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 for gravitational Chern-Simons terms by squashed cone method
International Nuclear Information System (INIS)
Guo, Wu-Zhong; Miao, Rong-Xin
2016-01-01
In this paper we investigate the entropy of gravitational Chern-Simons terms for the horizon with non-vanishing extrinsic curvatures, or the holographic entanglement entropy for arbitrary entangling surface. In 3D there is no anomaly of entropy. But the original squashed cone method can not be used directly to get the correct result. For higher dimensions the anomaly of entropy would appear, still, we can not use the squashed cone method directly. That is becasuse the Chern-Simons action is not gauge invariant. To get a reasonable result we suggest two methods. One is by adding a boundary term to recover the gauge invariance. This boundary term can be derived from the variation of the Chern-Simons action. The other one is by using the Chern-Simons relation dΩ_4_n_−_1=tr(R"2"n). We notice that the entropy of tr(R"2"n) is a total derivative locally, i.e. S=ds_C_S. We propose to identify s_C_S with the entropy of gravitational Chern-Simons terms Ω_4_n_−_1. In the first method we could get the correct result for Wald entropy in arbitrary dimension. In the second approach, in addition to Wald entropy, we can also obtain the anomaly of entropy with non-zero extrinsic curvatures. Our results imply that the entropy of a topological invariant, such as the Pontryagin term tr(R"2"n) and the Euler density, is a topological invariant on the entangling surface.
The positive-entropy constraint for the classical ideal gas
International Nuclear Information System (INIS)
Ciccariello, Salvino
2004-01-01
The problem of determining the state parameters' sub-domain where the behaviour of the classical ideal gas approximates that of the Bose and Fermi ideal gases is tutorially discussed. The entropy of any quantum system being always positive, the classical approximation can only be satisfactory within the parameters' sub-domain where the classical entropy turns out to be positive. We show that the sub-domain determined by this condition is close to that where de Broglie's thermal wavelength is smaller than the mean interparticle distance. The exact determination of the state parameters' region, where the particle number density, the grand potential and the entropy of quantum ideal gases differ from those of the classical gas less than a specified quantity, is also illustrated
Zaletel, Michael P; Bardarson, Jens H; Moore, Joel E
2011-07-08
Universal logarithmic terms in the entanglement entropy appear at quantum critical points (QCPs) in one dimension (1D) and have been predicted in 2D at QCPs described by 2D conformal field theories. The entanglement entropy in a strip geometry at such QCPs can be obtained via the "Shannon entropy" of a 1D spin chain with open boundary conditions. The Shannon entropy of the XXZ chain is found to have a logarithmic term that implies, for the QCP of the square-lattice quantum dimer model, a logarithm with universal coefficient ±0.25. However, the logarithm in the Shannon entropy of the transverse-field Ising model, which corresponds to entanglement in the 2D Ising conformal QCP, is found to have a singular dependence on the replica or Rényi index resulting from flows to different boundary conditions at the entanglement cut.
On the maximum entropy distributions of inherently positive nuclear data
Energy Technology Data Exchange (ETDEWEB)
Taavitsainen, A., E-mail: aapo.taavitsainen@gmail.com; Vanhanen, R.
2017-05-11
The multivariate log-normal distribution is used by many authors and statistical uncertainty propagation programs for inherently positive quantities. Sometimes it is claimed that the log-normal distribution results from the maximum entropy principle, if only means, covariances and inherent positiveness of quantities are known or assumed to be known. In this article we show that this is not true. Assuming a constant prior distribution, the maximum entropy distribution is in fact a truncated multivariate normal distribution – whenever it exists. However, its practical application to multidimensional cases is hindered by lack of a method to compute its location and scale parameters from means and covariances. Therefore, regardless of its theoretical disadvantage, use of other distributions seems to be a practical necessity. - Highlights: • Statistical uncertainty propagation requires a sampling distribution. • The objective distribution of inherently positive quantities is determined. • The objectivity is based on the maximum entropy principle. • The maximum entropy distribution is the truncated normal distribution. • Applicability of log-normal or normal distribution approximation is limited.
A Graphical Proof of the Positive Entropy Change in Heat Transfer between Two Objects
Kiatgamolchai, Somchai
2015-01-01
It is well known that heat transfer between two objects results in a positive change in the total entropy of the two-object system. The second law of thermodynamics states that the entropy change of a naturally irreversible process is positive. In other words, if the entropy change of any process is positive, it can be inferred that such a process…
Quantum information entropies for position-dependent mass Schrödinger problem
Energy Technology Data Exchange (ETDEWEB)
Yañez-Navarro, G. [Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, UPALM, Mexico D. F. 07738 (Mexico); 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); Dytrych, T., E-mail: tdytrych@gmail.com [Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001 (United States); Launey, K.D., E-mail: kristina@baton.phys.lsu.edu [Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001 (United States); Dong, Shi-Hai, E-mail: dongsh2@yahoo.com [Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, UPALM, Mexico 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)
2014-09-15
The Shannon entropy for the position-dependent Schrödinger equation for a particle with a nonuniform solitonic mass density is evaluated in the case of a trivial null potential. The position S{sub x} and momentum S{sub p} information entropies for the three lowest-lying states are calculated. In particular, for these states, we are able to derive analytical solutions for the S{sub x} entropy as well as for the Fourier transformed wave functions, while the S{sub p} quantity is calculated numerically. We notice the behavior of the S{sub x} entropy, namely, it decreases as the mass barrier width narrows and becomes negative beyond a particular width. The negative Shannon entropy exists for the probability densities that are highly localized. The mass barrier determines the stability of the system. The dependence of S{sub p} on the width is contrary to the one for S{sub x}. Some interesting features of the information entropy densities ρ{sub s}(x) and ρ{sub s}(p) are demonstrated. In addition, the Bialynicki-Birula–Mycielski (BBM) inequality is tested for a number of states and found to hold for all the cases.
Quantum information entropies for position-dependent mass Schrödinger problem
International Nuclear Information System (INIS)
Yañez-Navarro, G.; Sun, Guo-Hua; Dytrych, T.; Launey, K.D.; Dong, Shi-Hai; Draayer, J.P.
2014-01-01
The Shannon entropy for the position-dependent Schrödinger equation for a particle with a nonuniform solitonic mass density is evaluated in the case of a trivial null potential. The position S x and momentum S p information entropies for the three lowest-lying states are calculated. In particular, for these states, we are able to derive analytical solutions for the S x entropy as well as for the Fourier transformed wave functions, while the S p quantity is calculated numerically. We notice the behavior of the S x entropy, namely, it decreases as the mass barrier width narrows and becomes negative beyond a particular width. The negative Shannon entropy exists for the probability densities that are highly localized. The mass barrier determines the stability of the system. The dependence of S p on the width is contrary to the one for S x . Some interesting features of the information entropy densities ρ s (x) and ρ s (p) are demonstrated. In addition, the Bialynicki-Birula–Mycielski (BBM) inequality is tested for a number of states and found to hold for all the cases
International Nuclear Information System (INIS)
Park, Mu-In
2008-01-01
Recently, the Banados-Teitelboim-Zanelli (BTZ) black hole in the presence of the gravitational Chern-Simons term has been studied, and it is found that the usual thermodynamic quantities, like the black hole mass, angular momentum, and entropy, are modified. But, for large values of the gravitational Chern-Simons coupling where the modification terms dominate the original terms some exotic behaviors occur, like the roles of the mass and angular momentum are interchanged and the entropy depends more on the inner horizon area than the outer one. A basic physical problem of this system is that the form of entropy does not guarantee the second law of thermodynamics, in contrast to the Bekenstein-Hawking entropy. Moreover, this entropy does not agree with the statistical entropy, in contrast to a good agreement for small values of the gravitational Chern-Simons coupling. Here I find that there is another entropy formula where the usual Bekenstein-Hawking form dominates the inner-horizon term again, as in the small gravitational Chern-Simons coupling case, such that the second law of thermodynamics can be guaranteed. I also find that the new entropy formula agrees with the statistical entropy based on the holographic anomalies for the whole range of the gravitational Chern-Simons coupling. This reproduces, in the limit of a vanishing Einstein-Hilbert term, the recent result about the exotic BTZ black holes, where their masses and angular momenta are completely interchanged and the entropies depend only on the area of the inner horizon. I compare the result of the holographic approach with the classical-symmetry-algebra-based approach, and I find exact agreements even with the higher-derivative corrections of the gravitational Chern-Simons term. This provides a nontrivial check of the AdS/CFT correspondence, in the presence of higher-derivative terms in the gravity action
The Positive Topological Entropy Not Equivalent to Chaos——A Class of Subshifts
Institute of Scientific and Technical Information of China (English)
周作领; 廖公夫; 王兰宇
1994-01-01
In this paper,we have formed a class of the minimal chaotic subshifts having zero topological entropy and proved that the positive topological entropy is not equivalent to chaos occurring on the measure centre.
Evaluating the Wald entropy from two-derivative terms in quadratic actions
International Nuclear Information System (INIS)
Brustein, Ram; Gorbonos, Dan; Hadad, Merav; Medved, A. J. M.
2011-01-01
We evaluate the Wald Noether charge entropy for a black hole in generalized theories of gravity. Expanding the Lagrangian to second order in gravitational perturbations, we show that contributions to the entropy density originate only from the coefficients of two-derivative terms. The same considerations are extended to include matter fields and to show that arbitrary powers of matter fields and their symmetrized covariant derivatives cannot contribute to the entropy density. We also explain how to use the linearized gravitational field equation rather than quadratic actions to obtain the same results. Several explicit examples are presented that allow us to clarify subtle points in the derivation and application of our method.
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
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.
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.
Van Assche, W.; Yáñez, R. J.; Dehesa, J. S.
1995-08-01
The information entropy of the harmonic oscillator potential V(x)=1/2λx2 in both position and momentum spaces can be expressed in terms of the so-called ``entropy of Hermite polynomials,'' i.e., the quantity Sn(H):= -∫-∞+∞H2n(x)log H2n(x) e-x2dx. These polynomials are instances of the polynomials orthogonal with respect to the Freud weights w(x)=exp(-||x||m), m≳0. Here, a very precise and general result of the entropy of Freud polynomials recently established by Aptekarev et al. [J. Math. Phys. 35, 4423-4428 (1994)], specialized to the Hermite kernel (case m=2), leads to an important refined asymptotic expression for the information entropies of very excited states (i.e., for large n) in both position and momentum spaces, to be denoted by Sρ and Sγ, respectively. Briefly, it is shown that, for large values of n, Sρ+1/2logλ≂log(π√2n/e)+o(1) and Sγ-1/2log λ≂log(π√2n/e)+o(1), so that Sρ+Sγ≂log(2π2n/e2)+o(1) in agreement with the generalized indetermination relation of Byalinicki-Birula and Mycielski [Commun. Math. Phys. 44, 129-132 (1975)]. Finally, the rate of convergence of these two information entropies is numerically analyzed. In addition, using a Rakhmanov result, we describe a totally new proof of the leading term of the entropy of Freud polynomials which, naturally, is just a weak version of the aforementioned general result.
International Nuclear Information System (INIS)
Luo Qiang; Schwarz, Bjoern; Mattern, Norbert; Eckert, Juergen
2010-01-01
We study the effects of amorphous structure and random anisotropy on the magnetic entropy change in a series of Tb-based amorphous alloys. The amorphous structure broadens the peak of magnetic entropy change and facilitates the adjustment of properties. The peak magnetic entropy change above the spin freezing temperature first depends on the average magnetic moment approximately linearly and second on the exchange interaction and random anisotropy. Large and broad reversible negative magnetic entropy changes are observed above the spin freezing temperature and giant positive irreversible magnetic entropy changes which associate with the internal entropy production are obtained well below.
