determines the direction of entropy flow among cells. The entropy flow is the carrier of information flow. The entropy flow from cancerous cells to healthy cells takes along the harmful information of cancerous cells, propagating its toxic action to healthy tissues. We demonstrate that a low-frequency and low- intensity electromagnetic field or ultrasound irradiation may increase the entropy production rate of a cell in normal tissue than that in cancer and consequently re- verse the direction of entropy current between two kinds of cells. The modification of the PH value of cells may also cause the reversal of the direction of entropy flow between healthy and cancerous cells. Therefore, the bio- logical tissue under the irradiation of an electromagnetic field or ultrasound or under the appropriate change of cell acidity can avoid the propagation of harmful infor- marion from cancer cells. We suggest that this entropy mechanism possibly provides a basis for a novel approach to anticancer therapy.
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.
Entropy of Vaidya-deSitter Spacetime
Institute of Scientific and Technical Information of China (English)
LI Xiang; ZHAO Zheng
2001-01-01
As a statistical model of black hole entropy, the brick-wall method based on the thermal equilibrium in a large scale cannot be applied to the cases out of equilibrium, such as the non-static hole or the case with two horizons.However, the leading term of hole entropy called the Bekenstein-Hawking entropy comes from the contribution of the field near the horizon. According to this idea, the entropy of Vaidya-deSitter spacetime is calculated. A difference from the static case is that the result proportional to the area of horizon relies on a time-dependent cut-off. The condition of local equilibrium near the horizon is used as a working postulate.
Linear entropy in quantum phase space
International Nuclear Information System (INIS)
Rosales-Zarate, Laura E. C.; Drummond, P. D.
2011-01-01
We calculate the quantum Renyi entropy in a phase-space representation for either fermions or bosons. This can also be used to calculate purity and fidelity, or the entanglement between two systems. We show that it is possible to calculate the entropy from sampled phase-space distributions in normally ordered representations, although this is not possible for all quantum states. We give an example of the use of this method in an exactly soluble thermal case. The quantum entropy cannot be calculated at all using sampling methods in classical symmetric (Wigner) or antinormally ordered (Husimi) phase spaces, due to inner-product divergences. The preferred method is to use generalized Gaussian phase-space methods, which utilize a distribution over stochastic Green's functions. We illustrate this approach by calculating the reduced entropy and entanglement of bosonic or fermionic modes coupled to a time-evolving, non-Markovian reservoir.
Examples of algebrae with equal dynamic entropy
International Nuclear Information System (INIS)
Narnhofer, H.
1988-01-01
For given dynamical entropy we construct uncountably many examples of corresponding algebras, some of them are quantum K systems, whereas at least one explicit example is not. Consequences for cluster properties are studied. 12 refs. (Author)
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....
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.
Topological entropy for induced hyperspace maps
International Nuclear Information System (INIS)
Canovas Pena, Jose S.; Lopez, Gabriel Soler
2006-01-01
Let (X,d) be a compact metric space and let f:X->X be continuous. Let K(X) be the family of compact subsets of X endowed with the Hausdorff metric and define the extension f-bar :K(X)->K(X) by f-bar (K)=f(K) for any K-bar K(X). We prove that the topological entropy of f-bar is greater or equal than the topological entropy of f, and this inequality can be strict. On the other hand, we prove that the topological entropy of f is positive if and only if the topological entropy of f-bar is also positive
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.
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
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
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.
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)
Non-equilibrium entropy in excited nuclei
International Nuclear Information System (INIS)
Betak, E.
1991-06-01
The time-dependent behaviour of entropy in excited nuclei is investigated. In distinction to recent claims, it is shown that no self-organization is involved in pre-equilibrium nuclear reactions. (author). 9 refs.; 4 figs
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)
Linear entropy in quantum phase space
Energy Technology Data Exchange (ETDEWEB)
Rosales-Zarate, Laura E. C.; Drummond, P. D. [Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne 3122 (Australia)
2011-10-15
We calculate the quantum Renyi entropy in a phase-space representation for either fermions or bosons. This can also be used to calculate purity and fidelity, or the entanglement between two systems. We show that it is possible to calculate the entropy from sampled phase-space distributions in normally ordered representations, although this is not possible for all quantum states. We give an example of the use of this method in an exactly soluble thermal case. The quantum entropy cannot be calculated at all using sampling methods in classical symmetric (Wigner) or antinormally ordered (Husimi) phase spaces, due to inner-product divergences. The preferred method is to use generalized Gaussian phase-space methods, which utilize a distribution over stochastic Green's functions. We illustrate this approach by calculating the reduced entropy and entanglement of bosonic or fermionic modes coupled to a time-evolving, non-Markovian reservoir.
Entropy estimates for simple random fields
DEFF Research Database (Denmark)
Forchhammer, Søren; Justesen, Jørn
1995-01-01
We consider the problem of determining the maximum entropy of a discrete random field on a lattice subject to certain local constraints on symbol configurations. The results are expected to be of interest in the analysis of digitized images and two dimensional codes. We shall present some examples...... of binary and ternary fields with simple constraints. Exact results on the entropies are known only in a few cases, but we shall present close bounds and estimates that are computationally efficient...
Growth rate, population entropy, and perturbation theory.
Demetrius, L.
1989-01-01
This paper is concerned with the connection between two classes of population variables: measures of population growth rate—the Malthusian parameter, the net reproduction rate, the gross reproduction rate, and the mean life expectancy; and measures of demographic heterogeneity—population entropy. It is shown that the entropy functions predict the response of the growth rate parameters to perturbations in the age-specific fecundity and mortality schedule. These results are invoked to introduce...
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.
Quantum Entropy of Black Hole with Internal Global Monopole
Institute of Scientific and Technical Information of China (English)
HAN Yi-Wen; YANG Shu-Zheng; LIU Wen-Biao
2005-01-01
Using the generalized uncertainty relation, the new equation of state density is obtained, and then the entropy of black hole with an internal global monopole is discussed. The divergence that appears in black hole entropy calculation through original brick-wall model is overcome. The result of the direct proportion between black hole entropy and its event horizon area is drawn and given. The result shows that the black hole entropy must be the entropy of quantum state near the event horizon.
1976-01-01
The entropy of a gas system with the number of particles subject to external control is maximized to derive relations between the thermodynamic variables that obtain at equilibrium. These relations are described in terms of the chemical potential, defined as equivalent partial derivatives of entropy, energy, enthalpy, free energy, or free enthalpy. At equilibrium, the change in total chemical potential must vanish. This fact is used to derive the equilibrium constants for chemical reactions in terms of the partition functions of the species involved in the reaction. Thus the equilibrium constants can be determined accurately, just as other thermodynamic properties, from a knowledge of the energy levels and degeneracies for the gas species involved. These equilibrium constants permit one to calculate the equilibrium concentrations or partial pressures of chemically reacting species that occur in gas mixtures at any given condition of pressure and temperature or volume and temperature.
The relative entropy in the quantum mechanics
International Nuclear Information System (INIS)
Lecomte Montes, A.
1983-06-01
Relative Entropy is a generalization of entropy which substitutes the Liouville measure from classical mechanics or the trace from quantum mechanics by an arbitrary state. There are many different defintions of it in quantum mechanics because the algebra of observables is not commutative. In this work, three known defintions of the quantum relative entropy are studied and compared but specifically their common properties are presented. The best known defintion was proposed many years ago by Umegaki and later on by Lindblad. This defintion can be realized through a functional calculus for quadratic forms introduced by Pusz and Woronowicz, for two arbitrary states on a Csup(*)-algebra. The two other definitions investigated are the Naudt's entropy and the inference function of Marchand and Wyss. The first one can be expressed through the functional calculus too, it has then almost the same properties as the Umegaki-Lindblad defintion. The inference function can be considered only as some kind of 1/2-relative entropy. The function is nevertheless very important because it can be expressed as the logarithm of the transition probability between the basis state and the actual state. A general theory which includes the three defintions is not found yet, but it is shown that the functional calculus provides a great family of relative entropies. This is important for a unified theory of all defintions and their properties. (Author)
A review of entropy generation in microchannels
Directory of Open Access Journals (Sweden)
Mohamed M Awad
2015-12-01
Full Text Available In this study, a critical review of thermodynamic optimum of microchannels based on entropy generation analysis is presented. Using entropy generation analysis as evaluation parameter of microchannels has been reported by many studies in the literature. In these studies, different working fluids such as nanofluids, air, water, engine oil, aniline, ethylene glycol, and non-Newtonian fluids have been used. For the case of nanofluids, “nanoparticles” has been used in various kinds such as Al2O3 and Cu, and “base fluid” has been used in various kinds such as water and ethylene glycol. Furthermore, studies on thermodynamic optimum of microchannels based on entropy generation analysis are summarized in a table. At the end, recommendations of future work for thermodynamic optimum of microchannels based on entropy generation analysis are given. As a result, this article can not only be used as the starting point for the researcher interested in entropy generation in microchannels, but it also includes recommendations for future studies on entropy generation in microchannels.
Trajectories entropy in dynamical graphs with memory
Directory of Open Access Journals (Sweden)
Francesco eCaravelli
2016-04-01
Full Text Available In this paper we investigate the application of non-local graph entropy to evolving and dynamical graphs. The measure is based upon the notion of Markov diffusion on a graph, and relies on the entropy applied to trajectories originating at a specific node. In particular, we study the model of reinforcement-decay graph dynamics, which leads to scale free graphs. We find that the node entropy characterizes the structure of the network in the two parameter phase-space describing the dynamical evolution of the weighted graph. We then apply an adapted version of the entropy measure to purely memristive circuits. We provide evidence that meanwhile in the case of DC voltage the entropy based on the forward probability is enough to characterize the graph properties, in the case of AC voltage generators one needs to consider both forward and backward based transition probabilities. We provide also evidence that the entropy highlights the self-organizing properties of memristive circuits, which re-organizes itself to satisfy the symmetries of the underlying graph.
Entanglement entropy and nonabelian gauge symmetry
International Nuclear Information System (INIS)
Donnelly, William
2014-01-01
Entanglement entropy has proven to be an extremely useful concept in quantum field theory. Gauge theories are of particular interest, but for these systems the entanglement entropy is not clearly defined because the physical Hilbert space does not factor as a tensor product according to regions of space. Here we review a definition of entanglement entropy that applies to abelian and nonabelian lattice gauge theories. This entanglement entropy is obtained by embedding the physical Hilbert space into a product of Hilbert spaces associated to regions with boundary. The latter Hilbert spaces include degrees of freedom on the entangling surface that transform like surface charges under the gauge symmetry. These degrees of freedom are shown to contribute to the entanglement entropy, and the form of this contribution is determined by the gauge symmetry. We test our definition using the example of two-dimensional Yang–Mills theory, and find that it agrees with the thermal entropy in de Sitter space, and with the results of the Euclidean replica trick. We discuss the possible implications of this result for more complicated gauge theories, including quantum gravity. (paper)
Gradient Dynamics and Entropy Production Maximization
Janečka, Adam; Pavelka, Michal
2018-01-01
We compare two methods for modeling dissipative processes, namely gradient dynamics and entropy production maximization. Both methods require similar physical inputs-how energy (or entropy) is stored and how it is dissipated. Gradient dynamics describes irreversible evolution by means of dissipation potential and entropy, it automatically satisfies Onsager reciprocal relations as well as their nonlinear generalization (Maxwell-Onsager relations), and it has statistical interpretation. Entropy production maximization is based on knowledge of free energy (or another thermodynamic potential) and entropy production. It also leads to the linear Onsager reciprocal relations and it has proven successful in thermodynamics of complex materials. Both methods are thermodynamically sound as they ensure approach to equilibrium, and we compare them and discuss their advantages and shortcomings. In particular, conditions under which the two approaches coincide and are capable of providing the same constitutive relations are identified. Besides, a commonly used but not often mentioned step in the entropy production maximization is pinpointed and the condition of incompressibility is incorporated into gradient dynamics.
On variational definition of quantum entropy
International Nuclear Information System (INIS)
Belavkin, Roman V.
2015-01-01
Entropy of distribution P can be defined in at least three different ways: 1) as the expectation of the Kullback-Leibler (KL) divergence of P from elementary δ-measures (in this case, it is interpreted as expected surprise); 2) as a negative KL-divergence of some reference measure ν from the probability measure P; 3) as the supremum of Shannon’s mutual information taken over all channels such that P is the output probability, in which case it is dual of some transportation problem. In classical (i.e. commutative) probability, all three definitions lead to the same quantity, providing only different interpretations of entropy. In non-commutative (i.e. quantum) probability, however, these definitions are not equivalent. In particular, the third definition, where the supremum is taken over all entanglements of two quantum systems with P being the output state, leads to the quantity that can be twice the von Neumann entropy. It was proposed originally by V. Belavkin and Ohya [1] and called the proper quantum entropy, because it allows one to define quantum conditional entropy that is always non-negative. Here we extend these ideas to define also quantum counterpart of proper cross-entropy and cross-information. We also show inequality for the values of classical and quantum information
Prediction of Protein Configurational Entropy (Popcoen).
Goethe, Martin; Gleixner, Jan; Fita, Ignacio; Rubi, J Miguel
2018-03-13
A knowledge-based method for configurational entropy prediction of proteins is presented; this methodology is extremely fast, compared to previous approaches, because it does not involve any type of configurational sampling. Instead, the configurational entropy of a query fold is estimated by evaluating an artificial neural network, which was trained on molecular-dynamics simulations of ∼1000 proteins. The predicted entropy can be incorporated into a large class of protein software based on cost-function minimization/evaluation, in which configurational entropy is currently neglected for performance reasons. Software of this type is used for all major protein tasks such as structure predictions, proteins design, NMR and X-ray refinement, docking, and mutation effect predictions. Integrating the predicted entropy can yield a significant accuracy increase as we show exemplarily for native-state identification with the prominent protein software FoldX. The method has been termed Popcoen for Prediction of Protein Configurational Entropy. An implementation is freely available at http://fmc.ub.edu/popcoen/ .
Entropy as a collective variable
Parrinello, Michele
Sampling complex free energy surfaces that exhibit long lived metastable states separated by kinetic bottlenecks is one of the most pressing issues in the atomistic simulations of matter. Not surprisingly many solutions to this problem have been suggested. Many of them are based on the identification of appropriate collective variables that span the manifold of the slow varying modes of the system. While much effort has been put in devising and even constructing on the fly appropriate collective variables there is still a cogent need of introducing simple, generic, physically transparent, and yet effective collective variables. Motivated by the physical observation that in many case transitions between one metastable state and another result from a trade off between enthalpy and entropy we introduce appropriate collective variables that are able to represent in a simple way these two physical properties. We use these variables in the context of the recently introduced variationally enhanced sampling and apply it them with success to the simulation of crystallization from the liquid and to conformational transitions in protein. Department of Chemistry and Applied Biosciences, ETH Zurich, and Facolta' di Informatica, Istituto di Scienze Computazionali, Universita' della Svizzera Italiana, Via G. Buffi 13, 6900 Lugano, Switzerland.
Entropy in an expanding universe
International Nuclear Information System (INIS)
Frautschi, S.C.
1986-01-01
The present picture of the evolution of the universe, based on the Big Bang, suggests a remarkably different and more interesting situation. In the beginning there is a hot gas, nearly homogeneous and in thermal equilibrium [the 3 0 blackbody radiation, reaching us isotropically from all directions, is a relic of, and evidence for, this early state]. The picture of cosmic evolution, seemingly paradoxical in the light of the law of thermodynamics, motivates the questions the author considers in this paper: How can disequilibrium, order, and in particular the free energy supplies which enable life to maintain its organization, emerge from an apparently chaotic early universe in thermal and chemical equilibrium; will free energy supplies continue to become available and be utilized in the future, or will some sort of heat death eventually settle in? The evolution of free energy and entropy in the universe could not be treated accurately on the basis of physics known in the 19th century. However, various 20th century discoveries and ideas make informed discussion of such issues possible, even though definitive answers are not yet in hand. The author discusses some of the ideas which are quite recent, and are currently undergoing rapid development
Mechanical Entropy and Its Implications
Directory of Open Access Journals (Sweden)
Pharis E. Williams
2001-06-01
Full Text Available Abstract: It is shown that the classical laws of thermodynamics require that mechanical systems must exhibit energy that becomes unavailable to do useful work. In thermodynamics, this type of energy is called entropy. It is further shown that these laws require two metrical manifolds, equations of motion, field equations, and Weyl's quantum principles. Weyl's quantum principle requires quantization of the electrostatic potential of a particle and that this potential be non-singular. The interactions of particles through these non-singular electrostatic potentials are analyzed in the low velocity limit and in the relativistic limit. It is shown that writing the two particle interactions for unlike particles allows an examination in two limiting cases: large and small separations. These limits are shown to have the limiting motions of: all motions are ABOUT the center of mass or all motion is OF the center of mass. The first limit leads to the standard Dirac equation. The second limit is shown to have equations of which the electroweak theory is a subset. An extension of the gauge principle into a five-dimensional manifold, then restricting the generality of the five-dimensional manifold by using the conservation principle, shows that the four-dimensional hypersurface that is embedded within the 5-D manifold is required to obey Einstein's field equations. The 5-D gravitational quantum equations of the solar system are presented.
Maximum entropy and Bayesian methods
International Nuclear Information System (INIS)
Smith, C.R.; Erickson, G.J.; Neudorfer, P.O.
1992-01-01
Bayesian probability theory and Maximum Entropy methods are at the core of a new view of scientific inference. These 'new' ideas, along with the revolution in computational methods afforded by modern computers allow astronomers, electrical engineers, image processors of any type, NMR chemists and physicists, and anyone at all who has to deal with incomplete and noisy data, to take advantage of methods that, in the past, have been applied only in some areas of theoretical physics. The title workshops have been the focus of a group of researchers from many different fields, and this diversity is evident in this book. There are tutorial and theoretical papers, and applications in a very wide variety of fields. Almost any instance of dealing with incomplete and noisy data can be usefully treated by these methods, and many areas of theoretical research are being enhanced by the thoughtful application of Bayes' theorem. Contributions contained in this volume present a state-of-the-art overview that will be influential and useful for many years to come
Morowitz, Harold J.
1996-10-01
Harold Morowitz has long been highly regarded both as an eminent scientist and as an accomplished science writer. The essays in The Wine of Life , his first collection, were hailed by C.P. Snow as "some of the wisest, wittiest and best informed I have ever read," and Carl Sagan called them "a delight to read." In later volumes he established a reputation for a wide-ranging intellect, an ability to see unexpected connections and draw striking parallels, and a talent for communicating scientific ideas with optimism and wit. With Entropy and the Magic Flute , Morowitz once again offers an appealing mix of brief reflections on everything from litmus paper to the hippopotamus to the sociology of Palo Alto coffee shops. Many of these pieces are appreciations of scientists that Morowitz holds in high regard, while others focus on health issues, such as America's obsession with cheese toppings. There is also a fascinating piece on the American Type Culture Collection, a zoo or warehouse for microbes that houses some 11,800 strains of bacteria, and over 3,000 specimens of protozoa, algae, plasmids, and oncogenes. Here then are over forty light, graceful essays in which one of our wisest experimental biologists comments on issues of science, technology, society, philosophy, and the arts.
Another short and elementary proof of strong subadditivity of quantum entropy
Ruskai, Mary Beth
2007-08-01
A short and elementary proof of the joint convexity of relative entropy is presented, using nothing beyond linear algebra. The key ingredients are an easily verified integral representation and the strategy used to prove the Cauchy-Schwarz inequality in elementary courses. Several consequences are proved in a way which allows an elementary proof of strong subadditivity in a few more lines. Some expository material on Schwarz inequalities for operators and the Holevo bound for partial measurements is also included.
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
Maximum entropy principal for transportation
International Nuclear Information System (INIS)
Bilich, F.; Da Silva, R.
2008-01-01
In this work we deal with modeling of the transportation phenomenon for use in the transportation planning process and policy-impact studies. The model developed is based on the dependence concept, i.e., the notion that the probability of a trip starting at origin i is dependent on the probability of a trip ending at destination j given that the factors (such as travel time, cost, etc.) which affect travel between origin i and destination j assume some specific values. The derivation of the solution of the model employs the maximum entropy principle combining a priori multinomial distribution with a trip utility concept. This model is utilized to forecast trip distributions under a variety of policy changes and scenarios. The dependence coefficients are obtained from a regression equation where the functional form is derived based on conditional probability and perception of factors from experimental psychology. The dependence coefficients encode all the information that was previously encoded in the form of constraints. In addition, the dependence coefficients encode information that cannot be expressed in the form of constraints for practical reasons, namely, computational tractability. The equivalence between the standard formulation (i.e., objective function with constraints) and the dependence formulation (i.e., without constraints) is demonstrated. The parameters of the dependence-based trip-distribution model are estimated, and the model is also validated using commercial air travel data in the U.S. In addition, policy impact analyses (such as allowance of supersonic flights inside the U.S. and user surcharge at noise-impacted airports) on air travel are performed.
Entropy of balance - some recent results
Directory of Open Access Journals (Sweden)
Laxåback Gerd
2010-07-01
Full Text Available Abstract Background Entropy when applied to biological signals is expected to reflect the state of the biological system. However the physiological interpretation of the entropy is not always straightforward. When should high entropy be interpreted as a healthy sign, and when as marker of deteriorating health? We address this question for the particular case of human standing balance and the Center of Pressure data. Methods We have measured and analyzed balance data of 136 participants (young, n = 45; elderly, n = 91 comprising in all 1085 trials, and calculated the Sample Entropy (SampEn for medio-lateral (M/L and anterior-posterior (A/P Center of Pressure (COP together with the Hurst self-similariy (ss exponent α using Detrended Fluctuation Analysis (DFA. The COP was measured with a force plate in eight 30 seconds trials with eyes closed, eyes open, foam, self-perturbation and nudge conditions. Results 1 There is a significant difference in SampEn for the A/P-direction between the elderly and the younger groups Old > young. 2 For the elderly we have in general A/P > M/L. 3 For the younger group there was no significant A/P-M/L difference with the exception for the nudge trials where we had the reverse situation, A/P Eyes Open. 5 In case of the Hurst ss-exponent we have for the elderly, M/L > A/P. Conclusions These results seem to be require some modifications of the more or less established attention-constraint interpretation of entropy. This holds that higher entropy correlates with a more automatic and a less constrained mode of balance control, and that a higher entropy reflects, in this sense, a more efficient balancing.
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.
Quantum statistical entropy for Kerr-de Sitter black hole
Institute of Scientific and Technical Information of China (English)
Zhang Li-Chun; Wu Yue-Qin; Zhao Ren
2004-01-01
Improving the membrane model by which the entropy of the black hole is studied, we study the entropy of the black hole in the non-thermal equilibrium state. To give the problem stated here widespread meaning, we discuss the (n+2)-dimensional de Sitter spacetime. Through discussion, we obtain that the black hole's entropy which contains two horizons (a black hole's horizon and a cosmological horizon) in the non-thermal equilibrium state comprises the entropy corresponding to the black hole's horizon and the entropy corresponding to the cosmological horizon. Furthermore, the entropy of the black hole is a natural property of the black hole. The entropy is irrelevant to the radiation field out of the horizon. This deepens the understanding of the relationship between black hole's entropy and horizon's area. A way to study the bosonic and fermionic entropy of the black hole in high non-thermal equilibrium spacetime is given.
Progress in Preparation and Research of High Entropy Alloys
Directory of Open Access Journals (Sweden)
CHEN Yong-xing
2017-11-01
Full Text Available The current high entropy alloys' studies are most in block, powder, coating, film and other areas. There are few studies of high entropy alloys in other areas and they are lack of unified classification. According to the current high entropy alloys' research situation, The paper has focused on the classification on all kinds of high entropy alloys having been researched, introduced the selecting principle of elements, summarized the preparation methods, reviewed the research institutions, research methods and research contents of high entropy alloys, prospected the application prospect of high entropy alloys, put forward a series of scientific problems of high entropy alloys, including less research on mechanism, incomplete performance research, unsystematic thermal stability study, preparation process parameters to be optimized, lightweight high entropy alloys' design, the expansion on the research field, etc, and the solutions have been given. Those have certain guiding significance for the expansion of the application of high entropy alloys subjects in the future research direction.
Variations mechanism in entropy of wave height field and its relation with thermodynamic entropy
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This paper gives a brief description of annual period and seasonal variation in the wave height field entropy in the northeastern Pacific. A calculation of the quantity of the, received by lithosphere systems in the northern hemisphere is introduced. The wave heat field entropy is compared with the difference in the quantity of the sun's radiation heat. Analysis on the transfer method, period and lag of this seasonal variation led to the conclusion that the annual period and seasonal variation in the entropy of the wave height field in the Northwestern Pacific is due to the seasonal variation of the sun's radiation heat. Furthermore, the inconsistency between thermodynamic entropy and information entropy was studied.
Entanglement entropy of ABJM theory and entropy of topological black hole
Nian, Jun; Zhang, Xinyu
2017-07-01
In this paper we discuss the supersymmetric localization of the 4D N = 2 offshell gauged supergravity on the background of the AdS4 neutral topological black hole, which is the gravity dual of the ABJM theory defined on the boundary {S}^1× H^2 . We compute the large- N expansion of the supergravity partition function. The result gives the black hole entropy with the logarithmic correction, which matches the previous result of the entanglement entropy of the ABJM theory up to some stringy effects. Our result is consistent with the previous on-shell one-loop computation of the logarithmic correction to black hole entropy. It provides an explicit example of the identification of the entanglement entropy of the boundary conformal field theory with the bulk black hole entropy beyond the leading order given by the classical Bekenstein-Hawking formula, which consequently tests the AdS/CFT correspondence at the subleading order.
Properties of Risk Measures of Generalized Entropy in Portfolio Selection
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Rongxi Zhou
2017-12-01
Full Text Available This paper systematically investigates the properties of six kinds of entropy-based risk measures: Information Entropy and Cumulative Residual Entropy in the probability space, Fuzzy Entropy, Credibility Entropy and Sine Entropy in the fuzzy space, and Hybrid Entropy in the hybridized uncertainty of both fuzziness and randomness. We discover that none of the risk measures satisfy all six of the following properties, which various scholars have associated with effective risk measures: Monotonicity, Translation Invariance, Sub-additivity, Positive Homogeneity, Consistency and Convexity. Measures based on Fuzzy Entropy, Credibility Entropy, and Sine Entropy all exhibit the same properties: Sub-additivity, Positive Homogeneity, Consistency, and Convexity. These measures based on Information Entropy and Hybrid Entropy, meanwhile, only exhibit Sub-additivity and Consistency. Cumulative Residual Entropy satisfies just Sub-additivity, Positive Homogeneity, and Convexity. After identifying these properties, we develop seven portfolio models based on different risk measures and made empirical comparisons using samples from both the Shenzhen Stock Exchange of China and the New York Stock Exchange of America. The comparisons show that the Mean Fuzzy Entropy Model performs the best among the seven models with respect to both daily returns and relative cumulative returns. Overall, these results could provide an important reference for both constructing effective risk measures and rationally selecting the appropriate risk measure under different portfolio selection conditions.
Maximum entropy production rate in quantum thermodynamics
Energy Technology Data Exchange (ETDEWEB)
Beretta, Gian Paolo, E-mail: beretta@ing.unibs.i [Universita di Brescia, via Branze 38, 25123 Brescia (Italy)
2010-06-01
In the framework of the recent quest for well-behaved nonlinear extensions of the traditional Schroedinger-von Neumann unitary dynamics that could provide fundamental explanations of recent experimental evidence of loss of quantum coherence at the microscopic level, a recent paper [Gheorghiu-Svirschevski 2001 Phys. Rev. A 63 054102] reproposes the nonlinear equation of motion proposed by the present author [see Beretta G P 1987 Found. Phys. 17 365 and references therein] for quantum (thermo)dynamics of a single isolated indivisible constituent system, such as a single particle, qubit, qudit, spin or atomic system, or a Bose-Einstein or Fermi-Dirac field. As already proved, such nonlinear dynamics entails a fundamental unifying microscopic proof and extension of Onsager's reciprocity and Callen's fluctuation-dissipation relations to all nonequilibrium states, close and far from thermodynamic equilibrium. In this paper we propose a brief but self-contained review of the main results already proved, including the explicit geometrical construction of the equation of motion from the steepest-entropy-ascent ansatz and its exact mathematical and conceptual equivalence with the maximal-entropy-generation variational-principle formulation presented in Gheorghiu-Svirschevski S 2001 Phys. Rev. A 63 022105. Moreover, we show how it can be extended to the case of a composite system to obtain the general form of the equation of motion, consistent with the demanding requirements of strong separability and of compatibility with general thermodynamics principles. The irreversible term in the equation of motion describes the spontaneous attraction of the state operator in the direction of steepest entropy ascent, thus implementing the maximum entropy production principle in quantum theory. The time rate at which the path of steepest entropy ascent is followed has so far been left unspecified. As a step towards the identification of such rate, here we propose a possible
Objective Bayesianism and the Maximum Entropy Principle
Directory of Open Access Journals (Sweden)
Jon Williamson
2013-09-01
Full Text Available Objective Bayesian epistemology invokes three norms: the strengths of our beliefs should be probabilities; they should be calibrated to our evidence of physical probabilities; and they should otherwise equivocate sufficiently between the basic propositions that we can express. The three norms are sometimes explicated by appealing to the maximum entropy principle, which says that a belief function should be a probability function, from all those that are calibrated to evidence, that has maximum entropy. However, the three norms of objective Bayesianism are usually justified in different ways. In this paper, we show that the three norms can all be subsumed under a single justification in terms of minimising worst-case expected loss. This, in turn, is equivalent to maximising a generalised notion of entropy. We suggest that requiring language invariance, in addition to minimising worst-case expected loss, motivates maximisation of standard entropy as opposed to maximisation of other instances of generalised entropy. Our argument also provides a qualified justification for updating degrees of belief by Bayesian conditionalisation. However, conditional probabilities play a less central part in the objective Bayesian account than they do under the subjective view of Bayesianism, leading to a reduced role for Bayes’ Theorem.