On the entropy of four-dimensional near-extremal N = 2 black holes with R2-terms
International Nuclear Information System (INIS)
Gruss, Eyal; Oz, Yaron
2007-01-01
We consider the entropy of four-dimensional near-extremal N = 2 black holes. The Bekenstein-Hawking entropy formula has the structure of the extremal black holes entropy with a shift of the charges depending on the non-extremality parameter and the moduli at infinity. We construct a class of near-extremal horizon solutions with R 2 -terms, and show that the generalized Wald entropy formula exhibits the same property
Entanglement Entropy of Reissner—Nordström Black Hole and Quantum Isolated Horizon
International Nuclear Information System (INIS)
Ma Meng-Sen; Zhang Li-Chun; Zhao Ren
2014-01-01
Based on the work of Ghosh and Pereze, who view the black hole entropy as the logarithm of the number of quantum states on the Quantum Isolated Horizon (QIH) § the entropy of Reissner—Nordström black hole is studied. According to the Unruh temperature, the statistical entropy of quantum fields under the background of Reissner—Nordström spacetime is calculated by means of quantum statistics. In the calculations we take the integral from the position of QIH to infinity, so the obtained entropy is the entanglement entropy outside the QIH. In Reissner—Nordström spacetime it is shown that if only the position of QIH is properly chosen the leading term of logarithm of the number of quantum states on the QIH is equal to the leading term of the entanglement entropy outside the black hole horizon, and both are the Bekenstein—Hawking entropy. The results reveal the relation between the entanglement entropy of black hole and the logarithm of the number of quantum states. (general)
ENTROPY FLOW CHARACTERISTICS ANALYSIS OF TYPHOON MATSA (0509)
Institute of Scientific and Technical Information of China (English)
XU Hui; LIU Chong-jian
2008-01-01
The evolution of Typhoon Matsa (0509) is examined in terms of entropy flow through an entropy balance equation derived from the Gibbs relation, according to the second law of thermodynamics. The entropy flows in the various significant stages of (genesis, development and decaying) during its evolution are diagnosed based on the outputs of the PSU/NCAR mesoscale model (known as MM5). The results show that: (1) the vertical spatial distribution of entropy flow for Matsa is characterized by a predominantly negative entropy flow in a large portion of the troposphere and a positive flow in the upper levels; (2) the fields of entropy flows at the middle troposphere (500 hPa) show that the growth of the typhoon is greatly dependent on the negative entropy flows from its surroundings; and (3) the simulated centres of heavy rainfall associated with the typhoon match well with the zones of large negative entropy flows, suggesting that they may be a significant indicator for severe weather events.
Quantifying complexity of financial short-term time series by composite multiscale entropy measure
Niu, Hongli; Wang, Jun
2015-05-01
It is significant to study the complexity of financial time series since the financial market is a complex evolved dynamic system. Multiscale entropy is a prevailing method used to quantify the complexity of a time series. Due to its less reliability of entropy estimation for short-term time series at large time scales, a modification method, the composite multiscale entropy, is applied to the financial market. To qualify its effectiveness, its applications in the synthetic white noise and 1 / f noise with different data lengths are reproduced first in the present paper. Then it is introduced for the first time to make a reliability test with two Chinese stock indices. After conducting on short-time return series, the CMSE method shows the advantages in reducing deviations of entropy estimation and demonstrates more stable and reliable results when compared with the conventional MSE algorithm. Finally, the composite multiscale entropy of six important stock indices from the world financial markets is investigated, and some useful and interesting empirical results are obtained.
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.)
Generalized Uncertainty Principle and Black Hole Entropy of Higher-Dimensional de Sitter Spacetime
International Nuclear Information System (INIS)
Zhao Haixia; Hu Shuangqi; Zhao Ren; Li Huaifan
2007-01-01
Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein-Hawking black hole entropy. In particular, many researchers have expressed a vested interest in the coefficient of the logarithmic term of the black hole entropy correction term. In this paper, we calculate the correction value of the black hole entropy by utilizing the generalized uncertainty principle and obtain the correction term caused by the generalized uncertainty principle. Because in our calculation we think that the Bekenstein-Hawking area theorem is still valid after considering the generalized uncertainty principle, we derive that the coefficient of the logarithmic term of the black hole entropy correction term is positive. This result is different from the known result at present. Our method is valid not only for four-dimensional spacetimes but also for higher-dimensional spacetimes. In the whole process, the physics idea is clear and calculation is simple. It offers a new way for studying the entropy correction of the complicated spacetime.
Relative entropy, mixed gauge-gravitational anomaly and causality
Energy Technology Data Exchange (ETDEWEB)
Bhattacharyya, Arpan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Centre For High Energy Phsyics, Indian Institute of Science,560012 Bangalore (India); Cheng, Long [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Hung, Ling-Yan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Collaborative Innovation Center of Advanced Microstructures, Fudan University,220 Handan Road, 200433 Shanghai (China)
2016-07-25
In this note we explored the holographic relative entropy in the presence of the 5d Chern-Simons term, which introduces a mixed gauge-gravity anomaly to the dual CFT. The theory trivially satisfies an entanglement first law. However, to quadratic order in perturbations of the stress tensor T and current density J, there is a mixed contribution to the relative entropy bi-linear in T and J, signalling a potential violation of the positivity of the relative entropy. Miraculously, the term vanishes up to linear order in a derivative expansion. This prompted a closer inspection on a different consistency check, that involves time-delay of a graviton propagating in a charged background, scattered via a coupling supplied by the Chern-Simons term. The analysis suggests that the time-delay can take either sign, potentially violating causality for any finite value of the CS coupling.
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.)
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.)
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
Finite entanglement entropy and spectral dimension in quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Arzano, Michele [Rome Univ. (Italy). Dipt. di Fisica; INFN, Rome (Italy); Calcagni, Gianluca [CSIC, Madrid (Spain). Inst. de Estructura de la Materia
2017-12-15
What are the conditions on a field theoretic model leading to a finite entanglement entropy density? We prove two very general results: (1) Ultraviolet finiteness of a theory does not guarantee finiteness of the entropy density; (2) If the spectral dimension of the spatial boundary across which the entropy is calculated is non-negative at all scales, then the entanglement entropy cannot be finite. These conclusions, which we verify in several examples, negatively affect all quantum-gravity models, since their spectral dimension is always positive. Possible ways out are considered, including abandoning the definition of the entanglement entropy in terms of the boundary return probability or admitting an analytic continuation (not a regularization) of the usual definition. In the second case, one can get a finite entanglement entropy density in multi-fractional theories and causal dynamical triangulations. (orig.)
Finite entanglement entropy and spectral dimension in quantum gravity
Arzano, Michele; Calcagni, Gianluca
2017-12-01
What are the conditions on a field theoretic model leading to a finite entanglement entropy density? We prove two very general results: (1) Ultraviolet finiteness of a theory does not guarantee finiteness of the entropy density; (2) If the spectral dimension of the spatial boundary across which the entropy is calculated is non-negative at all scales, then the entanglement entropy cannot be finite. These conclusions, which we verify in several examples, negatively affect all quantum-gravity models, since their spectral dimension is always positive. Possible ways out are considered, including abandoning the definition of the entanglement entropy in terms of the boundary return probability or admitting an analytic continuation (not a regularization) of the usual definition. In the second case, one can get a finite entanglement entropy density in multi-fractional theories and causal dynamical triangulations.
Finite entanglement entropy and spectral dimension in quantum gravity
International Nuclear Information System (INIS)
Arzano, Michele; Calcagni, Gianluca
2017-01-01
What are the conditions on a field theoretic model leading to a finite entanglement entropy density? We prove two very general results: (1) Ultraviolet finiteness of a theory does not guarantee finiteness of the entropy density; (2) If the spectral dimension of the spatial boundary across which the entropy is calculated is non-negative at all scales, then the entanglement entropy cannot be finite. These conclusions, which we verify in several examples, negatively affect all quantum-gravity models, since their spectral dimension is always positive. Possible ways out are considered, including abandoning the definition of the entanglement entropy in terms of the boundary return probability or admitting an analytic continuation (not a regularization) of the usual definition. In the second case, one can get a finite entanglement entropy density in multi-fractional theories and causal dynamical triangulations. (orig.)
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.
Entropy correlation and entanglement for mixed states in an algebraic model
International Nuclear Information System (INIS)
Hou Xiwen; Chen Jinghua; Wan Mingfang; Ma Zhongqi
2009-01-01
As an alternative with potential connections to actual experiments, other than the systems more usually used in the field of entanglement, the dynamics of entropy correlation and entanglement between two anharmonic vibrations in a well-established algebraic model, with parameters extracted from fitting to highly excited spectral experimental results for molecules H 2 O and SO 2 , is studied in terms of the linear entropy and two negativities for various initial states that are respectively taken to be the mixed density matrices of thermal states and squeezed states on each mode. For a suitable parameter in initial states the entropies in two stretches can show positive correlation or anti-correlation. And the linear entropy of each mode is positively correlated with the negativities just for the mixed-squeezed states with small parameters in H 2 O while they do not display any correlation in other cases. For the mixed-squeezed states the negativities exhibit dominantly positive correlations with an effective mutual entropy. The differences in the linear entropy and the negativities between H 2 O and SO 2 are discussed as well. Those are useful for molecular quantum computing and quantum information processing
Chaoticity of interval self-maps with positive entropy
International Nuclear Information System (INIS)
Xiong Jincheng.
1988-12-01
Li and Yorke originally introduced the notion of chaos for continuous self-map of the interval I = (0,1). In the present paper we show that an interval self-map with positive topological entropy has a chaoticity more complicated than the chaoticity in the sense of Li and Yorke. The main result is that if f:I → I is continuous and has a periodic point with odd period > 1 then there exists a closed subset K of I invariant with respect to f such that the periodic points are dense in K, the periods of periodic points in K form an infinite set and f|K is topologically mixing. (author). 9 refs
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.
Universal terms of entanglement entropy for 6d CFTs
International Nuclear Information System (INIS)
Miao, Rong-Xin
2015-01-01
We derive the universal terms of entanglement entropy for 6d CFTs by applying the holographic and the field theoretical approaches, respectively. Our formulas are conformal invariant and agree with the results of http://dx.doi.org/10.1007/JHEP04(2011)025 http://dx.doi.org/10.1007/JHEP12(2012)005. Remarkably, we find that the holographic and the field theoretical results match exactly for the C 2 and Ck 2 terms, where C and k denote the Weyl tensor and the extrinsic curvature, respectively. As for the k 4 terms, we meet the splitting problem of the conical metrics. The splitting problem in the bulk can be fixed by equations of motion. As for the splitting on the boundary, we assume the general forms and find that there indeed exists suitable splitting which can make the holographic and the field theoretical k 4 terms match. Since we have much more equations than the free parameters, the match for k 4 terms is non-trivial.
Noether Current of the Surface Term of Einstein-Hilbert Action, Virasoro Algebra, and Entropy
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Bibhas Ranjan Majhi
2013-01-01
Full Text Available A derivation of Noether current from the surface term of Einstein-Hilbert action is given. We show that the corresponding charge, calculated on the horizon, is related to the Bekenstein-Hawking entropy. Also using the charge, the same entropy is found based on the Virasoro algebra and Cardy formula approach. In this approach, the relevant diffeomorphisms are found by imposing a very simple physical argument: diffeomorphisms keep the horizon structure invariant. This complements similar earlier results (Majhi and Padmanabhan (2012 (arXiv:1204.1422 obtained from York-Gibbons-Hawking surface term. Finally we discuss the technical simplicities and improvements over the earlier attempts and also various important physical implications.
Comparison of transfer entropy methods for financial time series
He, Jiayi; Shang, Pengjian
2017-09-01
There is a certain relationship between the global financial markets, which creates an interactive network of global finance. Transfer entropy, a measurement for information transfer, offered a good way to analyse the relationship. In this paper, we analysed the relationship between 9 stock indices from the U.S., Europe and China (from 1995 to 2015) by using transfer entropy (TE), effective transfer entropy (ETE), Rényi transfer entropy (RTE) and effective Rényi transfer entropy (ERTE). We compared the four methods in the sense of the effectiveness for identification of the relationship between stock markets. In this paper, two kinds of information flows are given. One reveals that the U.S. took the leading position when in terms of lagged-current cases, but when it comes to the same date, China is the most influential. And ERTE could provide superior results.
A New Chaotic System with Positive Topological Entropy
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Zhonglin Wang
2015-08-01
Full Text Available This paper introduces a new simple system with a butterfly chaotic attractor. This system has rich and complex dynamics. With some typical parameters, its Lyapunov dimension is greater than other known three dimensional chaotic systems. It exhibits chaotic behavior over a large range of parameters, and the divergence of flow of this system is not a constant. The dynamics of this new system are analyzed via Lyapunov exponent spectrum, bifurcation diagrams, phase portraits and the Poincaré map. The compound structures of this new system are also analyzed. By means of topological horseshoe theory and numerical computation, the Poincaré map defined for the system is proved to be semi-conjugate to 3-shift map, and thus the system has positive topological entropy.