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.
An entropy-assisted musculoskeletal shoulder model.
Xu, Xu; Lin, Jia-Hua; McGorry, Raymond W
2017-04-01
Optimization combined with a musculoskeletal shoulder model has been used to estimate mechanical loading of musculoskeletal elements around the shoulder. Traditionally, the objective function is to minimize the summation of the total activities of the muscles with forces, moments, and stability constraints. Such an objective function, however, tends to neglect the antagonist muscle co-contraction. In this study, an objective function including an entropy term is proposed to address muscle co-contractions. A musculoskeletal shoulder model is developed to apply the proposed objective function. To find the optimal weight for the entropy term, an experiment was conducted. In the experiment, participants generated various 3-D shoulder moments in six shoulder postures. The surface EMG of 8 shoulder muscles was measured and compared with the predicted muscle activities based on the proposed objective function using Bhattacharyya distance and concordance ratio under different weight of the entropy term. The results show that a small weight of the entropy term can improve the predictability of the model in terms of muscle activities. Such a result suggests that the concept of entropy could be helpful for further understanding the mechanism of muscle co-contractions as well as developing a shoulder biomechanical model with greater validity. Copyright © 2017 Elsevier Ltd. All rights reserved.
Enzyme catalysis by entropy without Circe effect.
Kazemi, Masoud; Himo, Fahmi; Åqvist, Johan
2016-03-01
Entropic effects have often been invoked to explain the extraordinary catalytic power of enzymes. In particular, the hypothesis that enzymes can use part of the substrate-binding free energy to reduce the entropic penalty associated with the subsequent chemical transformation has been very influential. The enzymatic reaction of cytidine deaminase appears to be a distinct example. Here, substrate binding is associated with a significant entropy loss that closely matches the activation entropy penalty for the uncatalyzed reaction in water, whereas the activation entropy for the rate-limiting catalytic step in the enzyme is close to zero. Herein, we report extensive computer simulations of the cytidine deaminase reaction and its temperature dependence. The energetics of the catalytic reaction is first evaluated by density functional theory calculations. These results are then used to parametrize an empirical valence bond description of the reaction, which allows efficient sampling by molecular dynamics simulations and computation of Arrhenius plots. The thermodynamic activation parameters calculated by this approach are in excellent agreement with experimental data and indeed show an activation entropy close to zero for the rate-limiting transition state. However, the origin of this effect is a change of reaction mechanism compared the uncatalyzed reaction. The enzyme operates by hydroxide ion attack, which is intrinsically associated with a favorable activation entropy. Hence, this has little to do with utilization of binding free energy to pay the entropic penalty but rather reflects how a preorganized active site can stabilize a reaction path that is not operational in solution.
Differential effects of gender on entropy perception
Satcharoen, Kleddao
2017-12-01
The purpose of this research is to examine differences in perception of entropy (color intensity) between male and female computer users. The objectives include identifying gender-based differences in entropy intention and exploring the potential effects of these differences (if any) on user interface design. The research is an effort to contribute to an emerging field of interest in gender as it relates to science, engineering and technology (SET), particularly user interface design. Currently, there is limited evidence on the role of gender in user interface design and in use of technology generally, with most efforts at gender-differentiated or customized design based on stereotypes and assumptions about female use of technology or the assumption of a default position based on male preferences. Image entropy was selected as a potential characteristic where gender could be a factor in perception because of known differences in color perception acuity between male and female individuals, even where there is no known color perception abnormality (which is more common with males). Although the literature review suggested that training could offset differences in color perception and identification, tests in untrained subject groups routinely show that females are more able to identify, match, and differentiate colors, and that there is a stronger emotional and psychosocial association of color for females. Since image entropy is associated with information content and image salience, the ability to identify areas of high entropy could make a difference in user perception and technological capabilities.
Entropy and black-hole thermodynamics
International Nuclear Information System (INIS)
Wald, R.M.
1979-01-01
The concept of entropy is examined with an eye toward gaining insight into the nature of black-hole thermodynamics. Definitions of entropy are given for ordinary classical and quantum-mechanical systems which lead to plausibility arguments for the ordinary laws of thermodynamics. The treatment of entropy for a classical system is in the spirit of the information-theory viewpoint, but by explicitly incorporating the coarse-grained observable into the definition of entropy, we eliminate any nonobjective features. The definition of entropy for a quantum-mechanical system is new, but directly parallels the classical treatment. We then apply these ideas to a self-gravitating quantum system which contains a black hole. Under some assumptions: which, although nontrivial, are by no means exotic: about the nature of such a system, it is seen that the same plausibility arguments which lead to the ordinary laws of thermodynamics for ordinary systems now lead to the laws of black-hole mechanics, including the generalized second law of thermodynamics. Thus, it appears perfectly plausible that black-hole thermodynamics is nothing more than ordinary thermodynamics applied to a self-gravitating quantum system
Entropy Measurement for Biometric Verification Systems.
Lim, Meng-Hui; Yuen, Pong C
2016-05-01
Biometric verification systems are designed to accept multiple similar biometric measurements per user due to inherent intrauser variations in the biometric data. This is important to preserve reasonable acceptance rate of genuine queries and the overall feasibility of the recognition system. However, such acceptance of multiple similar measurements decreases the imposter's difficulty of obtaining a system-acceptable measurement, thus resulting in a degraded security level. This deteriorated security needs to be measurable to provide truthful security assurance to the users. Entropy is a standard measure of security. However, the entropy formula is applicable only when there is a single acceptable possibility. In this paper, we develop an entropy-measuring model for biometric systems that accepts multiple similar measurements per user. Based on the idea of guessing entropy, the proposed model quantifies biometric system security in terms of adversarial guessing effort for two practical attacks. Excellent agreement between analytic and experimental simulation-based measurement results on a synthetic and a benchmark face dataset justify the correctness of our model and thus the feasibility of the proposed entropy-measuring approach.
Entropy and Entanglement of the Electromagnetically Induced Transparency System
Institute of Scientific and Technical Information of China (English)
LIU Xiao-Juan; FANG Mao-Fa; ZHOU Qing-Ping
2004-01-01
@@ We study the entropy and the entanglement of an electromagnetically induced transparency system. The quantum entanglement between the atom and the two quantized laser fields is discussed by using quantum reduced entropy and that between the two quantized laser fields by using quantum relative entropy. We also examine whether influences of EIT on entropy and quantum entanglement of the system considered occur or not. Our results show that the minimum value of the atomic reduced entropy may be regarded as an entropy criterion on the electromagnetically induced transparency occurring.
Holographic entropy inequalities and gapped phases of matter
Energy Technology Data Exchange (ETDEWEB)
Bao, Ning [Institute for Quantum Information and Matter, California Institute of Technology,Pasadena, CA 91125 (United States); Walter Burke Institute for Theoretical Physics, California Institute of Technology,Pasadena, CA 91125 (United States); Cao, ChunJun [Walter Burke Institute for Theoretical Physics, California Institute of Technology,Pasadena, CA 91125 (United States); Walter, Michael [Stanford Institute for Theoretical Physics,Stanford University, Stanford, CA 94305 (United States); Wang, Zitao [Institute for Quantum Information and Matter, California Institute of Technology,Pasadena, CA 91125 (United States); Walter Burke Institute for Theoretical Physics, California Institute of Technology,Pasadena, CA 91125 (United States)
2015-09-29
We extend our studies of holographic entropy inequalities to gapped phases of matter. For any number of regions, we determine the linear entropy inequalities satisfied by systems in which the entanglement entropy satisfies an exact area law. In particular, we find that all holographic entropy inequalities are valid in such systems. In gapped systems with topological order, the “cyclic inequalities” derived recently for the holographic entanglement entropy generalize the Kitaev-Preskill formula for the topological entanglement entropy. Finally, we propose a candidate linear inequality for general 4-party quantum states.
Entropy of the system formed in heavy ion collision
International Nuclear Information System (INIS)
Gudima, K.K.; Schulz, H.; Toneev, V.D.
1985-01-01
In frames of a cascade model the entropy evolution in a system producted in heavy ion collisions is investigated. Entropy calculation is based on smoothing of the distribution function over the momentum space by the temperature field introduction. The resulting entropy per one nucleon is shown to be rather sensitive to phase space subdivision into cells at the stage of free scattering of reaction products. Compared to recent experimental results for specific entropy values inferred from the composite particle yield of 4π measurements, it is found that cascade calculations do not favour some particular entropy model treatments and suggest smaller entropy values than following from consideration within equilibrium statistics
Holographic entropy inequalities and gapped phases of matter
International Nuclear Information System (INIS)
Bao, Ning; Cao, ChunJun; Walter, Michael; Wang, Zitao
2015-01-01
We extend our studies of holographic entropy inequalities to gapped phases of matter. For any number of regions, we determine the linear entropy inequalities satisfied by systems in which the entanglement entropy satisfies an exact area law. In particular, we find that all holographic entropy inequalities are valid in such systems. In gapped systems with topological order, the “cyclic inequalities” derived recently for the holographic entanglement entropy generalize the Kitaev-Preskill formula for the topological entanglement entropy. Finally, we propose a candidate linear inequality for general 4-party quantum states.
Information-theoretical aspects of quantum-mechanical entropy
International Nuclear Information System (INIS)
Wehrl, A.
1990-01-01
Properties of the quantum ( = von Neumann) entropy S(ρ) -k Trρ lnρ, ρ being a compact operator, are proved first, and differences against the classical case, e.g. the Shannon entropy, are worked out. The main result is on the strong subadditivity of this quantum entropy. Then another entropy, a function not of the state but of the dynamics of the system, is considered as a quantum analogue of the classical Kolmogorov-Sinai-entropy. An attempt in defining such a quantity had only recently sucess in a paper of Connes, Narnhofer and Thirring. A definition of this entropy is given. 34 refs
Holographic entanglement entropy of surface defects
Energy Technology Data Exchange (ETDEWEB)
Gentle, Simon A.; Gutperle, Michael; Marasinou, Chrysostomos [Department of Physics and Astronomy, University of California,Los Angeles, CA 90095 (United States)
2016-04-12
We calculate the holographic entanglement entropy in type IIB supergravity solutions that are dual to half-BPS disorder-type surface defects in N=4 supersymmetric Yang-Mills theory. The entanglement entropy is calculated for a ball-shaped region bisected by a surface defect. Using the bubbling supergravity solutions we also compute the expectation value of the defect operator. Combining our result with the previously-calculated one-point function of the stress tensor in the presence of the defect, we adapt the calculation of Lewkowycz and Maldacena http://dx.doi.org/10.1007/JHEP05(2014)025 to obtain a second expression for the entanglement entropy. Our two expressions agree up to an additional term, whose possible origin and significance is discussed.
Probing renormalization group flows using entanglement entropy
International Nuclear Information System (INIS)
Liu, Hong; Mezei, Márk
2014-01-01
In this paper we continue the study of renormalized entanglement entropy introduced in http://dx.doi.org/10.1007/JHEP04(2013)162. In particular, we investigate its behavior near an IR fixed point using holographic duality. We develop techniques which, for any static holographic geometry, enable us to extract the large radius expansion of the entanglement entropy for a spherical region. We show that for both a sphere and a strip, the approach of the renormalized entanglement entropy to the IR fixed point value contains a contribution that depends on the whole RG trajectory. Such a contribution is dominant, when the leading irrelevant operator is sufficiently irrelevant. For a spherical region such terms can be anticipated from a geometric expansion, while for a strip whether these terms have geometric origins remains to be seen
Holographic entanglement entropy of surface defects
International Nuclear Information System (INIS)
Gentle, Simon A.; Gutperle, Michael; Marasinou, Chrysostomos
2016-01-01
We calculate the holographic entanglement entropy in type IIB supergravity solutions that are dual to half-BPS disorder-type surface defects in N=4 supersymmetric Yang-Mills theory. The entanglement entropy is calculated for a ball-shaped region bisected by a surface defect. Using the bubbling supergravity solutions we also compute the expectation value of the defect operator. Combining our result with the previously-calculated one-point function of the stress tensor in the presence of the defect, we adapt the calculation of Lewkowycz and Maldacena http://dx.doi.org/10.1007/JHEP05(2014)025 to obtain a second expression for the entanglement entropy. Our two expressions agree up to an additional term, whose possible origin and significance is discussed.
Zipf's law, power laws and maximum entropy
International Nuclear Information System (INIS)
Visser, Matt
2013-01-01
Zipf's law, and power laws in general, have attracted and continue to attract considerable attention in a wide variety of disciplines—from astronomy to demographics to software structure to economics to linguistics to zoology, and even warfare. A recent model of random group formation (RGF) attempts a general explanation of such phenomena based on Jaynes' notion of maximum entropy applied to a particular choice of cost function. In the present paper I argue that the specific cost function used in the RGF model is in fact unnecessarily complicated, and that power laws can be obtained in a much simpler way by applying maximum entropy ideas directly to the Shannon entropy subject only to a single constraint: that the average of the logarithm of the observable quantity is specified. (paper)
Spatial-dependence recurrence sample entropy
Pham, Tuan D.; Yan, Hong
2018-03-01
Measuring complexity in terms of the predictability of time series is a major area of research in science and engineering, and its applications are spreading throughout many scientific disciplines, where the analysis of physiological signals is perhaps the most widely reported in literature. Sample entropy is a popular measure for quantifying signal irregularity. However, the sample entropy does not take sequential information, which is inherently useful, into its calculation of sample similarity. Here, we develop a method that is based on the mathematical principle of the sample entropy and enables the capture of sequential information of a time series in the context of spatial dependence provided by the binary-level co-occurrence matrix of a recurrence plot. Experimental results on time-series data of the Lorenz system, physiological signals of gait maturation in healthy children, and gait dynamics in Huntington's disease show the potential of the proposed method.