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.
Fisher-Renyi entropy product and information plane
International Nuclear Information System (INIS)
Romera, E.; Nagy, A.
2008-01-01
Connection between Fisher information and Renyi entropy has been established. This link allows us to define the Fisher-Renyi information plane and an entropic product in terms of these quantities. New Renyi uncertainty relations are obtained for single particle densities of many particle systems in position-momentum conjugate spaces
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)
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)
Entanglement Entropy of AdS Black Holes
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Maurizio Melis
2010-11-01
Full Text Available We review recent progress in understanding the entanglement entropy of gravitational configurations for anti-de Sitter gravity in two and three spacetime dimensions using the AdS/CFT correspondence. We derive simple expressions for the entanglement entropy of two- and three-dimensional black holes. In both cases, the leading term of the entanglement entropy in the large black hole mass expansion reproduces exactly the Bekenstein-Hawking entropy, whereas the subleading term behaves logarithmically. In particular, for the BTZ black hole the leading term of the entanglement entropy can be obtained from the large temperature expansion of the partition function of a broad class of 2D CFTs on the torus.
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 .
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...
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}.
International Nuclear Information System (INIS)
Tang, Pingzhou; Chen, Di; Hou, Yushuo
2016-01-01
As the world’s energy problem becomes more severe day by day, photovoltaic power generation has opened a new door for us with no doubt. It will provide an effective solution for this severe energy problem and meet human’s needs for energy if we can apply photovoltaic power generation in real life, Similar to wind power generation, photovoltaic power generation is uncertain. Therefore, the forecast of photovoltaic power generation is very crucial. In this paper, entropy method and extreme learning machine (ELM) method were combined to forecast a short-term photovoltaic power generation. First, entropy method is used to process initial data, train the network through the data after unification, and then forecast electricity generation. Finally, the data results obtained through the entropy method with ELM were compared with that generated through generalized regression neural network (GRNN) and radial basis function neural network (RBF) method. We found that entropy method combining with ELM method possesses higher accuracy and the calculation is faster.
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.
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)
Maximum entropy method approach to the θ term
International Nuclear Information System (INIS)
Imachi, Masahiro; Shinno, Yasuhiko; Yoneyama, Hiroshi
2004-01-01
In Monte Carlo simulations of lattice field theory with a θ term, one confronts the complex weight problem, or the sign problem. This is circumvented by performing the Fourier transform of the topological charge distribution P(Q). This procedure, however, causes flattening phenomenon of the free energy f(θ), which makes study of the phase structure unfeasible. In order to treat this problem, we apply the maximum entropy method (MEM) to a Gaussian form of P(Q), which serves as a good example to test whether the MEM can be applied effectively to the θ term. We study the case with flattering as well as that without flattening. In the latter case, the results of the MEM agree with those obtained from the direct application of the Fourier transform. For the former, the MEM gives a smoother f(θ) than that of the Fourier transform. Among various default models investigated, the images which yield the least error do not show flattening, although some others cannot be excluded given the uncertainly related to statistical error. (author)
Entanglement Entropy for the charged BTZ black hole
International Nuclear Information System (INIS)
Larrañaga, A.
2011-01-01
Using the AdS/CFT correspondence we calculate the explicit form of the entanglement entropy for the charged BTZ (Banados-Teitelboim-Zanelli) black hole. The leading term in the large temperature expansion of the entropy function for this black hole reproduces its Bekenstein-Hawking entropy and the subleading term, representing the first corrections due to quantum entanglement, behaves as a logarithm of the BH entropy. It has also been obtained an inverse of area term in subleading order similar to the reported when considering Hawking radiation as quantum tunneling of particles through the event horizon
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.
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.
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.
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.
Dynamics of entropy perturbations in assisted dark energy with mixed kinetic terms
International Nuclear Information System (INIS)
Karwan, Khamphee
2011-01-01
We study dynamics of entropy perturbations in the two-field assisted dark energy model. Based on the scenario of assisted dark energy, in which one scalar field is subdominant compared with the other in the early epoch, we show that the entropy perturbations in this two-field system tend to be constant on large scales in the early epoch and hence survive until the present era for a generic evolution of both fields during the radiation and matter eras. This behaviour of the entropy perturbations is preserved even when the fields are coupled via kinetic interaction. Since, for assisted dark energy, the subdominant field in the early epoch becomes dominant at late time, the entropy perturbations can significantly influence the dynamics of density perturbations in the universe. Assuming correlations between the entropy and curvature perturbations, the entropy perturbations can enhance the integrated Sachs-Wolfe (ISW) effect if the signs of the contributions from entropy perturbations and curvature perturbations are opposite after the matter era, otherwise the ISW contribution is suppressed. For canonical scalar field the effect of entropy perturbations on ISW effect is small because the initial value of the entropy perturbations estimated during inflation cannot be sufficiently large. However, in the case of k-essence, the initial value of the entropy perturbations can be large enough to affect the ISW effect to leave a significant imprint on the CMB power spectrum
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
Quantumness of bipartite states in terms of conditional entropies
International Nuclear Information System (INIS)
Li, Nan; Luo, Shunlong; Zhang, Zhengmin
2007-01-01
Quantum discord, as defined by Olliver and Zurek (2002 Phys. Rev. Lett. 88 017901) as the difference of two natural quantum extensions of the classical mutual information, plays an interesting role in characterizing quantumness of correlations. Inspired by this idea, we will study quantumness of bipartite states arising from different quantum analogs of the classical conditional entropy. Our approach is intrinsic, in contrast to the Olliver-Zurek method that involves extrinsic local measurements. For this purpose, we introduce two alternative variants of quantum conditional entropies via conditional density operators, which in turn are intuitive quantum extensions of equivalent classical expressions for the conditional probability. The significance of these quantum conditional entropies in characterizing quantumness of bipartite states is illustrated through several examples
Thermal Expansion Anomaly Regulated by Entropy
Liu, Zi-Kui; Wang, Yi; Shang, Shunli
2014-11-01
Thermal expansion, defined as the temperature dependence of volume under constant pressure, is a common phenomenon in nature and originates from anharmonic lattice dynamics. However, it has been poorly understood how thermal expansion can show anomalies such as colossal positive, zero, or negative thermal expansion (CPTE, ZTE, or NTE), especially in quantitative terms. Here we show that changes in configurational entropy due to metastable micro(scopic)states can lead to quantitative prediction of these anomalies. We integrate the Maxwell relation, statistic mechanics, and first-principles calculations to demonstrate that when the entropy is increased by pressure, NTE occurs such as in Invar alloy (Fe3Pt, for example), silicon, ice, and water, and when the entropy is decreased dramatically by pressure, CPTE is expected such as in anti-Invar cerium, ice and water. Our findings provide a theoretic framework to understand and predict a broad range of anomalies in nature in addition to thermal expansion, which may include gigantic electrocaloric and electromechanical responses, anomalously reduced thermal conductivity, and spin distributions.
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
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.
Fermion Fields in BTZ Black Hole Space-Time and Entanglement Entropy
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Dharm Veer Singh
2015-01-01
Full Text Available We study the entanglement entropy of fermion fields in BTZ black hole space-time and calculate prefactor of the leading and subleading terms and logarithmic divergence term of the entropy using the discretized model. The leading term is the standard Bekenstein-Hawking area law and subleading term corresponds to first quantum corrections in black hole entropy. We also investigate the corrections to entanglement entropy for massive fermion fields in BTZ space-time. The mass term does not affect the area law.
RNA Thermodynamic Structural Entropy.
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Juan Antonio Garcia-Martin
Full Text Available Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe the first two accurate and efficient algorithms to compute the conformational entropy for RNA secondary structures, with respect to the Turner energy model, where free energy parameters are determined from UV absorption experiments. An algorithm to compute the derivational entropy for RNA secondary structures had previously been introduced, using stochastic context free grammars (SCFGs. However, the numerical value of derivational entropy depends heavily on the chosen context free grammar and on the training set used to estimate rule probabilities. Using data from the Rfam database, we determine that both of our thermodynamic methods, which agree in numerical value, are substantially faster than the SCFG method. Thermodynamic structural entropy is much smaller than derivational entropy, and the correlation between length-normalized thermodynamic entropy and derivational entropy is moderately weak to poor. In applications, we plot the structural entropy as a function of temperature for known thermoswitches, such as the repression of heat shock gene expression (ROSE element, we determine that the correlation between hammerhead ribozyme cleavage activity and total free energy is improved by including an additional free energy term arising from conformational entropy, and we plot the structural entropy of windows of the HIV-1 genome. Our software RNAentropy can compute structural entropy for any user-specified temperature, and supports both the Turner'99 and Turner'04 energy parameters. It follows that RNAentropy is state-of-the-art software to compute RNA secondary structure conformational entropy. Source code is available at https://github.com/clotelab/RNAentropy/; a full web server is available at http
RNA Thermodynamic Structural Entropy.
Garcia-Martin, Juan Antonio; Clote, Peter
2015-01-01
Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe the first two accurate and efficient algorithms to compute the conformational entropy for RNA secondary structures, with respect to the Turner energy model, where free energy parameters are determined from UV absorption experiments. An algorithm to compute the derivational entropy for RNA secondary structures had previously been introduced, using stochastic context free grammars (SCFGs). However, the numerical value of derivational entropy depends heavily on the chosen context free grammar and on the training set used to estimate rule probabilities. Using data from the Rfam database, we determine that both of our thermodynamic methods, which agree in numerical value, are substantially faster than the SCFG method. Thermodynamic structural entropy is much smaller than derivational entropy, and the correlation between length-normalized thermodynamic entropy and derivational entropy is moderately weak to poor. In applications, we plot the structural entropy as a function of temperature for known thermoswitches, such as the repression of heat shock gene expression (ROSE) element, we determine that the correlation between hammerhead ribozyme cleavage activity and total free energy is improved by including an additional free energy term arising from conformational entropy, and we plot the structural entropy of windows of the HIV-1 genome. Our software RNAentropy can compute structural entropy for any user-specified temperature, and supports both the Turner'99 and Turner'04 energy parameters. It follows that RNAentropy is state-of-the-art software to compute RNA secondary structure conformational entropy. Source code is available at https://github.com/clotelab/RNAentropy/; a full web server is available at http
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)
Properties of Risk Measures of Generalized Entropy in Portfolio Selection
Directory of Open Access Journals (Sweden)
Rongxi Zhou
2017-12-01
Full Text Available This paper systematically investigates the properties of six kinds of entropy-based risk measures: Information Entropy and Cumulative Residual Entropy in the probability space, Fuzzy Entropy, Credibility Entropy and Sine Entropy in the fuzzy space, and Hybrid Entropy in the hybridized uncertainty of both fuzziness and randomness. We discover that none of the risk measures satisfy all six of the following properties, which various scholars have associated with effective risk measures: Monotonicity, Translation Invariance, Sub-additivity, Positive Homogeneity, Consistency and Convexity. Measures based on Fuzzy Entropy, Credibility Entropy, and Sine Entropy all exhibit the same properties: Sub-additivity, Positive Homogeneity, Consistency, and Convexity. These measures based on Information Entropy and Hybrid Entropy, meanwhile, only exhibit Sub-additivity and Consistency. Cumulative Residual Entropy satisfies just Sub-additivity, Positive Homogeneity, and Convexity. After identifying these properties, we develop seven portfolio models based on different risk measures and made empirical comparisons using samples from both the Shenzhen Stock Exchange of China and the New York Stock Exchange of America. The comparisons show that the Mean Fuzzy Entropy Model performs the best among the seven models with respect to both daily returns and relative cumulative returns. Overall, these results could provide an important reference for both constructing effective risk measures and rationally selecting the appropriate risk measure under different portfolio selection conditions.
Unification of Quantum and Gravity by Non Classical Information Entropy Space
Directory of Open Access Journals (Sweden)
Davide Fiscaletti
2013-09-01
Full Text Available A quantum entropy space is suggested as the fundamental arena describing the quantum effects. In the quantum regime the entropy is expressed as the superposition of many different Boltzmann entropies that span the space of the entropies before any measure. When a measure is performed the quantum entropy collapses to one component. A suggestive reading of the relational interpretation of quantum mechanics and of Bohm’s quantum potential in terms of the quantum entropy are provided. The space associated with the quantum entropy determines a distortion in the classical space of position, which appears as a Weyl-like gauge potential connected with Fisher information. This Weyl-like gauge potential produces a deformation of the moments which changes the classical action in such a way that Bohm’s quantum potential emerges as consequence of the non classical definition of entropy, in a non-Euclidean information space under the constraint of a minimum condition of Fisher information (Fisher Bohm- entropy. Finally, the possible quantum relativistic extensions of the theory and the connections with the problem of quantum gravity are investigated. The non classical thermodynamic approach to quantum phenomena changes the geometry of the particle phase space. In the light of the representation of gravity in ordinary phase space by torsion in the flat space (Teleparallel gravity, the change of geometry in the phase space introduces quantum phenomena in a natural way. This gives a new force to F. Shojai’s and A. Shojai’s theory where the geometry of space-time is highly coupled with a quantum potential whose origin is not the Schrödinger equation but the non classical entropy of a system of many particles that together change the geometry of the phase space of the positions (entanglement. In this way the non classical thermodynamic changes the classical geodetic as a consequence of the quantum phenomena and quantum and gravity are unified. Quantum
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...
Asymptotics of the information entropy of the Airy function
Energy Technology Data Exchange (ETDEWEB)
Sanchez-Moreno, P [Departamento de Fisica Moderna, Universidad de Granada, Granada (Spain); Instituto ' Carlos I' de Fisica Teorica y Computacional, Universidad de Granada, Granada (Spain); Yanez, R J [Instituto ' Carlos I' de Fisica Teorica y Computacional, Universidad de Granada, Granada (Spain); Departamento de Matematica Aplicada, Universidad de Granada, Granada (Spain); Buyarov, V [Moscow State University (Russian Federation)
2005-11-18
The Boltzmann-Shannon information entropy of linear potential wavefunctions is known to be controlled by the information entropy of the Airy function Ai(x). Here, the entropy asymptotics is analysed so that the first two leading terms (previously calculated in the WKB approximation) as well as the following term (already conjectured) are derived by using only the specific properties of the Airy function.
Entropy, pricing and macroeconomics of pumped-storage systems
Karakatsanis, Georgios; Mamassis, Nikos; Koutsoyiannis, Demetris; Efstratiadis, Andreas
2014-05-01
We propose a pricing scheme for the enhancement of macroeconomic performance of pumped-storage systems, based on the statistical properties of both geophysical and economic variables. The main argument consists in the need of a context of economic values concerning the hub energy resource; defined as the resource that comprises the reference energy currency for all involved renewable energy sources (RES) and discounts all related uncertainty. In the case of pumped-storage systems the hub resource is the reservoir's water, as a benchmark for all connected intermittent RES. The uncertainty of all involved natural and economic processes is statistically quantifiable by entropy. It is the relation between the entropies of all involved RES that shapes the macroeconomic state of the integrated pumped-storage system. Consequently, there must be consideration on the entropy of wind, solar and precipitation patterns, as well as on the entropy of economic processes -such as demand preferences on either current energy use or storage for future availability. For pumped-storage macroeconomics, a price on the reservoir's capacity scarcity should also be imposed in order to shape a pricing field with upper and lower limits for the long-term stability of the pricing range and positive net energy benefits, which is the primary issue of the generalized deployment of pumped-storage technology. Keywords: Entropy, uncertainty, pricing, hub energy resource, RES, energy storage, capacity scarcity, macroeconomics
International Nuclear Information System (INIS)
Cvetic, Mirjam; Nojiri, Shin'ichi; Odintsov, S.D.
2002-01-01
We investigate the charged Schwarzschild-anti-de Sitter (SAdS) BH thermodynamics in 5d Einstein-Gauss-Bonnet gravity with electromagnetic field. The Hawking-Page phase transitions between SAdS BH and pure AdS space are studied. The corresponding phase diagrams (with critical line defined by GB term coefficient and electric charge) are drawn. The possibility to account for higher derivative Maxwell terms is mentioned. In frames of proposed dS/CFT correspondence it is demonstrated that brane gravity maybe localized similarly to AdS/CFT. SdS BH thermodynamics in 5d Einstein and Einstein-Gauss-Bonnet gravity is considered. The corresponding (complicated) surface counterterms are found and used to get the conserved BH mass, free energy and entropy. The interesting feature of higher derivative gravity is the possibility for negative (or zero) SdS (or SAdS) BH entropy which depends on the parameters of higher derivative terms. We speculate that the appearance of negative entropy may indicate a new type instability where a transition between SdS (SAdS) BH with negative entropy to SAdS (SdS) BH with positive entropy would occur
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...
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...
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
Frenetic Bounds on the Entropy Production
Maes, Christian
2017-10-01
We give a systematic derivation of positive lower bounds for the expected entropy production (EP) rate in classical statistical mechanical systems obeying a dynamical large deviation principle. The logic is the same for the return to thermodynamic equilibrium as it is for steady nonequilibria working under the condition of local detailed balance. We recover there recently studied "uncertainty" relations for the EP, appearing in studies about the effectiveness of mesoscopic machines. In general our refinement of the positivity of the expected EP rate is obtained in terms of a positive and even function of the expected current(s) which measures the dynamical activity in the system, a time-symmetric estimate of the changes in the system's configuration. Also underdamped diffusions can be included in the analysis.
International Nuclear Information System (INIS)
Ejtehadi, Omid; Esfahani, Javad Abolfazli; Roohi, Ehsan
2012-01-01
In the present work, compressible flow of argon gas in the famous problem of Couette flow in micro/nano-scale is considered and numerically analyzed using the direct simulation Monte Carlo (DSMC) method. The effects of compressibility and rarefaction on entropy and entropy generation in terms of viscous dissipation and thermal diffusion are studied in a wide range of Mach and Knudsen numbers and the observed physics are discussed. In this regard, we computed entropy by using its kinetic theory formulation in a microscopic way while the entropy generation distribution is achieved by applying a semi-microscopic approach and thoroughly free from equilibrium assumptions. The results of our simulations demonstrated that the entropy profiles are in accordance with the temperature profiles. It is also illustrated that the increase of Mach number will result in non-uniform entropy profiles with increase in the vicinity of the central regions of the channel. Moreover, generation of entropy in all regions of the domain stages clear growth. By contrast, increasing the Knudsen number has inverse effects such as: uniform entropy profiles and a falling off in entropy generation amount throughout the channel.
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.
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.
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.
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
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.
Entropy Error Model of Planar Geometry Features in GIS
Institute of Scientific and Technical Information of China (English)
LI Dajun; GUAN Yunlan; GONG Jianya; DU Daosheng
2003-01-01
Positional error of line segments is usually described by using "g-band", however, its band width is in relation to the confidence level choice. In fact, given different confidence levels, a series of concentric bands can be obtained. To overcome the effect of confidence level on the error indicator, by introducing the union entropy theory, we propose an entropy error ellipse index of point, then extend it to line segment and polygon,and establish an entropy error band of line segment and an entropy error donut of polygon. The research shows that the entropy error index can be determined uniquely and is not influenced by confidence level, and that they are suitable for positional uncertainty of planar geometry features.
Proof of the holographic formula for entanglement entropy
International Nuclear Information System (INIS)
Fursaev, Dmitri V.
2006-01-01
Entanglement entropy for a spatial partition of a quantum system is studied in theories which admit a dual description in terms of the anti-de Sitter (AdS) gravity one dimension higher. A general proof of the holographic formula which relates the entropy to the area of a codimension 2 minimal hypersurface embedded in the bulk AdS space is given. The entanglement entropy is determined by a partition function which is defined as a path integral over Riemannian AdS geometries with non-trivial boundary conditions. The topology of the Riemannian spaces puts restrictions on the choice of the minimal hypersurface for a given boundary conditions. The entanglement entropy is also considered in Randall-Sundrum braneworld models where its asymptotic expansion is derived when the curvature radius of the brane is much larger than the AdS radius. Special attention is paid to the geometrical structure of anomalous terms in the entropy in four dimensions. Modification of the holographic formula by the higher curvature terms in the bulk is briefly discussed
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...
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.
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
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.
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)
Kadanoff, Leo P.
2017-05-01
The science of thermodynamics was put together in the Nineteenth Century to describe large systems in equilibrium. One part of thermodynamics defines entropy for equilibrium systems and demands an ever-increasing entropy for non-equilibrium ones. Since thermodynamics does not define entropy out of equilibrium, pure thermodynamics cannot follow the details of how this increase occurs. However, starting with the work of Ludwig Boltzmann in 1872, and continuing to the present day, various models of non-equilibrium behavior have been put together with the specific aim of generalizing the concept of entropy to non-equilibrium situations. This kind of entropy has been termed kinetic entropy to distinguish it from the thermodynamic variety. Knowledge of kinetic entropy started from Boltzmann's insight about his equation for the time dependence of gaseous systems. In this paper, his result is stated as a definition of kinetic entropy in terms of a local equation for the entropy density. This definition is then applied to Landau's theory of the Fermi liquid thereby giving the kinetic entropy within that theory. The dynamics of many condensed matter systems including Fermi liquids, low temperature superfluids, and ordinary metals lend themselves to the definition of kinetic entropy. In fact, entropy has been defined and used for a wide variety of situations in which a condensed matter system has been allowed to relax for a sufficient period so that the very most rapid fluctuations have been ironed out. One of the broadest applications of non-equilibrium analysis considers quantum degenerate systems using Martin-Schwinger Green's functions (Phys Rev 115:1342-1373, 1959) as generalized Wigner functions, g^({p},ω ,{R},T). This paper describes once again how the quantum kinetic equations for these functions give locally defined conservation laws for mass momentum and energy. In local thermodynamic equilibrium, this kinetic theory enables a reasonable definition of the density
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 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.
Multiscale Shannon entropy and its application in the stock market
Gu, Rongbao
2017-10-01
In this paper, we perform a multiscale entropy analysis on the Dow Jones Industrial Average Index using the Shannon entropy. The stock index shows the characteristic of multi-scale entropy that caused by noise in the market. The entropy is demonstrated to have significant predictive ability for the stock index in both long-term and short-term, and empirical results verify that noise does exist in the market and can affect stock price. It has important implications on market participants such as noise traders.
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
Quantum information entropies of the eigenstates for the Pöschl—Teller-like potential
International Nuclear Information System (INIS)
Sun Guo-Hua; Aoki, M. Avila; Dong Shi-Hai
2013-01-01
Shannon entropy for lower position and momentum eigenstates of Pöschl—Teller-like potential is evaluated. Based on the entropy densities demonstrated graphically, we note that the wave through of the position information entropy density ρ(x) moves right when the potential parameter V 1 increases and its amplitude decreases. However, its wave through moves left with the increase in the potential parameter |V 2 |. Concerning the momentum information entropy density ρ(p), we observe that its amplitude increases with increasing potential parameter V 1 , but its amplitude decreases with increasing |V 2 |. The Bialynicki—Birula—Mycielski (BBM) inequality has also been tested for a number of states. Moreover, there exist eigenstates that exhibit squeezing in the momentum information entropy. Finally, we note that position information entropy increases with V 1 , but decreases with |V 2 |. However, the variation of momentum information entropy is contrary to that of the position information entropy. (general)
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.
A Note on Burg’s Modified Entropy in Statistical Mechanics
Directory of Open Access Journals (Sweden)
Amritansu Ray
2016-02-01
Full Text Available Burg’s entropy plays an important role in this age of information euphoria, particularly in understanding the emergent behavior of a complex system such as statistical mechanics. For discrete or continuous variable, maximization of Burg’s Entropy subject to its only natural and mean constraint always provide us a positive density function though the Entropy is always negative. On the other hand, Burg’s modified entropy is a better measure than the standard Burg’s entropy measure since this is always positive and there is no computational problem for small probabilistic values. Moreover, the maximum value of Burg’s modified entropy increases with the number of possible outcomes. In this paper, a premium has been put on the fact that if Burg’s modified entropy is used instead of conventional Burg’s entropy in a maximum entropy probability density (MEPD function, the result yields a better approximation of the probability distribution. An important lemma in basic algebra and a suitable example with tables and graphs in statistical mechanics have been given to illustrate the whole idea appropriately.