Horizon Entropy from Quantum Gravity Condensates.
Oriti, Daniele; Pranzetti, Daniele; Sindoni, Lorenzo
2016-05-27
We construct condensate states encoding the continuum spherically symmetric quantum geometry of a horizon in full quantum gravity, i.e., without any classical symmetry reduction, in the group field theory formalism. Tracing over the bulk degrees of freedom, we show how the resulting reduced density matrix manifestly exhibits a holographic behavior. We derive a complete orthonormal basis of eigenstates for the reduced density matrix of the horizon and use it to compute the horizon entanglement entropy. By imposing consistency with the horizon boundary conditions and semiclassical thermodynamical properties, we recover the Bekenstein-Hawking entropy formula for any value of the Immirzi parameter. Our analysis supports the equivalence between the von Neumann (entanglement) entropy interpretation and the Boltzmann (statistical) one.
Microcanonical entropy of a black hole
International Nuclear Information System (INIS)
Bhaduri, Rajat K.; Tran, Muoi N.; Das, Saurya
2004-01-01
It has been suggested recently that the microcanonical entropy of a system may be accurately reproduced by including a logarithmic correction to the canonical entropy. In this paper we test this claim both analytically and numerically by considering three simple thermodynamic models whose energy spectrum may be defined in terms of one quantum number only, as in a non-rotating black hole. The first two pertain to collections of noninteracting bosons, with logarithmic and power-law spectra. The last is an area ensemble for a black hole with equi-spaced area spectrum. In this case, the many-body degeneracy factor can be obtained analytically in a closed form. We also show that in this model, the leading term in the entropy is proportional to the horizon area A, and the next term is ln A with a negative coefficient
Revisiting entanglement entropy of lattice gauge theories
Energy Technology Data Exchange (ETDEWEB)
Hung, Ling-Yan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Lu, Shanghai 200433 (China); Collaborative Innovation Center of Advanced Microstructures, Fudan University,220 Handan Lu, Shanghai 200433 (China); Wan, Yidun [Perimeter Institute for Theoretical Physics,31 Caroline Street, Waterloo, ON N2L 2Y5 (Canada)
2015-04-22
It is realized recently that the entanglement entropy in gauge theories is ambiguous because the Hilbert space cannot be expressed as a simple direct product of Hilbert spaces defined on the two regions; different ways of dividing the Hilbert spaces near the boundary leads to significantly different result, to the extreme that it could annihilate the otherwise finite topological entanglement entropy between two regions altogether. In this article, we first show that the topological entanglement entropy in the Kitaev model http://dx.doi.org/10.1016/S0003-4916(02)00018-0 which is not a true gauge theory, is free of ambiguity. Then, we give a physical interpretation, from the perspectives of what can be measured in an experiment, to the purported ambiguity of true gauge theories, where the topological entanglement arises as redundancy in counting the degrees of freedom along the boundary separating two regions. We generalize these discussions to non-Abelian gauge theories.
Braneworld black holes and entropy bounds
Directory of Open Access Journals (Sweden)
Y. Heydarzade
2018-01-01
Full Text Available The Bousso's D-bound entropy for the various possible black hole solutions on a 4-dimensional brane is checked. It is found that the D-bound entropy here is apparently different from that of obtained for the 4-dimensional black hole solutions. This difference is interpreted as the extra loss of information, associated to the extra dimension, when an extra-dimensional black hole is moved outward the observer's cosmological horizon. Also, it is discussed that N-bound entropy is hold for the possible solutions here. Finally, by adopting the recent Bohr-like approach to black hole quantum physics for the excited black holes, the obtained results are written also in terms of the black hole excited states.
Entropy Concept for Paramacrosystems with Complex States
Directory of Open Access Journals (Sweden)
Yuri S. Popkov
2012-05-01
Full Text Available Consideration is given to macrosystems called paramacrosystems with states of finite capacity and distinguishable and undistinguishable elements with stochastic behavior. The paramacrosystems fill a gap between Fermi and Einstein macrosystems. Using the method of the generating functions, we have obtained expressions for probabilistic characteristics (distribution of the macrostate probabilities, physical and information entropies of the paramacrosystems. The cases with equal and unequal prior probabilities for elements to occupy the states with finite capacities are considered. The unequal prior probabilities influence the morphological properties of the entropy functions and the functions of the macrostate probabilities, transforming them in the multimodal functions. The examples of the paramacrosystems with two-modal functions of the entropy and distribution of the macrostate probabilities are presented. The variation principle does not work for such cases.
An entropy model for artificial grammar learning
Directory of Open Access Journals (Sweden)
Emmanuel Pothos
2010-06-01
Full Text Available A model is proposed to characterize the type of knowledge acquired in Artificial Grammar Learning (AGL. In particular, Shannon entropy is employed to compute the complexity of different test items in an AGL task, relative to the training items. According to this model, the more predictable a test item is from the training items, the more likely it is that this item should be selected as compatible with the training items. The predictions of the entropy model are explored in relation to the results from several previous AGL datasets and compared to other AGL measures. This particular approach in AGL resonates well with similar models in categorization and reasoning which also postulate that cognitive processing is geared towards the reduction of entropy.
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.
Autonomous entropy-based intelligent experimental design
Malakar, Nabin Kumar
2011-07-01
The aim of this thesis is to explore the application of probability and information theory in experimental design, and to do so in a way that combines what we know about inference and inquiry in a comprehensive and consistent manner. Present day scientific frontiers involve data collection at an ever-increasing rate. This requires that we find a way to collect the most relevant data in an automated fashion. By following the logic of the scientific method, we couple an inference engine with an inquiry engine to automate the iterative process of scientific learning. The inference engine involves Bayesian machine learning techniques to estimate model parameters based upon both prior information and previously collected data, while the inquiry engine implements data-driven exploration. By choosing an experiment whose distribution of expected results has the maximum entropy, the inquiry engine selects the experiment that maximizes the expected information gain. The coupled inference and inquiry engines constitute an autonomous learning method for scientific exploration. We apply it to a robotic arm to demonstrate the efficacy of the method. Optimizing inquiry involves searching for an experiment that promises, on average, to be maximally informative. If the set of potential experiments is described by many parameters, the search involves a high-dimensional entropy space. In such cases, a brute force search method will be slow and computationally expensive. We develop an entropy-based search algorithm, called nested entropy sampling, to select the most informative experiment. This helps to reduce the number of computations necessary to find the optimal experiment. We also extended the method of maximizing entropy, and developed a method of maximizing joint entropy so that it could be used as a principle of collaboration between two robots. This is a major achievement of this thesis, as it allows the information-based collaboration between two robotic units towards a same
Maximum entropy decomposition of quadrupole mass spectra
International Nuclear Information System (INIS)
Toussaint, U. von; Dose, V.; Golan, A.
2004-01-01
We present an information-theoretic method called generalized maximum entropy (GME) for decomposing mass spectra of gas mixtures from noisy measurements. In this GME approach to the noisy, underdetermined inverse problem, the joint entropies of concentration, cracking, and noise probabilities are maximized subject to the measured data. This provides a robust estimation for the unknown cracking patterns and the concentrations of the contributing molecules. The method is applied to mass spectroscopic data of hydrocarbons, and the estimates are compared with those received from a Bayesian approach. We show that the GME method is efficient and is computationally fast
Direct measurements of the magnetic entropy change
DEFF Research Database (Denmark)
Nielsen, Kaspar Kirstein; Neves Bez, Henrique; von Moos, Lars
2015-01-01
An experimental device that can accurately measure the magnetic entropy change, Δs, as a function of temperature, T, and magnetic field, H, is presented. The magnetic field source is in this case a set of counter-rotating concentric Halbach-type magnets, which produce a highly homogeneous applied...... to the ambient are negligible in terms of the calorimetric determination of the magnetic entropy change, while the losses cannot be ignored when correcting for the actual sample temperature. We apply the device to two different types of samples; one is commercial grade Gd, i.e., a pure second-order phase...
Entropy fluxes, endoreversibility, and solar energy conversion
de Vos, A.; Landsberg, P. T.; Baruch, P.; Parrott, J. E.
1993-09-01
A formalism illustrating the conversion of radiation energy into work can be obtained in terms of energy and entropy fluxes. Whereas the Landsberg equality was derived for photothermal conversion with zero bandgap, a generalized inequality for photothermal/photovoltaic conversion with a single, but arbitrary, bandgap was deduced. This result was derived for a direct energy and entropy balance. The formalism of endoreversible dynamics was adopted in order to show the correlation with the latter approach. It was a surprising fact that the generalized Landsberg inequality was derived by optimizing some quantity W(sup *), which obtains it maximum value under short-circuit condition.
Black hole entropy, universality, and horizon constraints
International Nuclear Information System (INIS)
Carlip, Steven
2006-01-01
To ask a question about a black hole in quantum gravity, one must restrict initial or boundary data to ensure that a black hole is actually present. For two-dimensional dilaton gravity, and probably a much wider class of theories, I show that the imposition of a 'stretched horizon' constraint modifies the algebra of symmetries at the horizon, allowing the use of conformal field theory techniques to determine the asymptotic density of states. The result reproduces the Bekenstein-Hawking entropy without any need for detailed assumptions about the microscopic theory. Horizon symmetries may thus offer an answer to the problem of universality of black hole entropy
Black hole entropy, universality, and horizon constraints
Energy Technology Data Exchange (ETDEWEB)
Carlip, Steven [Department of Physics, University of California, Davis, CA 95616 (United States)
2006-03-01
To ask a question about a black hole in quantum gravity, one must restrict initial or boundary data to ensure that a black hole is actually present. For two-dimensional dilaton gravity, and probably a much wider class of theories, I show that the imposition of a 'stretched horizon' constraint modifies the algebra of symmetries at the horizon, allowing the use of conformal field theory techniques to determine the asymptotic density of states. The result reproduces the Bekenstein-Hawking entropy without any need for detailed assumptions about the microscopic theory. Horizon symmetries may thus offer an answer to the problem of universality of black hole entropy.
Entropy Inequality Violations from Ultraspinning Black Holes.
Hennigar, Robie A; Mann, Robert B; Kubizňák, David
2015-07-17
We construct a new class of rotating anti-de Sitter (AdS) black hole solutions with noncompact event horizons of finite area in any dimension and study their thermodynamics. In four dimensions these black holes are solutions to gauged supergravity. We find that their entropy exceeds the maximum implied from the conjectured reverse isoperimetric inequality, which states that for a given thermodynamic volume, the black hole entropy is maximized for Schwarzschild-AdS space. We use this result to suggest more stringent conditions under which this conjecture may hold.
Maximum entropy PDF projection: A review
Baggenstoss, Paul M.
2017-06-01
We review maximum entropy (MaxEnt) PDF projection, a method with wide potential applications in statistical inference. The method constructs a sampling distribution for a high-dimensional vector x based on knowing the sampling distribution p(z) of a lower-dimensional feature z = T (x). Under mild conditions, the distribution p(x) having highest possible entropy among all distributions consistent with p(z) may be readily found. Furthermore, the MaxEnt p(x) may be sampled, making the approach useful in Monte Carlo methods. We review the theorem and present a case study in model order selection and classification for handwritten character recognition.
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)
Entropy and the Typicality of Universes
Barbour, Julian; Koslowski, Tim; Mercati, Flavio
2015-01-01
The universal validity of the second law of thermodynamics is widely attributed to a finely tuned initial condition of the universe. This creates a problem: why is the universe atypical? We suggest that the problem is an artefact created by inappropriate transfer of the traditional concept of entropy to the whole universe. Use of what we call the relational $N$-body problem as a model indicates the need to employ two distinct entropy-type concepts to describe the universe. One, which we call ...
Entropy and energy quantization: Planck thermodynamic calculation
International Nuclear Information System (INIS)
Mota e Albuquerque, Ivone Freire da.
1988-01-01
This dissertation analyses the origins and development of the concept of entropy and its meaning of the second Law of thermodynamics, as well as the thermodynamics derivation of the energy quantization. The probabilistic interpretation of that law and its implication in physics theory are evidenciated. Based on Clausius work (which follows Carnot's work), we analyse and expose in a original way the entropy concept. Research upon Boltzmann's work and his probabilistic interpretation of the second Law of thermodynamics is made. The discuss between the atomistic and the energeticist points of view, which were actual at that time are also commented. (author). 38 refs., 3 figs
Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains
Cofré, Rodrigo; Maldonado, Cesar
2018-01-01
We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful in this context to describe properties of accuracy and convergence in terms of sampling size. We use these results to study the statistical fluctuation of correlations, distinguishability and irreversibility of maximum entropy Markov chains. We illustrate these applications using simple examples where the large deviation rate function is explicitly obtained for maximum entropy models of relevance in this field.
A Modified Entropy Generation Number for Heat Exchangers
Institute of Scientific and Technical Information of China (English)
无
1996-01-01
This paper demonstrates the difference between the entropy generation number method proposed by Bejian and the method of entropy generation per unit amount of heat transferred in analyzing the ther-modynamic performance of heat exchangers,points out the reason for leading to the above difference.A modified entropy generation number for evaluating the irreversibility of heat exchangers is proposed which is in consistent with the entropy generation per unit amount of heat transferred in entropy generation analysis.The entropy generated by friction is also investigated.Results show that when the entropy generated by friction in heat exchangers in taken into account,there is a minimum total entropy generation number while the NTU and the ratio of heat capacity rates vary.The existence of this minimum is the prerequisite of heat exchanger optimization.
ENTROPIES AND FLUX-SPLITTINGS FOR THE ISENTROPIC EULER EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The authors establish the existence of a large class of mathematical entropies (the so-called weak entropies) associated with the Euler equations for an isentropic, compressible fluid governed by a general pressure law. A mild assumption on the behavior of the pressure law near the vacuum is solely required. The analysis is based on an asymptotic expansion of the fundamental solution (called here the entropy kernel) of a highly singular Euler-Poisson-Darboux equation. The entropy kernel is only H lder continuous and its regularity is carefully investigated. Relying on a notion introduced earlier by the authors, it is also proven that, for the Euler equations, the set of entropy flux-splittings coincides with the set of entropies-entropy fluxes. These results imply the existence of a flux-splitting consistent with all of the entropy inequalities.