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.
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/ .
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.
Single interval Rényi entropy at low temperature
Chen, Bin; Wu, Jie-qiang
2014-08-01
In this paper, we calculate the Rényi entropy of one single interval on a circle at finite temperature in 2D CFT. In the low temperature limit, we expand the thermal density matrix level by level in the vacuum Verma module, and calculate the first few leading terms in e -π/ T L explicitly. On the other hand, we compute the same Rényi entropy holographically. After considering the dependence of the Rényi entropy on the temperature, we manage to fix the interval-independent constant terms in the classical part of holographic Rényi entropy. We furthermore extend the analysis in [9] to higher orders and find exact agreement between the results from field theory and bulk computations in the large central charge limit. Our work provides another piece of evidence to support holographic computation of Rényi entropy in AdS3/CFT2 correspondence, even with thermal effect.
Analysis of the anomalous mean-field like properties of Gaussian core model in terms of entropy
Nandi, Manoj Kumar; Maitra Bhattacharyya, Sarika
2018-01-01
Studies of the Gaussian core model (GCM) have shown that it behaves like a mean-field model and the properties are quite different from standard glass former. In this work, we investigate the entropies, namely, the excess entropy (Sex) and the configurational entropy (Sc) and their different components to address these anomalies. Our study corroborates most of the earlier observations and also sheds new light on the high and low temperature dynamics. We find that unlike in standard glass former where high temperature dynamics is dominated by two-body correlation and low temperature by many-body correlations, in the GCM both high and low temperature dynamics are dominated by many-body correlations. We also find that the many-body entropy which is usually positive at low temperatures and is associated with activated dynamics is negative in the GCM suggesting suppression of activation. Interestingly despite the suppression of activation, the Adam-Gibbs (AG) relation that describes activated dynamics holds in the GCM, thus suggesting a non-activated contribution in AG relation. We also find an overlap between the AG relation and mode coupling power law regime leading to a power law behavior of Sc. From our analysis of this power law behavior, we predict that in the GCM the high temperature dynamics will disappear at dynamical transition temperature and below that there will be a transition to the activated regime. Our study further reveals that the activated regime in the GCM is quite narrow.
Entropy Generation in a Chemical Reaction
Miranda, E. N.
2010-01-01
Entropy generation in a chemical reaction is analysed without using the general formalism of non-equilibrium thermodynamics at a level adequate for advanced undergraduates. In a first approach to the problem, the phenomenological kinetic equation of an elementary first-order reaction is used to show that entropy production is always positive. A…
Quantum information entropies of ultracold atomic gases in a ...
Indian Academy of Sciences (India)
The position and momentum space information entropies of weakly interacting trapped atomic Bose–Einstein condensates and spin-polarized trapped atomic Fermi gases at absolute zero temperature are evaluated. We ﬁnd that sum of the position and momentum space information entropies of these quantum systems ...
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.
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.
Self-adjusting entropy-stable scheme for compressible Euler equations
Institute of Scientific and Technical Information of China (English)
程晓晗; 聂玉峰; 封建湖; LuoXiao-Yu; 蔡力
2015-01-01
In this work, a self-adjusting entropy-stable scheme is proposed for solving compressible Euler equations. The entropy-stable scheme is constructed by combining the entropy conservative flux with a suitable diffusion operator. The entropy has to be preserved in smooth solutions and be dissipated at shocks. To achieve this, a switch function, based on entropy variables, is employed to make the numerical diffusion term added around discontinuities automatically. The resulting scheme is still entropy-stable. A number of numerical experiments illustrating the robustness and accuracy of the scheme are presented. From these numerical results, we observe a remarkable gain in accuracy.
Quantum information entropies of the eigenstates for the P(o)schl-Teller-like potential
Institute of Scientific and Technical Information of China (English)
Guo-Hua Sun; M.Avila Aoki; Shi-Hai Dong
2013-01-01
Shannon entropy for lower position and momentum eigenstates of P(o)schl-Teller-like potential is evaluated.Based on the entropy densities demonstrated graphically,we note that the wave through of the position information entropy density ρ(x) moves right when the potential parameter V1 increases and its amplitude decreases.However,its wave through moves left with the increase in the potential parameter |V2|.Concerning the momentum information entropy density p(p),we observe that its amplitude increases with increasing potential parameter V1,but its amplitude decreases with increasing |V2|.The Bialynicki-Birula-Mycielski (BBM) inequality has also been tested for a number of states.Moreover,there exist eigenstates that exhibit squeezing in the momentum information entropy.Finally,we note that position information entropy increases with V1,but decreases with |V2|.However,the variation of momentum information entropy is contrary to that of the position information entropy.
Zero-contingent entropy of quantum states of a Hydrogen atom
International Nuclear Information System (INIS)
Charvot, R.; Majernik, V.
1996-01-01
We calculated the zero-contingent entropy for the position of electron in H-atom as a function of its quantum numbers and compared it with the corresponding value of the Shannon entropy. The values of zero-contingent entropy of quantum states of H-atom correlate well with the corresponding values of Shannon's entropy. This points out that, besides the Shannon entropy, the zero-contingent entropy represents an appropriate, and mathematically rather simple, measure of the spreading out of the wave functions in H-atom. (authors)
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.
Self-adjusting entropy-stable scheme for compressible Euler equations
International Nuclear Information System (INIS)
Cheng Xiao-Han; Nie Yu-Feng; Cai Li; Feng Jian-Hu; Luo Xiao-Yu
2015-01-01
In this work, a self-adjusting entropy-stable scheme is proposed for solving compressible Euler equations. The entropy-stable scheme is constructed by combining the entropy conservative flux with a suitable diffusion operator. The entropy has to be preserved in smooth solutions and be dissipated at shocks. To achieve this, a switch function, which is based on entropy variables, is employed to make the numerical diffusion term be automatically added around discontinuities. The resulting scheme is still entropy-stable. A number of numerical experiments illustrating the robustness and accuracy of the scheme are presented. From these numerical results, we observe a remarkable gain in accuracy. (paper)
Machine learning with quantum relative entropy
International Nuclear Information System (INIS)
Tsuda, Koji
2009-01-01
Density matrices are a central tool in quantum physics, but it is also used in machine learning. A positive definite matrix called kernel matrix is used to represent the similarities between examples. Positive definiteness assures that the examples are embedded in an Euclidean space. When a positive definite matrix is learned from data, one has to design an update rule that maintains the positive definiteness. Our update rule, called matrix exponentiated gradient update, is motivated by the quantum relative entropy. Notably, the relative entropy is an instance of Bregman divergences, which are asymmetric distance measures specifying theoretical properties of machine learning algorithms. Using the calculus commonly used in quantum physics, we prove an upperbound of the generalization error of online learning.
Machine learning with quantum relative entropy
Energy Technology Data Exchange (ETDEWEB)
Tsuda, Koji [Max Planck Institute for Biological Cybernetics, Spemannstr. 38, Tuebingen, 72076 (Germany)], E-mail: koji.tsuda@tuebingen.mpg.de
2009-12-01
Density matrices are a central tool in quantum physics, but it is also used in machine learning. A positive definite matrix called kernel matrix is used to represent the similarities between examples. Positive definiteness assures that the examples are embedded in an Euclidean space. When a positive definite matrix is learned from data, one has to design an update rule that maintains the positive definiteness. Our update rule, called matrix exponentiated gradient update, is motivated by the quantum relative entropy. Notably, the relative entropy is an instance of Bregman divergences, which are asymmetric distance measures specifying theoretical properties of machine learning algorithms. Using the calculus commonly used in quantum physics, we prove an upperbound of the generalization error of online learning.
AMBIVALENCE OF THE ENTROPY CONCEPT IN THE HUMANITIES
Directory of Open Access Journals (Sweden)
Mr. Andrei V. Matyushko
2016-12-01
Full Text Available The paper deals with various views on the concept of entropy. The author gives examples of entropy actualization from different spheres of existence and comes to conclusion about the ambiguity of the treatment of this term in the Humanities.
Asymptotics of information entropies of some Toda-like potentials
International Nuclear Information System (INIS)
Dehesa, J. S.; Martinez-Finkelshtein, A.; Sorokin, V. N.
2003-01-01
The spreading of the quantum probability density for the highly-excited states of a single-particle system with an exponential-type potential on the positive semiaxis is quantitatively determined in both position and momentum spaces by means of the Boltzmann-Shannon information entropy. This problem boils down to the calculation of the asymptotics of the entropy-like integrals of the modified Bessel function of the second kind (also called the Mcdonald function or Basset function). The dependence of the two physical entropies on the large quantum number n is given in detail. It is shown that the semiclassical (WKB) position-space entropy grows slower than the corresponding quantity of not only the harmonic oscillator but also the single-particle systems with any power-type potential of the form V(x)=x 2k , x(set-membership sign)R and k(set-membership sign)N. The momentum-space entropy, calculated with a method based on the properties of the Mcdonald function, is rigorously found to have a behavior of the form -ln ln n, in strong contrast with the corresponding quantity of other one-dimensional systems known up to now (power-type potentials, infinite well)
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
Holographic entanglement entropy for gravitational anomaly in four dimensions
Energy Technology Data Exchange (ETDEWEB)
Ali, Tibra [Perimeter Institute for Theoretical Physics, 31 Caroline Street N., Waterloo, ON N2L 2Y5 (Canada); Haque, S. Shajidul [Laboratory for Quantum Gravity & Strings, Department of Mathematics & Applied Mathematics,University of Cape Town, Mathematics Building, Rondebosch, Cape Town, 7700 (South Africa); Murugan, Jeff [Laboratory for Quantum Gravity & Strings, Department of Mathematics & Applied Mathematics,University of Cape Town, Mathematics Building, Rondebosch, Cape Town, 7700 (South Africa); School of Natural Sciences, Institute for Advanced Study,1 Einstein Dr., Princeton, NJ 08540 (United States)
2017-03-15
We compute the holographic entanglement entropy for the anomaly polynomial TrR{sup 2} in 3+1 dimensions. Using the perturbative method developed for computing entanglement entropy for quantum field theories, we also compute the parity odd contribution to the entanglement entropy of the dual field theory that comes from a background gravitational Chern-Simons term. We find that, in leading order in the perturbation of the background geometry, the two contributions match except for a logarithmic divergent term on the field theory side. We interpret this extra contribution as encoding our ignorance of the source which creates the perturbation of the geometry.
Entropy of stable seasonal rainfall distribution in Kelantan
Azman, Muhammad Az-zuhri; Zakaria, Roslinazairimah; Satari, Siti Zanariah; Radi, Noor Fadhilah Ahmad
2017-05-01
Investigating the rainfall variability is vital for any planning and management in many fields related to water resources. Climate change can gives an impact of water availability and may aggravate water scarcity in the future. Two statistics measurements which have been used by many researchers to measure the rainfall variability are variance and coefficient of variation. However, these two measurements are insufficient since rainfall distribution in Malaysia especially in the East Coast of Peninsular Malaysia is not symmetric instead it is positively skewed. In this study, the entropy concept is used as a tool to measure the seasonal rainfall variability in Kelantan and ten rainfall stations were selected. In previous studies, entropy of stable rainfall (ESR) and apportionment entropy (AE) were used to describe the rainfall amount variability during years for Australian rainfall data. In this study, the entropy of stable seasonal rainfall (ESSR) is suggested to model rainfall amount variability during northeast monsoon (NEM) and southwest monsoon (SWM) seasons in Kelantan. The ESSR is defined to measure the long-term average seasonal rainfall amount variability within a given year (1960-2012). On the other hand, the AE measures the rainfall amounts variability across the months. The results of ESSR and AE values show that stations in east coastline are more variable as compared to other stations inland for Kelantan rainfall. The contour maps of ESSR for Kelantan rainfall stations are also presented.