Spectral entropy and haemodynamic response to surgery during ...
African Journals Online (AJOL)
Adele
Spectral entropy and haemodynamic response to surgery during sevoflurane anaesthesia. Introduction. Apart from somatic responses, surgery also evokes autonomic responses, including haemodynamic responses. Spectral entropy has been validated as a means to monitor the hypnotic state during sevoflurane ...
Pesin’s entropy formula for stochastic flows of diffeomorphisms
Institute of Scientific and Technical Information of China (English)
刘培东
1996-01-01
Pesin’s entropy formula relating entropy and Lyapunov exponents within the context of random dynamical systems generated by (discrete or continuous) stochastic flows of diffeomorphisms (including solution flows of stochastic differential equations on manifolds) is proved.
Quantum Statistical Entropy of Five-Dimensional Black Hole
Institute of Scientific and Technical Information of China (English)
ZHAO Ren; WU Yue-Qin; ZHANG Sheng-Li
2006-01-01
The generalized uncertainty relation is introduced to calculate quantum statistic entropy of a black hole.By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of the five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is not the divergent logarithmic term as in the original brick-wall method. And it is obtained that the quantum statistic entropy corresponding to black hole horizon is proportional to the area of the horizon. Further it is shown that the entropy of black hole is the entropy of quantum state on the surface of horizon. The black hole's entropy is the intrinsic property of the black hole. The entropy is a quantum effect. It makes people further understand the quantum statistic entropy.
Quantum Statistical Entropy of Five-Dimensional Black Hole
International Nuclear Information System (INIS)
Zhao Ren; Zhang Shengli; Wu Yueqin
2006-01-01
The generalized uncertainty relation is introduced to calculate quantum statistic entropy of a black hole. By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of the five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is not the divergent logarithmic term as in the original brick-wall method. And it is obtained that the quantum statistic entropy corresponding to black hole horizon is proportional to the area of the horizon. Further it is shown that the entropy of black hole is the entropy of quantum state on the surface of horizon. The black hole's entropy is the intrinsic property of the black hole. The entropy is a quantum effect. It makes people further understand the quantum statistic entropy.
The Conditional Entropy Power Inequality for Bosonic Quantum Systems
DEFF Research Database (Denmark)
de Palma, Giacomo; Trevisan, Dario
2018-01-01
We prove the conditional Entropy Power Inequality for Gaussian quantum systems. This fundamental inequality determines the minimum quantum conditional von Neumann entropy of the output of the beam-splitter or of the squeezing among all the input states where the two inputs are conditionally...... independent given the memory and have given quantum conditional entropies. We also prove that, for any couple of values of the quantum conditional entropies of the two inputs, the minimum of the quantum conditional entropy of the output given by the conditional Entropy Power Inequality is asymptotically...... achieved by a suitable sequence of quantum Gaussian input states. Our proof of the conditional Entropy Power Inequality is based on a new Stam inequality for the quantum conditional Fisher information and on the determination of the universal asymptotic behaviour of the quantum conditional entropy under...
The pigeon's discrimination of visual entropy: a logarithmic function.
Young, Michael E; Wasserman, Edward A
2002-11-01
We taught 8 pigeons to discriminate 16-icon arrays that differed in their visual variability or "entropy" to see whether the relationship between entropy and discriminative behavior is linear (in which equivalent differences in entropy should produce equivalent changes in behavior) or logarithmic (in which higher entropy values should be less discriminable from one another than lower entropy values). Pigeons received a go/no-go task in which the lower entropy arrays were reinforced for one group and the higher entropy arrays were reinforced for a second group. The superior discrimination of the second group was predicted by a theoretical analysis in which excitatory and inhibitory stimulus generalization gradients fall along a logarithmic, but not a linear scale. Reanalysis of previously published data also yielded results consistent with a logarithmic relationship between entropy and discriminative behavior.
Parametric optimization of CNC end milling using entropy ...
African Journals Online (AJOL)
Parametric optimization of CNC end milling using entropy measurement technique combined with grey-Taguchi method. ... International Journal of Engineering, Science and Technology ... Keywords: CNC end milling, surface finish, material removal rate (MRR), entropy measurement technique, Taguchi method ...
Entropy of the Kerr–Sen black hole
Indian Academy of Sciences (India)
We study the entropy of Kerr–Sen black hole of heterotic string theory beyond semiclas- ... differentials of black hole entropy, from the first law of thermodynamics with three param- eters. ..... Finally, note that the third term in the expansion.
Entropy-based implied volatility and its information content
X. Xiao (Xiao); C. Zhou (Chen)
2016-01-01
markdownabstractThis paper investigates the maximum entropy approach on estimating implied volatility. The entropy approach also allows to measure option implied skewness and kurtosis nonparametrically, and to construct confidence intervals. Simulations show that the en- tropy approach outperforms
Directory of Open Access Journals (Sweden)
Christian Corda
2018-01-01
Full Text Available In this paper we consider the metric entropies of the maps of an iterated function system deduced from a black hole which are known the Bekenstein–Hawking entropies and its subleading corrections. More precisely, we consider the recent model of a Bohr-like black hole that has been recently analysed in some papers in the literature, obtaining the intriguing result that the metric entropies of a black hole are created by the metric entropies of the functions, created by the black hole principal quantum numbers, i.e., by the black hole quantum levels. We present a new type of topological entropy for general iterated function systems based on a new kind of the inverse of covers. Then the notion of metric entropy for an Iterated Function System ( I F S is considered, and we prove that these definitions for topological entropy of IFS’s are equivalent. It is shown that this kind of topological entropy keeps some properties which are hold by the classic definition of topological entropy for a continuous map. We also consider average entropy as another type of topological entropy for an I F S which is based on the topological entropies of its elements and it is also an invariant object under topological conjugacy. The relation between Axiom A and the average entropy is investigated.
Entropy of charged dilaton-axion black hole
International Nuclear Information System (INIS)
Ghosh, Tanwi; SenGupta, Soumitra
2008-01-01
Using the brick wall method, the entropy of the charged dilaton-axion black hole is determined for both asymptotically flat and nonflat cases. The entropy turns out to be proportional to the horizon area of the black hole confirming the Bekenstein-Hawking area-entropy formula for black holes. The leading order logarithmic corrections to the entropy are also derived for such black holes.
Nonadditive entropy maximization is inconsistent with Bayesian updating
Pressé, Steve
2014-11-01
The maximum entropy method—used to infer probabilistic models from data—is a special case of Bayes's model inference prescription which, in turn, is grounded in basic propositional logic. By contrast to the maximum entropy method, the compatibility of nonadditive entropy maximization with Bayes's model inference prescription has never been established. Here we demonstrate that nonadditive entropy maximization is incompatible with Bayesian updating and discuss the immediate implications of this finding. We focus our attention on special cases as illustrations.
Towards Operational Definition of Postictal Stage: Spectral Entropy as a Marker of Seizure Ending
Directory of Open Access Journals (Sweden)
Ancor Sanz-García
2017-02-01
Full Text Available The postictal period is characterized by several neurological alterations, but its exact limits are clinically or even electroencephalographically hard to determine in most cases. We aim to provide quantitative functions or conditions with a clearly distinguishable behavior during the ictal-postictal transition. Spectral methods were used to analyze foramen ovale electrodes (FOE recordings during the ictal/postictal transition in 31 seizures of 15 patients with strictly unilateral drug resistant temporal lobe epilepsy. In particular, density of links, spectral entropy, and relative spectral power were analyzed. Partial simple seizures are accompanied by an ipsilateral increase in the relative Delta power and a decrease in synchronization in a 66% and 91% of the cases, respectively, after seizures offset. Complex partial seizures showed a decrease in the spectral entropy in 94% of cases, both ipsilateral and contralateral sides (100% and 73%, respectively mainly due to an increase of relative Delta activity. Seizure offset is defined as the moment at which the “seizure termination mechanisms” actually end, which is quantified in the spectral entropy value. We propose as a definition for the postictal start the time when the ipsilateral SE reaches the first global minimum.
Dynamical entropy of C* algebras and Von Neumann algebras
International Nuclear Information System (INIS)
Connes, A.; Narnhofer, H.; Thirring, W.
1986-01-01
The definition of the dynamical entropy is extended for automorphism groups of C * algebras. As example the dynamical entropy of the shift of a lattice algebra is studied and it is shown that in some cases it coincides with the entropy density. (Author)
MAXIMUM-LIKELIHOOD-ESTIMATION OF THE ENTROPY OF AN ATTRACTOR
SCHOUTEN, JC; TAKENS, F; VANDENBLEEK, CM
In this paper, a maximum-likelihood estimate of the (Kolmogorov) entropy of an attractor is proposed that can be obtained directly from a time series. Also, the relative standard deviation of the entropy estimate is derived; it is dependent on the entropy and on the number of samples used in the
Topological entropy of continuous functions on topological spaces
International Nuclear Information System (INIS)
Liu Lei; Wang Yangeng; Wei Guo
2009-01-01
Adler, Konheim and McAndrew introduced the concept of topological entropy of a continuous mapping for compact dynamical systems. Bowen generalized the concept to non-compact metric spaces, but Walters indicated that Bowen's entropy is metric-dependent. We propose a new definition of topological entropy for continuous mappings on arbitrary topological spaces (compactness, metrizability, even axioms of separation not necessarily required), investigate fundamental properties of the new entropy, and compare the new entropy with the existing ones. The defined entropy generates that of Adler, Konheim and McAndrew and is metric-independent for metrizable spaces. Yet, it holds various basic properties of Adler, Konheim and McAndrew's entropy, e.g., the entropy of a subsystem is bounded by that of the original system, topologically conjugated systems have a same entropy, the entropy of the induced hyperspace system is larger than or equal to that of the original system, and in particular this new entropy coincides with Adler, Konheim and McAndrew's entropy for compact systems
Entropy generation of nanofluid flow in a microchannel heat sink
Manay, Eyuphan; Akyürek, Eda Feyza; Sahin, Bayram
2018-06-01
Present study aims to investigate the effects of the presence of nano sized TiO2 particles in the base fluid on entropy generation rate in a microchannel heat sink. Pure water was chosen as base fluid, and TiO2 particles were suspended into the pure water in five different particle volume fractions of 0.25%, 0.5%, 1.0%, 1.5% and 2.0%. Under laminar, steady state flow and constant heat flux boundary conditions, thermal, frictional, total entropy generation rates and entropy generation number ratios of nanofluids were experimentally analyzed in microchannel flow for different channel heights of 200 μm, 300 μm, 400 μm and 500 μm. It was observed that frictional and total entropy generation rates increased as thermal entropy generation rate were decreasing with an increase in particle volume fraction. In microchannel flows, thermal entropy generation could be neglected due to its too low rate smaller than 1.10e-07 in total entropy generation. Higher channel heights caused higher thermal entropy generation rates, and increasing channel height yielded an increase from 30% to 52% in thermal entropy generation. When channel height decreased, an increase of 66%-98% in frictional entropy generation was obtained. Adding TiO2 nanoparticles into the base fluid caused thermal entropy generation to decrease about 1.8%-32.4%, frictional entropy generation to increase about 3.3%-21.6%.
Psychological Entropy: A Framework for Understanding Uncertainty-Related Anxiety
Hirsh, Jacob B.; Mar, Raymond A.; Peterson, Jordan B.
2012-01-01
Entropy, a concept derived from thermodynamics and information theory, describes the amount of uncertainty and disorder within a system. Self-organizing systems engage in a continual dialogue with the environment and must adapt themselves to changing circumstances to keep internal entropy at a manageable level. We propose the entropy model of…
Maximum-entropy clustering algorithm and its global convergence analysis
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Constructing a batch of differentiable entropy functions touniformly approximate an objective function by means of the maximum-entropy principle, a new clustering algorithm, called maximum-entropy clustering algorithm, is proposed based on optimization theory. This algorithm is a soft generalization of the hard C-means algorithm and possesses global convergence. Its relations with other clustering algorithms are discussed.
A comparison of EEG spectral entropy with conventional quantitative ...
African Journals Online (AJOL)
A comparison of EEG spectral entropy with conventional quantitative EEG at varying depths of sevoflurane anaesthesia. PR Bartel, FJ Smith, PJ Becker. Abstract. Background and Aim: Recently an electroencephalographic (EEG) spectral entropy module (M-ENTROPY) for an anaesthetic monitor has become commercially ...
An Accessible Approach to Understanding Entropy and Change
Johnson, Philip
2018-01-01
This article challenges the notion that entropy is something to be avoided. A line of argument is presented that is accessible to those not having specialist knowledge and that offers a new perspective to those more familiar with the concept. It shows that temperature is better understood by addressing entropy. Entropy change diagrams are…
Nonextensive Entropy, Prior PDFs and Spontaneous Symmetry Breaking
Shafee, Fariel
2008-01-01
We show that using nonextensive entropy can lead to spontaneous symmetry breaking when a parameter changes its value from that applicable for a symmetric domain, as in field theory. We give the physical reasons and also show that even for symmetric Dirichlet priors, such a defnition of the entropy and the parameter value can lead to asymmetry when entropy is maximized.
Tsallis Entropy and the Transition to Scaling in Fragmentation
Sotolongo-Costa, Oscar; Rodriguez, Arezky H.; Rodgers, G. J.
2000-12-01
By using the maximum entropy principle with Tsallis entropy we obtain a fragment size distribution function which undergoes a transition to scaling. This distribution function reduces to those obtained by other authors using Shannon entropy. The treatment is easily generalisable to any process of fractioning with suitable constraints.
Entropy function and universality of entropy-area relation for small black holes
International Nuclear Information System (INIS)
Cai Ronggen; Chen, C.-M.; Maeda, Kei-ichi; Ohta, Nobuyoshi; Pang Dawei
2008-01-01
We discuss the entropy-area relation for the small black holes with higher curvature corrections by using the entropy function formalism and field redefinition method. We show that the entropy S BH of the small black hole is proportional to its horizon area A. In particular, we find a universal result that S BH =A/2G, the ratio is 2 times of Bekenstein-Hawking entropy-area formula in many cases of physical interest. In four dimensions, the universal relation is always true irrespective of the coefficients of the higher-order terms if the dilaton couplings are the same, which is the case for string effective theory, while in five dimensions, the relation again holds irrespective of the overall coefficient if the higher-order corrections are in the GB combination. We also discuss how this result generalizes to known physically interesting cases with Lovelock correction terms in various dimensions, and possible implications of the universal relation.
Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro
2017-08-01
In this second part, we analyze the dissipation properties of generalized Poisson-Kac (GPK) processes, considering the decay of suitable L 2-norms and the definition of entropy functions. In both cases, consistent energy dissipation and entropy functions depend on the whole system of primitive statistical variables, the partial probability density functions \\{ p_α({x}, t) \\}α=1N , while the corresponding energy dissipation and entropy functions based on the overall probability density p({x}, t) do not satisfy monotonicity requirements as a function of time. These results provide new insights on the theory of Markov operators associated with irreversible stochastic dynamics. Examples from chaotic advection (standard map coupled to stochastic GPK processes) illustrate this phenomenon. Some complementary physical issues are also addressed: the ergodicity breaking in the presence of attractive potentials, and the use of GPK perturbations to mollify stochastic field equations.
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
Entropy-driven phase transitions of entanglement
Facchi, Paolo; Florio, Giuseppe; Parisi, Giorgio; Pascazio, Saverio; Yuasa, Kazuya
2013-05-01
We study the behavior of bipartite entanglement at fixed von Neumann entropy. We look at the distribution of the entanglement spectrum, that is, the eigenvalues of the reduced density matrix of a quantum system in a pure state. We report the presence of two continuous phase transitions, characterized by different entanglement spectra, which are deformations of classical eigenvalue distributions.
Rényi entropy and conformal defects
International Nuclear Information System (INIS)
Bianchi, Lorenzo; Meineri, Marco; Myers, Robert C.; Smolkin, Michael
2016-01-01
We propose a field theoretic framework for calculating the dependence of Rényi entropies on the shape of the entangling surface in a conformal field theory. Our approach rests on regarding the corresponding twist operator as a conformal defect and in particular, we define the displacement operator which implements small local deformations of the entangling surface. We identify a simple constraint between the coefficient defining the two-point function of the displacement operator and the conformal weight of the twist operator, which consolidates a number of distinct conjectures on the shape dependence of the Rényi entropy. As an example, using this approach, we examine a conjecture regarding the universal coefficient associated with a conical singularity in the entangling surface for CFTs in any number of spacetime dimensions. We also provide a general formula for the second order variation of the Rényi entropy arising from small deformations of a spherical entangling surface, extending Mezei’s results for the entanglement entropy.
A Note of Caution on Maximizing Entropy
Directory of Open Access Journals (Sweden)
Richard E. Neapolitan
2014-07-01
Full Text Available The Principle of Maximum Entropy is often used to update probabilities due to evidence instead of performing Bayesian updating using Bayes’ Theorem, and its use often has efficacious results. However, in some circumstances the results seem unacceptable and unintuitive. This paper discusses some of these cases, and discusses how to identify some of the situations in which this principle should not be used. The paper starts by reviewing three approaches to probability, namely the classical approach, the limiting frequency approach, and the Bayesian approach. It then introduces maximum entropy and shows its relationship to the three approaches. Next, through examples, it shows that maximizing entropy sometimes can stand in direct opposition to Bayesian updating based on reasonable prior beliefs. The paper concludes that if we take the Bayesian approach that probability is about reasonable belief based on all available information, then we can resolve the conflict between the maximum entropy approach and the Bayesian approach that is demonstrated in the examples.
Malleability of the blockchain’s entropy
C.A. Pierrot (Cécile); W. Wesolowski (Benjamin)
2017-01-01
textabstractTrustworthy generation of public random numbers is necessary for the security of a number of cryptographic applications. It was suggested to use the inherent unpredictability of blockchains as a source of public randomness. Entropy from the Bitcoin blockchain in particular has been used
Generalization of Gibbs Entropy and Thermodynamic Relation
Park, Jun Chul
2010-01-01
In this paper, we extend Gibbs's approach of quasi-equilibrium thermodynamic processes, and calculate the microscopic expression of entropy for general non-equilibrium thermodynamic processes. Also, we analyze the formal structure of thermodynamic relation in non-equilibrium thermodynamic processes.
Le Chatelier's Principle, Temperature Effects, and Entropy.
Campbell, J. Arthur
1985-01-01
One of the most useful methods of understanding chemical equilibria is provided by Le Chatelier's principle. The relationships between this principle, temperature, and entropy are discussed. Tables with thermodynamic data for some net reactions commonly used to illustrate the principle and for reactions involving gases are included. (JN)
Shaking the entropy out of a lattice
DEFF Research Database (Denmark)
C. Tichy, Malte; Mølmer, Klaus; F. Sherson, Jacob
2012-01-01
, for which we implement a protocol that circumvents the constraints of unitarity. The preparation of large regions with precisely one atom per lattice site is discussed for both bosons and fermions. The resulting low-entropy Mott-insulating states may serve as high-fidelity register states for quantum...
Carnot to Clausius: Caloric to Entropy
Newburgh, Ronald
2009-01-01
This paper discusses how the Carnot engine led to the formulation of the second law of thermodynamics and entropy. The operation of the engine is analysed both in terms of heat as the caloric fluid and heat as a form of energy. A keystone of Carnot's thinking was the absolute conservation of caloric. Although the Carnot analysis was partly…
Force-Time Entropy of Isometric Impulse.
Hsieh, Tsung-Yu; Newell, Karl M
2016-01-01
The relation between force and temporal variability in discrete impulse production has been viewed as independent (R. A. Schmidt, H. Zelaznik, B. Hawkins, J. S. Frank, & J. T. Quinn, 1979 ) or dependent on the rate of force (L. G. Carlton & K. M. Newell, 1993 ). Two experiments in an isometric single finger force task investigated the joint force-time entropy with (a) fixed time to peak force and different percentages of force level and (b) fixed percentage of force level and different times to peak force. The results showed that the peak force variability increased either with the increment of force level or through a shorter time to peak force that also reduced timing error variability. The peak force entropy and entropy of time to peak force increased on the respective dimension as the parameter conditions approached either maximum force or a minimum rate of force production. The findings show that force error and timing error are dependent but complementary when considered in the same framework with the joint force-time entropy at a minimum in the middle parameter range of discrete impulse.
The Statistical Interpretation of Entropy: An Activity
Timmberlake, Todd
2010-01-01
The second law of thermodynamics, which states that the entropy of an isolated macroscopic system can increase but will not decrease, is a cornerstone of modern physics. Ludwig Boltzmann argued that the second law arises from the motion of the atoms that compose the system. Boltzmann's statistical mechanics provides deep insight into the…
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 based fingerprint for local crystalline order
Piaggi, Pablo M.; Parrinello, Michele
2017-09-01
We introduce a new fingerprint that allows distinguishing between liquid-like and solid-like atomic environments. This fingerprint is based on an approximate expression for the entropy projected on individual atoms. When combined with local enthalpy, this fingerprint acquires an even finer resolution and it is capable of discriminating between different crystal structures.
Uncertainties in Forecasting Streamflow using Entropy Theory
Cui, H.; Singh, V. P.
2017-12-01
Streamflow forecasting is essential in river restoration, reservoir operation, power generation, irrigation, navigation, and water management. However, there is always uncertainties accompanied in forecast, which may affect the forecasting results and lead to large variations. Therefore, uncertainties must be considered and be assessed properly when forecasting streamflow for water management. The aim of our work is to quantify the uncertainties involved in forecasting streamflow and provide reliable streamflow forecast. Despite that streamflow time series are stochastic, they exhibit seasonal and periodic patterns. Therefore, streamflow forecasting entails modeling seasonality, periodicity, and its correlation structure, and assessing uncertainties. This study applies entropy theory to forecast streamflow and measure uncertainties during the forecasting process. To apply entropy theory for streamflow forecasting, spectral analysis is combined to time series analysis, as spectral analysis can be employed to characterize patterns of streamflow variation and identify the periodicity of streamflow. That is, it permits to extract significant information for understanding the streamflow process and prediction thereof. Application of entropy theory for streamflow forecasting involves determination of spectral density, determination of parameters, and extension of autocorrelation function. The uncertainties brought by precipitation input, forecasting model and forecasted results are measured separately using entropy. With information theory, how these uncertainties transported and aggregated during these processes will be described.
Information, entropy, and fidelity in visual communication
Huck, Friedrich O.; Fales, Carl L.; Alter-Gartenberg, Rachel; Rahman, Zia-ur
1992-10-01
This paper presents an assessment of visual communication that integrates the critical limiting factors of image gathering an display with the digital processing that is used to code and restore images. The approach focuses on two mathematical criteria, information and fidelity, and on their relationships to the entropy of the encoded data and to the visual quality of the restored image.
Rényi entropy and conformal defects
Energy Technology Data Exchange (ETDEWEB)
Bianchi, Lorenzo [Institut für Physik, Humboldt-Universität zu Berlin,Zum Großen Windkanal 6, 12489 Berlin (Germany); II. Institut für Theoretische Physik, Universität Hamburg,Luruper Chaussee 149, 22761 Hamburg (Germany); Meineri, Marco [Scuola Normale Superiore and Istituto Nazionale di Fisica Nucleare - Sezione di Pisa,Piazza dei Cavalieri 7, I-56126 Pisa (Italy); Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, ON N2L 2Y5 (Canada); Myers, Robert C. [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, ON N2L 2Y5 (Canada); Smolkin, Michael [Center for Theoretical Physics, Department of Physics, University of California,Berkeley, CA 94720 (United States)
2016-07-14
We propose a field theoretic framework for calculating the dependence of Rényi entropies on the shape of the entangling surface in a conformal field theory. Our approach rests on regarding the corresponding twist operator as a conformal defect and in particular, we define the displacement operator which implements small local deformations of the entangling surface. We identify a simple constraint between the coefficient defining the two-point function of the displacement operator and the conformal weight of the twist operator, which consolidates a number of distinct conjectures on the shape dependence of the Rényi entropy. As an example, using this approach, we examine a conjecture regarding the universal coefficient associated with a conical singularity in the entangling surface for CFTs in any number of spacetime dimensions. We also provide a general formula for the second order variation of the Rényi entropy arising from small deformations of a spherical entangling surface, extending Mezei’s results for the entanglement entropy.
Entropy generation in cosmological particle creation
International Nuclear Information System (INIS)
Castagnino, M.A.; Gaioli, F.H.; Sforza, D.M.
1996-01-01
A very simplified model of the Universe is considered in order to propose an alternative approach to the irreversible evolution of the Universe at very early times. The entropy generation at the quantum stage can be thought of as a consequence of an instability of the system. Then particle creation arises from this instability
New entropy formula for Kerr black holes
Directory of Open Access Journals (Sweden)
González Hernán A.
2018-01-01
Full Text Available We introduce a new entropy formula for Kerr black holes inspired by recent results for 3-dimensional black holes and cosmologies with soft Heisenberg hair. We show that also Kerr–Taub–NUT black holes obey the same formula.
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.
Texture analysis using Renyi's generalized entropies
Grigorescu, SE; Petkov, N
2003-01-01
We propose a texture analysis method based on Renyi's generalized entropies. The method aims at identifying texels in regular textures by searching for the smallest window through which the minimum number of different visual patterns is observed when moving the window over a given texture. The
Comprehensive entropy weight observability-controllability risk ...
African Journals Online (AJOL)
Decision making for water resource planning is often related to social, economic and environmental factors. There are various methods for making decisions about water resource planning alternatives and measures with various shortcomings. A comprehensive entropy weight observability-controllability risk analysis ...
Lattice-Valued Possibilistic Entropy Measure
Czech Academy of Sciences Publication Activity Database
Kramosil, Ivan
2008-01-01
Roč. 16, č. 6 (2008), s. 829-846 ISSN 0218-4885 R&D Projects: GA AV ČR IAA100300503 Institutional research plan: CEZ:AV0Z10300504 Keywords : complete lattice * lattice-valued possibilistic distribution * entropy measure * product of possibilistic distribution Subject RIV: BA - General Mathematics Impact factor: 1.000, year: 2008
The maximum-entropy method in superspace
Czech Academy of Sciences Publication Activity Database
van Smaalen, S.; Palatinus, Lukáš; Schneider, M.
2003-01-01
Roč. 59, - (2003), s. 459-469 ISSN 0108-7673 Grant - others:DFG(DE) XX Institutional research plan: CEZ:AV0Z1010914 Keywords : maximum-entropy method, * aperiodic crystals * electron density Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.558, year: 2003
Entropie analysis of floating car data systems
Directory of Open Access Journals (Sweden)
F. Gössel
2004-01-01
Full Text Available The knowledge of the actual traffic state is a basic prerequisite of modern traffic telematic systems. Floating Car Data (FCD systems are becoming more and more important for the provision of actual and reliable traffic data. In these systems the vehicle velocity is the original variable for the evaluation of the current traffic condition. As real FCDsystems are operating under conditions of limited transmission and processing capacity the analysis of the original variable vehicle speed is of special interest. Entropy considerations are especially useful for the deduction of fundamental restrictions and limitations. The paper analyses velocity-time profiles by means of information entropy. It emphasises in quantification of the information content of velocity-time profiles and the discussion of entropy dynamic in velocity-time profiles. Investigations are based on empirical data derived during field trials. The analysis of entropy dynamic is carried out in two different ways. On one hand velocity differences within a certain interval of time are used, on the other hand the transinformation between velocities in certain time distances was evaluated. One important result is an optimal sample-rate for the detection of velocity data in FCD-systems. The influence of spatial segmentation and of different states of traffic was discussed.
Black hole entropy and finite geometry
Czech Academy of Sciences Publication Activity Database
Levay, P.; Saniga, M.; Vrana, P.; Pracna, Petr
2009-01-01
Roč. 79, č. 8 (2009), 084036 ISSN 1550-7998 Institutional research plan: CEZ:AV0Z40400503 Keywords : Maxwell-Einstein supergravity * attractors * black hole entropy Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 4.922, year: 2009
Entropy viscosity method applied to Euler equations
International Nuclear Information System (INIS)
Delchini, M. O.; Ragusa, J. C.; Berry, R. A.
2013-01-01
The entropy viscosity method [4] has been successfully applied to hyperbolic systems of equations such as Burgers equation and Euler equations. The method consists in adding dissipative terms to the governing equations, where a viscosity coefficient modulates the amount of dissipation. The entropy viscosity method has been applied to the 1-D Euler equations with variable area using a continuous finite element discretization in the MOOSE framework and our results show that it has the ability to efficiently smooth out oscillations and accurately resolve shocks. Two equations of state are considered: Ideal Gas and Stiffened Gas Equations Of State. Results are provided for a second-order time implicit schemes (BDF2). Some typical Riemann problems are run with the entropy viscosity method to demonstrate some of its features. Then, a 1-D convergent-divergent nozzle is considered with open boundary conditions. The correct steady-state is reached for the liquid and gas phases with a time implicit scheme. The entropy viscosity method correctly behaves in every problem run. For each test problem, results are shown for both equations of state considered here. (authors)
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.
Information, entropy and fidelity in visual communication
Huck, Friedrich O.; Fales, Carl L.; Alter-Gartenberg, Rachel; Rahman, Zia-Ur
1992-01-01
This paper presents an assessment of visual communication that integrates the critical limiting factors of image gathering and display with the digital processing that is used to code and restore images. The approach focuses on two mathematical criteria, information and fidelity, and on their relationships to the entropy of the encoded data and to the visual quality of the restored image.
Generalized Entanglement Entropies of Quantum Designs
Liu, Zi-Wen; Lloyd, Seth; Zhu, Elton Yechao; Zhu, Huangjun
2018-03-01
The entanglement properties of random quantum states or dynamics are important to the study of a broad spectrum of disciplines of physics, ranging from quantum information to high energy and many-body physics. This Letter investigates the interplay between the degrees of entanglement and randomness in pure states and unitary channels. We reveal strong connections between designs (distributions of states or unitaries that match certain moments of the uniform Haar measure) and generalized entropies (entropic functions that depend on certain powers of the density operator), by showing that Rényi entanglement entropies averaged over designs of the same order are almost maximal. This strengthens the celebrated Page's theorem. Moreover, we find that designs of an order that is logarithmic in the dimension maximize all Rényi entanglement entropies and so are completely random in terms of the entanglement spectrum. Our results relate the behaviors of Rényi entanglement entropies to the complexity of scrambling and quantum chaos in terms of the degree of randomness, and suggest a generalization of the fast scrambling conjecture.
Holographic entanglement entropy and gravitational anomalies
Castro, A.; Detournay, S.; Iqbal, N.; Perlmutter, E.
2014-01-01
We study entanglement entropy in two-dimensional conformal field theories with a gravitational anomaly. In theories with gravity duals, this anomaly is holographically represented by a gravitational Chern-Simons term in the bulk action. We show that the anomaly broadens the Ryu-Takayanagi minimal
Proposal on entropy in quantum cosmology
International Nuclear Information System (INIS)
Li Miao.
1985-07-01
Starting from the proposal of Hartle and Hawking about the ground state wave functions of the universe, we propose a definition of the entropy of the universe and derive its form in a special case in which the matter density of the universe is constant. The result shows that our proposal is reasonable and worth further study. (author)
The Gibbs entropy production in general relativity
International Nuclear Information System (INIS)
Henneaux, M.
1983-01-01
The entropy production is analyzed in the case of homogeneous cosmological models of the Bianchi type. It is shown to vanish for class-A models and to be undefined for class-B ones, because of an ambiguity in the measure on the space of the true gravitational degrees of freedom. How this results extend to the full Einstein theory is discussed
Gibbs entropy production in general relativity
International Nuclear Information System (INIS)
Henneaux, M.
1983-01-01
The entropy production is analyzed in the case of homogeneous cosmological models of the Bianchi type. It is shown to vanish for class-A models and to be undefined for class-B ones, because of an ambiguity in the measure on the space of the true gravitational degrees of freedom. How this results extends to the full Einstein theory is discussed
Discussion of entanglement entropy in quantum gravity
International Nuclear Information System (INIS)
Ma, Chen-Te
2018-01-01
We study entanglement entropy in gravity theory with quantum effects. A simplest model is a two dimensional Einstein gravity theory. We use an n-sheet manifold to obtain an area term of entanglement entropy by summing over all background fields. Based on AdS/CFT correspondence, strongly coupled conformal field theory is expected to describe perturbative quantum gravity theory. An ultraviolet complete quantum gravity theory should not depend on a choice of an entangling surface. To analysis the problem explicitly, we analyze two dimensional conformal field theory. We find that a coefficient of a universal term of entanglement entropy is independent of a choice of an entangling surface in two dimensional conformal field theory for one interval to show a tentative evidence. Finally, we discuss that translational invariance in a quantum system at zero temperature, size goes to infinity and no mass scales, except for cut-off, possibly be a necessary condition in quantum gravity theory by ruing out a volume law of entanglement entropy. (copyright 2018 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Vranish, John M. (Inventor)
2010-01-01
A partial gear bearing including an upper half, comprising peak partial teeth, and a lower, or bottom, half, comprising valley partial teeth. The upper half also has an integrated roller section between each of the peak partial teeth with a radius equal to the gear pitch radius of the radially outwardly extending peak partial teeth. Conversely, the lower half has an integrated roller section between each of the valley half teeth with a radius also equal to the gear pitch radius of the peak partial teeth. The valley partial teeth extend radially inwardly from its roller section. The peak and valley partial teeth are exactly out of phase with each other, as are the roller sections of the upper and lower halves. Essentially, the end roller bearing of the typical gear bearing has been integrated into the normal gear tooth pattern.
Kantarci, T.
2012-01-01
The five essays in this dissertation address a range of topics in the micro-economic literature on partial retirement. The focus is on the labor market behavior of older age groups. The essays examine the economic and non-economic determinants of partial retirement behavior, the effect of partial
Energy Technology Data Exchange (ETDEWEB)
Xu, Kaixuan, E-mail: kaixuanxubjtu@yeah.net; Wang, Jun
2017-02-26
In this paper, recently introduced permutation entropy and sample entropy are further developed to the fractional cases, weighted fractional permutation entropy (WFPE) and fractional sample entropy (FSE). The fractional order generalization of information entropy is utilized in the above two complexity approaches, to detect the statistical characteristics of fractional order information in complex systems. The effectiveness analysis of proposed methods on the synthetic data and the real-world data reveals that tuning the fractional order allows a high sensitivity and more accurate characterization to the signal evolution, which is useful in describing the dynamics of complex systems. Moreover, the numerical research on nonlinear complexity behaviors is compared between the returns series of Potts financial model and the actual stock markets. And the empirical results confirm the feasibility of the proposed model. - Highlights: • Two new entropy approaches for estimation of nonlinear complexity are proposed for the financial market. • Effectiveness analysis of proposed methods is presented and their respective features are studied. • Empirical research of proposed analysis on seven world financial market indices. • Numerical simulation of Potts financial dynamics is preformed for nonlinear complexity behaviors.
International Nuclear Information System (INIS)
Xu, Kaixuan; Wang, Jun
2017-01-01
In this paper, recently introduced permutation entropy and sample entropy are further developed to the fractional cases, weighted fractional permutation entropy (WFPE) and fractional sample entropy (FSE). The fractional order generalization of information entropy is utilized in the above two complexity approaches, to detect the statistical characteristics of fractional order information in complex systems. The effectiveness analysis of proposed methods on the synthetic data and the real-world data reveals that tuning the fractional order allows a high sensitivity and more accurate characterization to the signal evolution, which is useful in describing the dynamics of complex systems. Moreover, the numerical research on nonlinear complexity behaviors is compared between the returns series of Potts financial model and the actual stock markets. And the empirical results confirm the feasibility of the proposed model. - Highlights: • Two new entropy approaches for estimation of nonlinear complexity are proposed for the financial market. • Effectiveness analysis of proposed methods is presented and their respective features are studied. • Empirical research of proposed analysis on seven world financial market indices. • Numerical simulation of Potts financial dynamics is preformed for nonlinear complexity behaviors.
Directory of Open Access Journals (Sweden)
Muhammad Mubashir Bhatti
2016-05-01
Full Text Available In this article, entropy generation with radiation on non-Newtonian Carreau nanofluid towards a shrinking sheet is investigated numerically. The effects of magnetohydrodynamics (MHD are also taken into account. Firstly, the governing flow problem is simplified into ordinary differential equations from partial differential equations with the help of similarity variables. The solution of the resulting nonlinear differential equations is solved numerically with the help of the successive linearization method and Chebyshev spectral collocation method. The influence of all the emerging parameters is discussed with the help of graphs and tables. It is observed that the influence of magnetic field and fluid parameters oppose the flow. It is also analyzed that thermal radiation effects and the Prandtl number show opposite behavior on temperature profile. Furthermore, it is also observed that entropy profile increases for all the physical parameters.
Entropy per baryon in a 'many-worlds' cosmology
International Nuclear Information System (INIS)
Clutton-Brock, M.
1977-01-01
The universe is imagined split into infinitely many branches, or 'worlds', only one of which can be observed. The world has an entropy per baryon xi approximately 10 9 : other worlds can have all possible values of entropy per baryon. High-entropy worlds with xi > 5x10 11 do not form galaxies, but only giant black holes. Low entropy worlds with xi 5 do form galaxies, but only metal-poor dwarf galaxies with no planets. Life can evolve only in worlds with entropy per baryon in the range 3x10 5 11 , and life is abundant only in a much narrower range. (Auth.)
Chain rules for smooth min-and max-entropies
DEFF Research Database (Denmark)
Vitanov, Alexande; Dupont-Dupuis, Fréderic; Tomamichel, Marco
2013-01-01
The chain rule for the Shannon and von Neumann en- tropy, which relates the total entropy of a system to the entropies of its parts, is of central importance to information theory. Here, we consider the chain rule for the more general smooth min- and max-entropies, used in one-shot in formation...... theory. For these en- tropy measures, the chain rule no longer holds as an equality. How- ever, the standard chain rule for the von Neum ann entropy is re- trieved asymptotically when evaluating the smooth entropies for many identical and independently distributed states....
A note on entanglement entropy and quantum geometry
International Nuclear Information System (INIS)
Bodendorfer, N
2014-01-01
It has been argued that the entropy computed in the isolated horizon framework of loop quantum gravity is closely related to the entanglement entropy of the gravitational field, and that the calculation performed is not restricted to horizons. We recall existing work on this issue and explain how recent work on generalizing these computations to arbitrary spacetime dimensions D+1⩾3 supports this point of view and makes the duality between entanglement entropy and the entropy computed from counting boundary states manifest. In a certain semiclassical regime in 3+1 dimensions, this entropy is given by the Bekenstein–Hawking formula. (paper)
Energy Technology Data Exchange (ETDEWEB)
2018-03-15
This Python package provides high-performance implementations of the functions and examples presented in "BiEntropy - The Approximate Entropy of a Finite Binary String" by Grenville J. Croll, presented at ANPA 34 in 2013. https://arxiv.org/abs/1305.0954 According to the paper, BiEntropy is "a simple algorithm which computes the approximate entropy of a finite binary string of arbitrary length" using "a weighted average of the Shannon Entropies of the string and all but the last binary derivative of the string."
Emergent Geometry from Entropy and Causality
Engelhardt, Netta
In this thesis, we investigate the connections between the geometry of spacetime and aspects of quantum field theory such as entanglement entropy and causality. This work is motivated by the idea that spacetime geometry is an emergent phenomenon in quantum gravity, and that the physics responsible for this emergence is fundamental to quantum field theory. Part I of this thesis is focused on the interplay between spacetime and entropy, with a special emphasis on entropy due to entanglement. In general spacetimes, there exist locally-defined surfaces sensitive to the geometry that may act as local black hole boundaries or cosmological horizons; these surfaces, known as holographic screens, are argued to have a connection with the second law of thermodynamics. Holographic screens obey an area law, suggestive of an association with entropy; they are also distinguished surfaces from the perspective of the covariant entropy bound, a bound on the total entropy of a slice of the spacetime. This construction is shown to be quite general, and is formulated in both classical and perturbatively quantum theories of gravity. The remainder of Part I uses the Anti-de Sitter/ Conformal Field Theory (AdS/CFT) correspondence to both expand and constrain the connection between entanglement entropy and geometry. The AdS/CFT correspondence posits an equivalence between string theory in the "bulk" with AdS boundary conditions and certain quantum field theories. In the limit where the string theory is simply classical General Relativity, the Ryu-Takayanagi and more generally, the Hubeny-Rangamani-Takayanagi (HRT) formulae provide a way of relating the geometry of surfaces to entanglement entropy. A first-order bulk quantum correction to HRT was derived by Faulkner, Lewkowycz and Maldacena. This formula is generalized to include perturbative quantum corrections in the bulk at any (finite) order. Hurdles to spacetime emergence from entanglement entropy as described by HRT and its quantum
Directory of Open Access Journals (Sweden)
Francine Blanchet-Sadri
2011-08-01
Full Text Available Partial words are sequences over a finite alphabet that may contain wildcard symbols, called holes, which match or are compatible with all letters; partial words without holes are said to be full words (or simply words. Given an infinite partial word w, the number of distinct full words over the alphabet that are compatible with factors of w of length n, called subwords of w, refers to a measure of complexity of infinite partial words so-called subword complexity. This measure is of particular interest because we can construct partial words with subword complexities not achievable by full words. In this paper, we consider the notion of recurrence over infinite partial words, that is, we study whether all of the finite subwords of a given infinite partial word appear infinitely often, and we establish connections between subword complexity and recurrence in this more general framework.
Entropy resistance minimization: An alternative method for heat exchanger analyses
International Nuclear Information System (INIS)
Cheng, XueTao
2013-01-01
In this paper, the concept of entropy resistance is proposed based on the entropy generation analyses of heat transfer processes. It is shown that smaller entropy resistance leads to larger heat transfer rate with fixed thermodynamic force difference and smaller thermodynamic force difference with fixed heat transfer rate, respectively. For the discussed two-stream heat exchangers in which the heat transfer rates are not given and the three-stream heat exchanger with prescribed heat capacity flow rates and inlet temperatures of the streams, smaller entropy resistance leads to larger heat transfer rate. For the two-stream heat exchangers with fixed heat transfer rate, smaller entropy resistance leads to larger effectiveness. Furthermore, it is shown that smaller values of the concepts of entropy generation numbers and modified entropy generation number do not always correspond to better performance of the discussed heat exchangers. - Highlights: • The concept of entropy resistance is defined for heat exchangers. • The concepts based on entropy generation are used to analyze heat exchangers. • Smaller entropy resistance leads to better performance of heat exchangers. • The applicability of entropy generation minimization is conditional
Entanglement entropy for descendent local operators in 2D CFTs
International Nuclear Information System (INIS)
Chen, Bin; Guo, Wu-Zhong; He, Song; Wu, Jie-qiang
2015-01-01
We mainly study the Rényi entropy and entanglement entropy of the states locally excited by the descendent operators in two dimensional conformal field theories (CFTs). In rational CFTs, we prove that the increase of entanglement entropy and Rényi entropy for a class of descendent operators, which are generated by L"("−")L̄"("−") onto the primary operator, always coincide with the logarithmic of quantum dimension of the corresponding primary operator. That means the Rényi entropy and entanglement entropy for these descendent operators are the same as the ones of their corresponding primary operator. For 2D rational CFTs with a boundary, we confirm that the Rényi entropy always coincides with the logarithmic of quantum dimension of the primary operator during some periods of the evolution. Furthermore, we consider more general descendent operators generated by ∑d_{_n__i_}_{_n__j_}(∏_iL_−_n__i∏_jL̄_−_n__j) on the primary operator. For these operators, the entanglement entropy and Rényi entropy get additional corrections, as the mixing of holomorphic and anti-holomorphic Virasoro generators enhance the entanglement. Finally, we employ perturbative CFT techniques to evaluate the Rényi entropy of the excited operators in deformed CFT. The Rényi and entanglement entropies are increased, and get contributions not only from local excited operators but also from global deformation of the theory.