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
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,
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
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)
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
Excess Entropy Production in Quantum System: Quantum Master Equation Approach
Nakajima, Satoshi; Tokura, Yasuhiro
2017-12-01
For open systems described by the quantum master equation (QME), we investigate the excess entropy production under quasistatic operations between nonequilibrium steady states. The average entropy production is composed of the time integral of the instantaneous steady entropy production rate and the excess entropy production. We propose to define average entropy production rate using the average energy and particle currents, which are calculated by using the full counting statistics with QME. The excess entropy production is given by a line integral in the control parameter space and its integrand is called the Berry-Sinitsyn-Nemenman (BSN) vector. In the weakly nonequilibrium regime, we show that BSN vector is described by ln \\breve{ρ }_0 and ρ _0 where ρ _0 is the instantaneous steady state of the QME and \\breve{ρ }_0 is that of the QME which is given by reversing the sign of the Lamb shift term. If the system Hamiltonian is non-degenerate or the Lamb shift term is negligible, the excess entropy production approximately reduces to the difference between the von Neumann entropies of the system. Additionally, we point out that the expression of the entropy production obtained in the classical Markov jump process is different from our result and show that these are approximately equivalent only in the weakly nonequilibrium regime.
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.
Implication of Negative Entropy Flow for Local Rainfall
Directory of Open Access Journals (Sweden)
Zhaohui Li
2013-08-01
Full Text Available The relation between the atmospheric entropy flow field and local rainfall is examined in terms of the theory of dissipative structures. In this paper, the entropy balance equation in a form suitable for describing the entropy budget of the Earth’s atmosphere is derived starting from the Gibbs relation, and, as examples, the entropy flows of the two severe weather events associated with the development of an extratropical cyclone and a tropical storm are calculated, respectively. The results show that negative entropy flow (NEF has a significant effect on the precipitation intensity and scope with an apparent matching of the NEF’s pattern with the rainfall distribution revealed and, that the diagnosis of NEF is able to provide a good indicator for precipitation forecasting.
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
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.
Entropy of Reissner-Nordstrom-De Sitter Black Hole in Nonthermal Equilibrium
Institute of Scientific and Technical Information of China (English)
ZHAO Ren; ZHANG Jun-Fang; ZHANG Li-Chun
2002-01-01
By making use of the method of quantum statistics, we directly derive the partition function of bosonic and fermionic fields in Reissner-Nordstrom-De Sitter black hole and obtain the integral expression of black hole's entropy and the entropy to which the cosmic horizon surface corresponds. It avoids the difficulty in solving the wave equation of various particles. Then via the improved brick-wall method, i.e. the membrane model, we calculate black hole's entropy and cosmic entropy and find out that if we let the integral upper limit and lower limit both tend to the horizon, the entropy of black hole is proportional to the area of horizon and the entropy to which cosmic horizon surface corresponds is proportional to the area of cosmic horizon. In our result, the stripped term and the divergent logarithmic term in the original brick-wall method no longer exist. In the whole process, the physical idea is clear and the calculation is simple.We offer a new simple and direct way for calculating the entropy of different complicated black holes.
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.
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.
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.
Dissecting Protein Configurational Entropy into Conformational and Vibrational Contributions.
Chong, Song-Ho; Ham, Sihyun
2015-10-01
Quantifying how the rugged nature of the underlying free-energy landscape determines the entropic cost a protein must incur upon folding and ligand binding is a challenging problem. Here, we present a novel computational approach that dissects the protein configurational entropy on the basis of the classification of protein dynamics on the landscape into two separate components: short-term vibrational dynamics related to individual free-energy wells and long-term conformational dynamics associated with transitions between wells. We apply this method to separate the configurational entropy of the protein villin headpiece subdomain into its conformational and vibrational components. We find that the change in configurational entropy upon folding is dominated by the conformational entropy despite the fact that the magnitude of the vibrational entropy is the significantly larger component in each of the folded and unfolded states, which is in accord with the previous empirical estimations. The straightforward applicability of our method to unfolded proteins promises a wide range of applications, including those related to intrinsically disordered proteins.
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 model of dissipative structure on corporate social responsibility
Li, Zuozhi; Jiang, Jie
2017-06-01
Enterprise is prompted to fulfill the social responsibility requirement by the internal and external environment. In this complex system, some studies suggest that firms have an orderly or chaotic entropy exchange behavior. Based on the theory of dissipative structure, this paper constructs the entropy index system of corporate social responsibility(CSR) and explores the dissipative structure of CSR through Brusselator model criterion. Picking up listed companies of the equipment manufacturing, the research shows that CSR has positive incentive to negative entropy and promotes the stability of dissipative structure. In short, the dissipative structure of CSR has a positive impact on the interests of stakeholders and corporate social images.
Cosmological model from the holographic equipartition law with a modified Renyi entropy
Energy Technology Data Exchange (ETDEWEB)
Komatsu, Nobuyoshi [Kanazawa University, Department of Mechanical Systems Engineering, Kanazawa, Ishikawa (Japan)
2017-04-15
Cosmological equations were recently derived by Padmanabhan from the expansion of cosmic space due to the difference between the degrees of freedom on the surface and in the bulk in a region of space. In this study, a modified Renyi entropy is applied to Padmanabhan's 'holographic equipartition law', by regarding the Bekenstein-Hawking entropy as a nonextensive Tsallis entropy and using a logarithmic formula of the original Renyi entropy. Consequently, the acceleration equation including an extra driving term (such as a time-varying cosmological term) can be derived in a homogeneous, isotropic, and spatially flat universe. When a specific condition is mathematically satisfied, the extra driving term is found to be constant-like as if it is a cosmological constant. Interestingly, the order of the constant-like term is naturally consistent with the order of the cosmological constant measured by observations, because the specific condition constrains the value of the constant-like term. (orig.)
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.
Logarithmic corrections to entropy of magnetically charged AdS4 black holes
Directory of Open Access Journals (Sweden)
Imtak Jeon
2017-11-01
Full Text Available Logarithmic terms are quantum corrections to black hole entropy determined completely from classical data, thus providing a strong check for candidate theories of quantum gravity purely from physics in the infrared. We compute these terms in the entropy associated to the horizon of a magnetically charged extremal black hole in AdS×4S7 using the quantum entropy function and discuss the possibility of matching against recently derived microscopic expressions.
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.
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 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.
The entropy concept for non-equilibrium states.
Lieb, Elliott H; Yngvason, Jakob
2013-10-08
In earlier work, we presented a foundation for the second law of classical thermodynamics in terms of the entropy principle. More precisely, we provided an empirically accessible axiomatic derivation of an entropy function defined on all equilibrium states of all systems that has the appropriate additivity and scaling properties, and whose increase is a necessary and sufficient condition for an adiabatic process between two states to be possible. Here, after a brief review of this approach, we address the question of defining entropy for non-equilibrium states. Our conclusion is that it is generally not possible to find a unique entropy that has all relevant physical properties. We do show, however, that one can define two entropy functions, called S - and S + , which, taken together, delimit the range of adiabatic processes that can occur between non-equilibrium states. The concept of comparability of states with respect to adiabatic changes plays an important role in our reasoning.
Entropy Rate of Time-Varying Wireless Networks
DEFF Research Database (Denmark)
Cika, Arta; Badiu, Mihai Alin; Coon, Justin P.
2018-01-01
In this paper, we present a detailed framework to analyze the evolution of the random topology of a time-varying wireless network via the information theoretic notion of entropy rate. We consider a propagation channel varying over time with random node positions in a closed space and Rayleigh...... fading affecting the connections between nodes. The existence of an edge between two nodes at given locations is modeled by a Markov chain, enabling memory effects in network dynamics. We then derive a lower and an upper bound on the entropy rate of the spatiotemporal network. The entropy rate measures...
Nernst Theorem and Statistical Entropy of 5-Dimensional Rotating Black Hole
Institute of Scientific and Technical Information of China (English)
ZHAO Ren; WU Yue-Qin; ZHANG Li-Chun
2003-01-01
In this paper, by using quantum statistical method, we obtain the partition function of Bose field and Fermi field on the background of the 5-dimensional rotating black hole. Then via the improved brick-wall method and membrane model, we calculate the entropy of Bose field and Fermi field of the black hole. And it is obtained that the entropy of the black hole is not only related to the area of the outer horizon but also is the function of inner horizon's area. In our results, there are not the left out term and the divergent logarithmic term in the original brick-wall method.The doubt that why the entropy of the scalar or Dirac field outside the event horizon is the entropy of the black hole in the original brick-wall method does not exist. The influence of spinning degeneracy of particles on entropy of the black hole is also given. It is shown that the entropy determined by the areas of the inner and outer horizons will approach zero,when the radiation temperature of the black hole approaches absolute zero. It satisfies Nernst theorem. The entropy can be taken as the Planck absolute entropy. We provide a way to study higher dimensional black hole.
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.
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
International Nuclear Information System (INIS)
Ghasemi, A; Hooshmandasl, M R; Tavassoly, M K
2011-01-01
In this paper we calculate the position and momentum space information entropies for the quantum states associated with a particular physical system, i.e. the isotonic oscillator Hamiltonian. We present our results for its ground states, as well as for its excited states. We observe that the lower bound of the sum of the position and momentum entropies expressed by the Beckner, Bialynicki-Birula and Mycielski (BBM) inequality is satisfied. Moreover, there exist eigenstates that exhibit squeezing in the position information entropy. In fact, entropy squeezing, which occurs in position, will be compensated for by an increase in momentum entropy, such that the BBM inequality is guaranteed. To complete our study we investigate the amplitude squeezing in x and p-quadratures corresponding to the eigenstates of the isotonic oscillator and show that amplitude squeezing, again in x, will be revealed as expected, while the Heisenberg uncertainty relationship is also satisfied. Finally, our numerical calculations of the entropy densities will be presented graphically.
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
Entropy and the Predictability of Online Life
Directory of Open Access Journals (Sweden)
Roberta Sinatra
2014-01-01
Full Text Available Using mobile phone records and information theory measures, our daily lives have been recently shown to follow strict statistical regularities, and our movement patterns are, to a large extent, predictable. Here, we apply entropy and predictability measures to two datasets of the behavioral actions and the mobility of a large number of players in the virtual universe of a massive multiplayer online game. We find that movements in virtual human lives follow the same high levels of predictability as offline mobility, where future movements can, to some extent, be predicted well if the temporal correlations of visited places are accounted for. Time series of behavioral actions show similar high levels of predictability, even when temporal correlations are neglected. Entropy conditional on specific behavioral actions reveals that in terms of predictability, negative behavior has a wider variety than positive actions. The actions that contain the information to best predict an individual’s subsequent action are negative, such as attacks or enemy markings, while the positive actions of friendship marking, trade and communication contain the least amount of predictive information. These observations show that predicting behavioral actions requires less information than predicting the mobility patterns of humans for which the additional knowledge of past visited locations is crucial and that the type and sign of a social relation has an essential impact on the ability to determine future behavior.
Stochastic thermodynamics and entropy production of chemical reaction systems
Tomé, Tânia; de Oliveira, Mário J.
2018-06-01
We investigate the nonequilibrium stationary states of systems consisting of chemical reactions among molecules of several chemical species. To this end, we introduce and develop a stochastic formulation of nonequilibrium thermodynamics of chemical reaction systems based on a master equation defined on the space of microscopic chemical states and on appropriate definitions of entropy and entropy production. The system is in contact with a heat reservoir and is placed out of equilibrium by the contact with particle reservoirs. In our approach, the fluxes of various types, such as the heat and particle fluxes, play a fundamental role in characterizing the nonequilibrium chemical state. We show that the rate of entropy production in the stationary nonequilibrium state is a bilinear form in the affinities and the fluxes of reaction, which are expressed in terms of rate constants and transition rates, respectively. We also show how the description in terms of microscopic states can be reduced to a description in terms of the numbers of particles of each species, from which follows the chemical master equation. As an example, we calculate the rate of entropy production of the first and second Schlögl reaction models.
A positive and entropy-satisfying finite volume scheme for the Baer-Nunziato model
Coquel, Frédéric; Hérard, Jean-Marc; Saleh, Khaled
2017-02-01
We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer-Nunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in [16] for the isentropic Baer-Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound are also proven to be maintained by the numerical scheme. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. The numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the Baer-Nunziato model, namely Schwendeman-Wahle-Kapila's Godunov-type scheme [39] and Tokareva-Toro's HLLC scheme [44]. The relaxation scheme also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard numerical scheme used in the nuclear industry, namely Rusanov's scheme. Finally, we assess the good behavior of the scheme when approximating vanishing phase solutions.
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.)
Canonical Entropy and Phase Transition of Rotating Black Hole
International Nuclear Information System (INIS)
Ren, Zhao; Yue-Qin, Wu; Li-Chun, Zhang
2008-01-01
Recently, the Hawking radiation of a black hole has been studied using the tunnel effect method. The radiation spectrum of a black hole is derived. By discussing the correction to spectrum of the rotating black hole, we obtain the canonical entropy. The derived canonical entropy is equal to the sum of Bekenstein–Hawking entropy and correction term. The correction term near the critical point is different from the one near others. This difference plays an important role in studying the phase transition of the black hole. The black hole thermal capacity diverges at the critical point. However, the canonical entropy is not a complex number at this point. Thus we think that the phase transition created by this critical point is the second order phase transition. The discussed black hole is a five-dimensional Kerr-AdS black hole. We provide a basis for discussing thermodynamic properties of a higher-dimensional rotating black hole. (general)
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
A note on entropy of de Sitter black holes
Energy Technology Data Exchange (ETDEWEB)
Bhattacharya, Sourav [University of Crete, ITCP and Department of Physics, Heraklion (Greece); Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune (India)
2016-03-15
A de Sitter black hole or a black hole spacetime endowed with a positive cosmological constant has two Killing horizons - a black hole and a cosmological event horizon surrounding it. It is natural to expect that the total Bekenstein-Hawking entropy of such spacetimes should be the sum of the two horizons' areas. In this work we apply the recently developed formalism using the Gibbons-Hawking-York boundary term and the near horizon symmetries to derive the total entropy of such two horizon spacetimes. We construct a suitable general geometric set up for general stationary axisymmetric spacetimes with two or more than two commuting Killing vector fields in an arbitrary spacetime dimensions. This framework helps us to deal with both horizons on an equal footing. We show that in order to obtain the total entropy of such spacetimes, the near horizon mode functions for the diffeomorphism generating vector fields have to be restricted in a certain manner, compared to the single horizon spacetimes. We next discuss specific known exact solutions belonging to the Kerr-Newman or the Plebanski-Demianski-de Sitter families to show that they fall into the category of our general framework. We end with a sketch of further possible extensions of this work. (orig.)
Entropy squeezing of the field interacting with a nearly degenerate V-type three-level atom
Institute of Scientific and Technical Information of China (English)
Zhou Qing-Chun; Zhu Shi-Ning
2005-01-01
The position- and momentum-entopic squeezing properties of the optical field in the system of a nearly degenerate three-level atom interacting with a single-mode field are investigated. Calculation results indicate that when the field is initially in the vacuum state, it may lead to squeezing of the position entropy or the momentum entropy of the field if the atom is prepared properly. The effects of initial atomic state and the splitting of the excited levels of the atom on field entropies are discussed in this case. When the initial field is in a coherent state, we find that position-entropy squeezing of the field is present even if the atom is prepared in the ground state. By comparing the variance squeezing and entropy squeezing of the field we confirm that entropy is more sensitive than variance in measuring quantum fluctuations.
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.
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.
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 of Kerr-de Sitter black hole
Li, Huai-Fan; Ma, Meng-Sen; Zhang, Li-Chun; Zhao, Ren
2017-07-01
Based on the consideration that the black hole horizon and the cosmological horizon of Kerr-de Sitter black hole are not independent of each other, we conjecture the total entropy of the system should have an extra term contributed from the correlations between the two horizons, except for the sum of the two horizon entropies. By employing globally effective first law and effective thermodynamic quantities, we obtain the corrected total entropy and find that the region of stable state for Kerr-de Sitter is related to the angular velocity parameter a, i.e., the region of stable state becomes bigger as the rotating parameters a is increases.
Entropy Flow Through Near-Critical Quantum Junctions
Friedan, Daniel
2017-05-01
This is the continuation of Friedan (J Stat Phys, 2017. doi: 10.1007/s10955-017-1752-8). Elementary formulas are derived for the flow of entropy through a circuit junction in a near-critical quantum circuit close to equilibrium, based on the structure of the energy-momentum tensor at the junction. The entropic admittance of a near-critical junction in a bulk-critical circuit is expressed in terms of commutators of the chiral entropy currents. The entropic admittance at low frequency, divided by the frequency, gives the change of the junction entropy with temperature—the entropic "capacitance". As an example, and as a check on the formalism, the entropic admittance is calculated explicitly for junctions in bulk-critical quantum Ising circuits (free fermions, massless in the bulk), in terms of the reflection matrix of the junction. The half-bit of information capacity per end of critical Ising wire is re-derived by integrating the entropic "capacitance" with respect to temperature, from T=0 to T=∞.
Correlations of multiscale entropy in the FX market
Stosic, Darko; Stosic, Dusan; Ludermir, Teresa; Stosic, Tatijana
2016-09-01
The regularity of price fluctuations in exchange rates plays a crucial role in FX market dynamics. Distinct variations in regularity arise from economic, social and political events, such as interday trading and financial crisis. This paper applies a multiscale time-dependent entropy method on thirty-three exchange rates to analyze price fluctuations in the FX. Correlation matrices of entropy values, termed entropic correlations, are in turn used to describe global behavior of the market. Empirical results suggest a weakly correlated market with pronounced collective behavior at bi-weekly trends. Correlations arise from cycles of low and high regularity in long-term trends. Eigenvalues of the correlation matrix also indicate a dominant European market, followed by shifting American, Asian, African, and Pacific influences. As a result, we find that entropy is a powerful tool for extracting important information from the FX market.
ENTROPY PRODUCTION IN COLLISIONLESS SYSTEMS. I. LARGE PHASE-SPACE OCCUPATION NUMBERS
International Nuclear Information System (INIS)
Barnes, Eric I.; Williams, Liliya L. R.
2011-01-01
Certain thermal non-equilibrium situations, outside of the astrophysical realm, suggest that entropy production extrema, instead of entropy extrema, are related to stationary states. In an effort to better understand the evolution of collisionless self-gravitating systems, we investigate the role of entropy production and develop expressions for the entropy production rate in two particular statistical families that describe self-gravitating systems. From these entropy production descriptions, we derive the requirements for extremizing the entropy production rate in terms of specific forms for the relaxation function in the Boltzmann equation. We discuss some implications of these relaxation functions and point to future work that will further test this novel thermodynamic viewpoint of collisionless relaxation.
Brain entropy and human intelligence: A resting-state fMRI study
Calderone, Daniel; Morales, Leah J.
2018-01-01
Human intelligence comprises comprehension of and reasoning about an infinitely variable external environment. A brain capable of large variability in neural configurations, or states, will more easily understand and predict variable external events. Entropy measures the variety of configurations possible within a system, and recently the concept of brain entropy has been defined as the number of neural states a given brain can access. This study investigates the relationship between human intelligence and brain entropy, to determine whether neural variability as reflected in neuroimaging signals carries information about intellectual ability. We hypothesize that intelligence will be positively associated with entropy in a sample of 892 healthy adults, using resting-state fMRI. Intelligence is measured with the Shipley Vocabulary and WASI Matrix Reasoning tests. Brain entropy was positively associated with intelligence. This relation was most strongly observed in the prefrontal cortex, inferior temporal lobes, and cerebellum. This relationship between high brain entropy and high intelligence indicates an essential role for entropy in brain functioning. It demonstrates that access to variable neural states predicts complex behavioral performance, and specifically shows that entropy derived from neuroimaging signals at rest carries information about intellectual capacity. Future work in this area may elucidate the links between brain entropy in both resting and active states and various forms of intelligence. This insight has the potential to provide predictive information about adaptive behavior and to delineate the subdivisions and nature of intelligence based on entropic patterns. PMID:29432427
Brain entropy and human intelligence: A resting-state fMRI study.
Saxe, Glenn N; Calderone, Daniel; Morales, Leah J
2018-01-01
Human intelligence comprises comprehension of and reasoning about an infinitely variable external environment. A brain capable of large variability in neural configurations, or states, will more easily understand and predict variable external events. Entropy measures the variety of configurations possible within a system, and recently the concept of brain entropy has been defined as the number of neural states a given brain can access. This study investigates the relationship between human intelligence and brain entropy, to determine whether neural variability as reflected in neuroimaging signals carries information about intellectual ability. We hypothesize that intelligence will be positively associated with entropy in a sample of 892 healthy adults, using resting-state fMRI. Intelligence is measured with the Shipley Vocabulary and WASI Matrix Reasoning tests. Brain entropy was positively associated with intelligence. This relation was most strongly observed in the prefrontal cortex, inferior temporal lobes, and cerebellum. This relationship between high brain entropy and high intelligence indicates an essential role for entropy in brain functioning. It demonstrates that access to variable neural states predicts complex behavioral performance, and specifically shows that entropy derived from neuroimaging signals at rest carries information about intellectual capacity. Future work in this area may elucidate the links between brain entropy in both resting and active states and various forms of intelligence. This insight has the potential to provide predictive information about adaptive behavior and to delineate the subdivisions and nature of intelligence based on entropic patterns.
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.
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.
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.
Triviality of entanglement entropy in the Galilean vacuum
Hason, Itamar
2018-05-01
We study the entanglement entropy of the vacuum in non-relativistic local theories with Galilean or Schrödinger symmetry. We clear some confusion in the literature on the free Schrödinger case. We find that with only positive U (1) charge particles (states) and a unique zero U (1) charge state (the vacuum) the entanglement entropy must vanish in that state.
Linking entropy flow with typhoon evolution: a case-study
International Nuclear Information System (INIS)
Liu, C; Xu, H; Liu, Y
2007-01-01
This paper is mainly aimed at investigating the relationship of entropy flow with an atmospheric system (typhoon), based on the observational analyses covering its whole life-cycle. The formula for calculating entropy flow is derived starting with the Gibbs relation with data from the NCEP/NCAR reanalysis. The results show that: (i) entropy flow characteristics at different vertical layers of the system are heterogeneous with predominant negative entropy flow in the large portion of the troposphere and positive ones at upper levels during its development; (ii) changes in the maximum surface wind velocity or the intensity of a typhoon are synchronous with the total entropy flow around the typhoon centre and its neighbourhood, suggesting that the growth of a severe atmospheric system relies greatly upon the negative entropy flow being strong enough, and that entropy flow analysis might provide a particular point of view and a powerful tool to understand the mechanism responsible for the life-cycle of an atmospheric system and associated weather events; and (iii) the horizontal pattern of negative entropy flow near the surface might contain some significant information conducive to the track forecast of typhoons
Entropy and information causality in general probabilistic theories
International Nuclear Information System (INIS)
Barnum, Howard; Leifer, Matthew; Spekkens, Robert; Barrett, Jonathan; Clark, Lisa Orloff; Stepanik, Nicholas; Wilce, Alex; Wilke, Robin
2010-01-01
We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality (IC) recently proposed by Pawlowski et al (2009 arXiv:0905.2292). We consider two entropic quantities, which we term measurement and mixing entropy. In the context of classical and quantum theory, these coincide, being given by the Shannon and von Neumann entropies, respectively; in general, however, they are very different. In particular, while measurement entropy is easily seen to be concave, mixing entropy need not be. In fact, as we show, mixing entropy is not concave whenever the state space is a non-simplicial polytope. Thus, the condition that measurement and mixing entropies coincide is a strong constraint on possible theories. We call theories with this property monoentropic. Measurement entropy is subadditive, but not in general strongly subadditive. Equivalently, if we define the mutual information between two systems A and B by the usual formula I(A: B)=H(A)+H(B)-H(AB), where H denotes the measurement entropy and AB is a non-signaling composite of A and B, then it can happen that I(A:BC)< I(A:B). This is relevant to IC in the sense of Pawlowski et al: we show that any monoentropic non-signaling theory in which measurement entropy is strongly subadditive, and also satisfies a version of the Holevo bound, is informationally causal, and on the other hand we observe that Popescu-Rohrlich boxes, which violate IC, also violate strong subadditivity. We also explore the interplay between measurement and mixing entropy and various natural conditions on theories that arise in quantum axiomatics.
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.
Entropy correction of BTZ black holes in a tunneling framework
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper, using the Parikh-Wilczek tunneling framework, we first calculate the emission rates of non-rotating BTZ black holes and rotating BTZ black holes to second order accuracy. Then, by assuming that the emission process satisfies an underlying unitary theory, we obtain the corrected entropy of the BTZ black holes. A log term emerges naturally in the expression of the corrected entropy. A discussion about the inverse area term is also presented.