Tsallis Entropy Theory for Modeling in Water Engineering: A Review
Directory of Open Access Journals (Sweden)
Vijay P. Singh
2017-11-01
Full Text Available Water engineering is an amalgam of engineering (e.g., hydraulics, hydrology, irrigation, ecosystems, environment, water resources and non-engineering (e.g., social, economic, political aspects that are needed for planning, designing and managing water systems. These aspects and the associated issues have been dealt with in the literature using different techniques that are based on different concepts and assumptions. A fundamental question that still remains is: Can we develop a unifying theory for addressing these? The second law of thermodynamics permits us to develop a theory that helps address these in a unified manner. This theory can be referred to as the entropy theory. The thermodynamic entropy theory is analogous to the Shannon entropy or the information theory. Perhaps, the most popular generalization of the Shannon entropy is the Tsallis entropy. The Tsallis entropy has been applied to a wide spectrum of problems in water engineering. This paper provides an overview of Tsallis entropy theory in water engineering. After some basic description of entropy and Tsallis entropy, a review of its applications in water engineering is presented, based on three types of problems: (1 problems requiring entropy maximization; (2 problems requiring coupling Tsallis entropy theory with another theory; and (3 problems involving physical relations.
On Equivalence of Nonequilibrium Thermodynamic and Statistical Entropies
Directory of Open Access Journals (Sweden)
Purushottam D. Gujrati
2015-02-01
Full Text Available We review the concept of nonequilibrium thermodynamic entropy and observables and internal variables as state variables, introduced recently by us, and provide a simple first principle derivation of additive statistical entropy, applicable to all nonequilibrium states by treating thermodynamics as an experimental science. We establish their numerical equivalence in several cases, which includes the most important case when the thermodynamic entropy is a state function. We discuss various interesting aspects of the two entropies and show that the number of microstates in the Boltzmann entropy includes all possible microstates of non-zero probabilities even if the system is trapped in a disjoint component of the microstate space. We show that negative thermodynamic entropy can appear from nonnegative statistical entropy.
Consumption of energy and release of entropy into the biosphere
International Nuclear Information System (INIS)
Deutscher, G.
2014-01-01
The short-term threat on humanity is not the shortage of energy but rather the contamination of the environment. The concept of entropy is useful to assess the impact of humane activities on the environment. During most of earth history the increase of entropy was more than compensated by the energy brought by the sun. Today the intensive use of fossil fuels has reversed the trend: the biosphere entropy increases as CO 2 piles up in the atmosphere. The release of entropy is linked to the amount of energy we consume and to the efficiency of the process we use to produce it. Nuclear power plants release entropy as low-temperature heat but this amount of entropy is far less than the entropy released by fossil-fuel power plants under the form of CO 2 . (A.C.)
Quantum information entropies for a squared tangent potential well
Energy Technology Data Exchange (ETDEWEB)
Dong, Shishan [Information and Engineering College, DaLian University, 116622 (China); Sun, Guo-Hua, E-mail: sunghdb@yahoo.com [Centro Universitario Valle de Chalco, Universidad Autónoma del Estado de México, Valle de Chalco Solidaridad, Estado de México, 56615 (Mexico); Dong, Shi-Hai, E-mail: dongsh2@yahoo.com [Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos, Edificio 9, México D.F. 07738 (Mexico); Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001 (United States); Draayer, J.P., E-mail: draayer@sura.org [Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001 (United States)
2014-01-10
The particle in a symmetrical squared tangent potential well is studied by examining its Shannon information entropy and standard deviations. The position and momentum information entropy densities ρ{sub s}(x), ρ{sub s}(p) and probability densities ρ(x), ρ(p) are illustrated with different potential range L and potential depth U. We present analytical position information entropies S{sub x} for the lowest two states. We observe that the sum of position and momentum entropies S{sub x} and S{sub p} expressed by Bialynicki-Birula–Mycielski (BBM) inequality is satisfied. Some eigenstates exhibit entropy squeezing in the position. The entropy squeezing in position will be compensated by an increase in momentum entropy. We also note that the S{sub x} increases with the potential range L, while decreases with the potential depth U. The variation of S{sub p} is contrary to that of S{sub x}.
Quantum information entropies for a squared tangent potential well
International Nuclear Information System (INIS)
Dong, Shishan; Sun, Guo-Hua; Dong, Shi-Hai; Draayer, J.P.
2014-01-01
The particle in a symmetrical squared tangent potential well is studied by examining its Shannon information entropy and standard deviations. The position and momentum information entropy densities ρ s (x), ρ s (p) and probability densities ρ(x), ρ(p) are illustrated with different potential range L and potential depth U. We present analytical position information entropies S x for the lowest two states. We observe that the sum of position and momentum entropies S x and S p expressed by Bialynicki-Birula–Mycielski (BBM) inequality is satisfied. Some eigenstates exhibit entropy squeezing in the position. The entropy squeezing in position will be compensated by an increase in momentum entropy. We also note that the S x increases with the potential range L, while decreases with the potential depth U. The variation of S p is contrary to that of S x .
Escort entropies and divergences and related canonical distribution
International Nuclear Information System (INIS)
Bercher, J.-F.
2011-01-01
We discuss two families of two-parameter entropies and divergences, derived from the standard Renyi and Tsallis entropies and divergences. These divergences and entropies are found as divergences or entropies of escort distributions. Exploiting the nonnegativity of the divergences, we derive the expression of the canonical distribution associated to the new entropies and a observable given as an escort-mean value. We show that this canonical distribution extends, and smoothly connects, the results obtained in nonextensive thermodynamics for the standard and generalized mean value constraints. -- Highlights: → Two-parameter entropies are derived from q-entropies and escort distributions. → The related canonical distribution is derived. → This connects and extends known results in nonextensive statistics.
Gravitational entropy of nonstationary black holes and spherical shells
International Nuclear Information System (INIS)
Hiscock, W.A.
1989-01-01
The problem of defining the gravitational entropy of a nonstationary black hole is considered in a simple model consisting of a spherical shell which collapses into a preexisting black hole. The second law of black-hole mechanics strongly suggests identifying one-quarter of the area of the event horizon as the gravitational entropy of the system. It is, however, impossible to accurately locate the position of the global event horizon using only local measurements. In order to maintain a local thermodynamics, it is suggested that the entropy of the black hole be identified with one-quarter the area of the apparent horizon. The difference between the event-horizon entropy (to the extent it can be determined) and the apparent-horizon entropy may then be interpreted as the gravitational entropy of the collapsing shell. The total (event-horizon) gravitational entropy evolves in a smooth (C 0 ) fashion, even in the presence of δ-functional shells of matter
Black hole entropy in the O(N) model
International Nuclear Information System (INIS)
Kabat, D.; Shenker, S.H.; Strassler, M.J.
1995-01-01
We consider corrections to the entropy of a black hole from an O(N)-invariant linear σ model. We obtain the entropy from a 1/N expansion of the partition function on a cone. The entropy arises from diagrams which are analogous to those introduced by Susskind and Uglum to explain black hole entropy in string theory. The interpretation of the σ-model entropy depends on scale. At short distances, it has a state counting interpretation, as the entropy of entanglement of the N fields φ a . In the infrared, the effective theory has a single composite field σ∼φ a φ a , and the state counting interpretation of the entropy is lost. copyright 1995 The American Physical Society
Entropy generation method to quantify thermal comfort
Boregowda, S. C.; Tiwari, S. N.; Chaturvedi, S. K.
2001-01-01
The present paper presents a thermodynamic approach to assess the quality of human-thermal environment interaction and quantify thermal comfort. The approach involves development of entropy generation term by applying second law of thermodynamics to the combined human-environment system. The entropy generation term combines both human thermal physiological responses and thermal environmental variables to provide an objective measure of thermal comfort. The original concepts and definitions form the basis for establishing the mathematical relationship between thermal comfort and entropy generation term. As a result of logic and deterministic approach, an Objective Thermal Comfort Index (OTCI) is defined and established as a function of entropy generation. In order to verify the entropy-based thermal comfort model, human thermal physiological responses due to changes in ambient conditions are simulated using a well established and validated human thermal model developed at the Institute of Environmental Research of Kansas State University (KSU). The finite element based KSU human thermal computer model is being utilized as a "Computational Environmental Chamber" to conduct series of simulations to examine the human thermal responses to different environmental conditions. The output from the simulation, which include human thermal responses and input data consisting of environmental conditions are fed into the thermal comfort model. Continuous monitoring of thermal comfort in comfortable and extreme environmental conditions is demonstrated. The Objective Thermal Comfort values obtained from the entropy-based model are validated against regression based Predicted Mean Vote (PMV) values. Using the corresponding air temperatures and vapor pressures that were used in the computer simulation in the regression equation generates the PMV values. The preliminary results indicate that the OTCI and PMV values correlate well under ideal conditions. However, an experimental study
Institute of Scientific and Technical Information of China (English)
Xie Wen-Xian; Xu Wei; Cai Li
2007-01-01
This paper shows the Fokker-Planck equation of a dynamical system driven by coloured cross-correlated white noises in the absence and presence of a small external force. Based on the Fokker-Planck equation and the definition of Shannon's information entropy, the time dependence of entropy flux and entropy production can be calculated. The present results can be used to explain the extremal behaviour of time dependence of entropy flux and entropy production in view of the dissipative parameter γ of the system, coloured cross-correlation time τ and coloured cross-correlation strength λ.
International Nuclear Information System (INIS)
Guo Yongfeng; Xu Wei; Li Dongxi; Xie Wenxian
2008-01-01
A stochastic dissipative dynamical system driven by non-Gaussian noise is investigated. A general approximate Fokker-Planck equation of the system is derived through a path-integral approach. Based on the definition of Shannon's information entropy, the exact time dependence of entropy flux and entropy production of the system is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculation can be used to interpret the interplay of the dissipative constant and non-Gaussian noise on the entropy flux and entropy production
On the entanglement entropy for gauge theories
International Nuclear Information System (INIS)
Ghosh, Sudip; Soni, Ronak M; Trivedi, Sandip P.
2015-01-01
We propose a definition for the entanglement entropy of a gauge theory on a spatial lattice. Our definition applies to any subset of links in the lattice, and is valid for both Abelian and Non-Abelian gauge theories. For ℤ_N and U(1) theories, without matter, our definition agrees with a particular case of the definition given by Casini, Huerta and Rosabal. We also argue that in general, both for Abelian and Non-Abelian theories, our definition agrees with the entanglement entropy calculated using a definition of the replica trick. Our definition, however, does not agree with some standard ways to measure entanglement, like the number of Bell pairs which can be produced by entanglement distillation.
Maximum-entropy description of animal movement.
Fleming, Chris H; Subaşı, Yiğit; Calabrese, Justin M
2015-03-01
We introduce a class of maximum-entropy states that naturally includes within it all of the major continuous-time stochastic processes that have been applied to animal movement, including Brownian motion, Ornstein-Uhlenbeck motion, integrated Ornstein-Uhlenbeck motion, a recently discovered hybrid of the previous models, and a new model that describes central-place foraging. We are also able to predict a further hierarchy of new models that will emerge as data quality improves to better resolve the underlying continuity of animal movement. Finally, we also show that Langevin equations must obey a fluctuation-dissipation theorem to generate processes that fall from this class of maximum-entropy distributions when the constraints are purely kinematic.
Entropy in Collisionless Self-gravitating Systems
Barnes, Eric; Williams, L.
2010-01-01
Collisionless systems, like simulated dark matter halos or gas-less elliptical galaxies, often times have properties suggesting that a common physical principle controls their evolution. For example, N-body simulations of dark matter halos present nearly scale-free density/velocity-cubed profiles. In an attempt to understand the origins of such relationships, we adopt a thermodynamics approach. While it is well-known that self-gravitating systems do not have physically realizable thermal equilibrium configurations, we are interested in the behavior of entropy as mechanical equilibrium is acheived. We will discuss entropy production in these systems from a kinetic theory point of view. This material is based upon work supported by the National Aeronautics and Space Administration under grant NNX07AG86G issued through the Science Mission Directorate.
Entropy estimates of small data sets
Energy Technology Data Exchange (ETDEWEB)
Bonachela, Juan A; Munoz, Miguel A [Departamento de Electromagnetismo y Fisica de la Materia and Instituto de Fisica Teorica y Computacional Carlos I, Facultad de Ciencias, Universidad de Granada, 18071 Granada (Spain); Hinrichsen, Haye [Fakultaet fuer Physik und Astronomie, Universitaet Wuerzburg, Am Hubland, 97074 Wuerzburg (Germany)
2008-05-23
Estimating entropies from limited data series is known to be a non-trivial task. Naive estimations are plagued with both systematic (bias) and statistical errors. Here, we present a new 'balanced estimator' for entropy functionals (Shannon, Renyi and Tsallis) specially devised to provide a compromise between low bias and small statistical errors, for short data series. This new estimator outperforms other currently available ones when the data sets are small and the probabilities of the possible outputs of the random variable are not close to zero. Otherwise, other well-known estimators remain a better choice. The potential range of applicability of this estimator is quite broad specially for biological and digital data series. (fast track communication)
Entropy estimates of small data sets
International Nuclear Information System (INIS)
Bonachela, Juan A; Munoz, Miguel A; Hinrichsen, Haye
2008-01-01
Estimating entropies from limited data series is known to be a non-trivial task. Naive estimations are plagued with both systematic (bias) and statistical errors. Here, we present a new 'balanced estimator' for entropy functionals (Shannon, Renyi and Tsallis) specially devised to provide a compromise between low bias and small statistical errors, for short data series. This new estimator outperforms other currently available ones when the data sets are small and the probabilities of the possible outputs of the random variable are not close to zero. Otherwise, other well-known estimators remain a better choice. The potential range of applicability of this estimator is quite broad specially for biological and digital data series. (fast track communication)