A positive and entropy-satisfying finite volume scheme for the Baer–Nunziato model
Energy Technology Data Exchange (ETDEWEB)
Coquel, Frédéric, E-mail: frederic.coquel@cmap.polytechnique.fr [CMAP, École Polytechnique CNRS, UMR 7641, Route de Saclay, F-91128 Palaiseau cedex (France); Hérard, Jean-Marc, E-mail: jean-marc.herard@edf.fr [EDF-R& D, Département MFEE, 6 Quai Watier, F-78401 Chatou Cedex (France); Saleh, Khaled, E-mail: saleh@math.univ-lyon1.fr [Université de Lyon, CNRS UMR 5208, Université Lyon 1, Institut Camille Jordan, 43 bd 11 novembre 1918, F-69622 Villeurbanne cedex (France)
2017-02-01
We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer–Nunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in for the isentropic Baer–Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound are also proven to be maintained by the numerical scheme. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. The numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the Baer–Nunziato model, namely Schwendeman–Wahle–Kapila's Godunov-type scheme and Tokareva–Toro's HLLC scheme . The relaxation scheme also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard numerical scheme used in the nuclear industry, namely Rusanov's scheme. Finally, we assess the good behavior of the scheme when approximating vanishing phase solutions.
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...
Entropy and complexity analysis of hydrogenic Rydberg atoms
Energy Technology Data Exchange (ETDEWEB)
Lopez-Rosa, S. [Instituto Carlos I de Fisica Teorica y Computacional, Universidad de Granada, 18071-Granada (Spain); Departamento de Fisica Aplicada II, Universidad de Sevilla, 41012-Sevilla (Spain); Toranzo, I. V.; Dehesa, J. S. [Instituto Carlos I de Fisica Teorica y Computacional, Universidad de Granada, 18071-Granada (Spain); Departamento de Fisica Atomica, Molecular y Nuclear, Universidad de Granada, 18071-Granada (Spain); Sanchez-Moreno, P. [Instituto Carlos I de Fisica Teorica y Computacional, Universidad de Granada, 18071-Granada (Spain); Departamento de Matematica Aplicada, Universidad de Granada, 18071-Granada (Spain)
2013-05-15
The internal disorder of hydrogenic Rydberg atoms as contained in their position and momentum probability densities is examined by means of the following information-theoretic spreading quantities: the radial and logarithmic expectation values, the Shannon entropy, and the Fisher information. As well, the complexity measures of Cramer-Rao, Fisher-Shannon, and Lopez Ruiz-Mancini-Calvet types are investigated in both reciprocal spaces. The leading term of these quantities is rigorously calculated by use of the asymptotic properties of the concomitant entropic functionals of the Laguerre and Gegenbauer orthogonal polynomials which control the wavefunctions of the Rydberg states in both position and momentum spaces. The associated generalized Heisenberg-like, logarithmic and entropic uncertainty relations are also given. Finally, application to linear (l= 0), circular (l=n- 1), and quasicircular (l=n- 2) states is explicitly done.
Entropy, energy and negativity in Fermi-resonance coupled states of substituted methanes
International Nuclear Information System (INIS)
Hou Xiwen; Wan Mingfang; Ma Zhongqi
2010-01-01
Several measures of entanglement have attracted considerable interest in the relationship of a measure of entanglement with other quantities. The dynamics of entropy, energy and negativity is studied for Fermi-resonance coupled vibrations in substituted methanes with three kinds of initial mixed states, which are the mixed density matrices of binomial states, thermal states and squeezed states on two vibrational modes, respectively. It is demonstrated that for mixed binomial states and mixed thermal states with small magnitudes the entropies of the stretch and the bend are anti-correlated in the same oscillatory frequency, so do the energies for each kind of state with small magnitudes, whereas the entropies exhibit positive correlations with the corresponding energies. Furthermore, for small magnitudes quantum mutual entropy is positively correlated with the interacting energy. Analytic forms of entropies and energies are provided with initial conditions in which they are stationary, and the agreement between analytic and numerical simulations is satisfactory. The dynamical entanglement measured by negativity is examined for those states and conditions. It is shown that negativity displays a sudden death for mixed binomial states and mixed thermal states with small magnitudes, and the time-averaged negativity has the minimal value under the conditions of stationary entropies and energies. Moreover, negativity is positively correlated with the mutual entropy and the interacting energy just for mixed squeezed states with small magnitudes. Those are useful for molecular quantum information processing and dynamical entanglement.
International Nuclear Information System (INIS)
Goswami, Gurupada; Mukherjee, Biswajit; Bag, Bidhan Chandra
2005-01-01
We have studied the relaxation of non-Markovian and thermodynamically closed system both in the absence and presence of non-equilibrium constraint in terms of the information entropy flux and entropy production based on the Fokker-Planck and the entropy balance equations. Our calculation shows how the relaxation time depends on noise correlation time. It also considers how the non-equilibrium constraint is affected by system parameters such as noise correlation time, strength of dissipation and frequency of dynamical system. The interplay of non-equilibrium constraint, frictional memory kernel, noise correlation time and frequency of dynamical system reveals the extremum nature of the entropy production
Goswami, Gurupada; Mukherjee, Biswajit; Bag, Bidhan Chandra
2005-06-01
We have studied the relaxation of non-Markovian and thermodynamically closed system both in the absence and presence of non-equilibrium constraint in terms of the information entropy flux and entropy production based on the Fokker-Planck and the entropy balance equations. Our calculation shows how the relaxation time depends on noise correlation time. It also considers how the non-equilibrium constraint is affected by system parameters such as noise correlation time, strength of dissipation and frequency of dynamical system. The interplay of non-equilibrium constraint, frictional memory kernel, noise correlation time and frequency of dynamical system reveals the extremum nature of the entropy production.
Pseudo information entropy of a three-level atom interaction with two ...
Indian Academy of Sciences (India)
of enormous utility in quantum computing, cryptography etc. A major ... The central object of information theory, the entropy, has been introduced in .... the interference terms and therefore [7], it is expected to use pseudo entropy as a measure.
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.
International Nuclear Information System (INIS)
Nuno Almirantearena, F; Introzzi, A; Clara, F; Burillo Lopez, P
2007-01-01
In this work we use 53 Arterial Diameter Variation (ADV) waves extracted from radial artery of normotense males, along with the values of variables that represent the ADV wave, obtained by means of multivariate analysis. Then, we specify the linguistic variables and the linguistic terms. The variables are fuzzified using triangular and trapezoidal fuzzy numbers. We analyze the fuzziness of the linguistic terms by applying discrete and continuous fuzzy entropies. Finally, we infer which variable presents the greatest disorder associated to the loss of arterial elasticity in radial artery
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)
Energy Technology Data Exchange (ETDEWEB)
Yan, Hao-Peng; Liu, Wen-Biao, E-mail: wbliu@bnu.edu.cn
2016-08-10
Using Parikh–Wilczek tunneling framework, we calculate the tunneling rate from a Schwarzschild black hole under the third order WKB approximation, and then obtain the expressions for emission spectrum and black hole entropy to the third order correction. The entropy contains four terms including the Bekenstein–Hawking entropy, the logarithmic term, the inverse area term, and the square of inverse area term. In addition, we analyse the correlation between sequential emissions under this approximation. It is shown that the entropy is conserved during the process of black hole evaporation, which consists with the request of quantum mechanics and implies the information is conserved during this process. We also compare the above result with that of pure thermal spectrum case, and find that the non-thermal correction played an important role.
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.
Irreversible entropy model for damage diagnosis in resistors
Energy Technology Data Exchange (ETDEWEB)
Cuadras, Angel, E-mail: angel.cuadras@upc.edu; Crisóstomo, Javier; Ovejas, Victoria J.; Quilez, Marcos [Instrumentation, Sensor and Interfaces Group, Electronic Engineering Department, Escola d' Enginyeria de Telecomunicació i Aeronàutica de Castelldefels EETAC, Universitat Politècnica de Catalunya, Barcelona Tech (UPC), Castelldefels-Barcelona (Spain)
2015-10-28
We propose a method to characterize electrical resistor damage based on entropy measurements. Irreversible entropy and the rate at which it is generated are more convenient parameters than resistance for describing damage because they are essentially positive in virtue of the second law of thermodynamics, whereas resistance may increase or decrease depending on the degradation mechanism. Commercial resistors were tested in order to characterize the damage induced by power surges. Resistors were biased with constant and pulsed voltage signals, leading to power dissipation in the range of 4–8 W, which is well above the 0.25 W nominal power to initiate failure. Entropy was inferred from the added power and temperature evolution. A model is proposed to understand the relationship among resistance, entropy, and damage. The power surge dissipates into heat (Joule effect) and damages the resistor. The results show a correlation between entropy generation rate and resistor failure. We conclude that damage can be conveniently assessed from irreversible entropy generation. Our results for resistors can be easily extrapolated to other systems or machines that can be modeled based on their resistance.
Irreversible entropy model for damage diagnosis in resistors
International Nuclear Information System (INIS)
Cuadras, Angel; Crisóstomo, Javier; Ovejas, Victoria J.; Quilez, Marcos
2015-01-01
We propose a method to characterize electrical resistor damage based on entropy measurements. Irreversible entropy and the rate at which it is generated are more convenient parameters than resistance for describing damage because they are essentially positive in virtue of the second law of thermodynamics, whereas resistance may increase or decrease depending on the degradation mechanism. Commercial resistors were tested in order to characterize the damage induced by power surges. Resistors were biased with constant and pulsed voltage signals, leading to power dissipation in the range of 4–8 W, which is well above the 0.25 W nominal power to initiate failure. Entropy was inferred from the added power and temperature evolution. A model is proposed to understand the relationship among resistance, entropy, and damage. The power surge dissipates into heat (Joule effect) and damages the resistor. The results show a correlation between entropy generation rate and resistor failure. We conclude that damage can be conveniently assessed from irreversible entropy generation. Our results for resistors can be easily extrapolated to other systems or machines that can be modeled based on their resistance
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.
Generalized uncertainty principle and entropy of three-dimensional rotating acoustic black hole
International Nuclear Information System (INIS)
Zhao, HuiHua; Li, GuangLiang; Zhang, LiChun
2012-01-01
Using the new equation of state density from the generalized uncertainty principle, we investigate statistics entropy of a 3-dimensional rotating acoustic black hole. When λ introduced in the generalized uncertainty principle takes a specific value, we obtain an area entropy and a correction term associated with the acoustic black hole. In this method, there does not exist any divergence and one needs not the small mass approximation in the original brick-wall model. -- Highlights: ► Statistics entropy of a 3-dimensional rotating acoustic black hole is studied. ► We obtain an area entropy and a correction term associated with it. ► We make λ introduced in the generalized uncertainty principle take a specific value. ► There does not exist any divergence in this method.
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.
International Nuclear Information System (INIS)
Garcia-Morales, Vladimir; Pellicer, Julio; Manzanares, Jose A.
2008-01-01
We present some novel thermodynamic ideas based on the Maupertuis principle. By considering Hamiltonians written in terms of appropriate action-angle variables we show that thermal states can be characterized by the action variables and by their evolution in time when the system is nonintegrable. We propose dynamical definitions for the equilibrium temperature and entropy as well as an expression for the nonequilibrium entropy valid for isolated systems with many degrees of freedom. This entropy is shown to increase in the relaxation to equilibrium of macroscopic systems with short-range interactions, which constitutes a dynamical justification of the Second Law of Thermodynamics. Several examples are worked out to show that this formalism yields the right microcanonical (equilibrium) quantities. The relevance of this approach to nonequilibrium situations is illustrated with an application to a network of coupled oscillators (Kuramoto model). We provide an expression for the entropy production in this system finding that its positive value is directly related to dissipation at the steady state in attaining order through synchronization
Spatial Decomposition of Translational Water–Water Correlation Entropy in Binding Pockets
2015-01-01
A number of computational tools available today compute the thermodynamic properties of water at surfaces and in binding pockets by using inhomogeneous solvation theory (IST) to analyze explicit-solvent simulations. Such methods enable qualitative spatial mappings of both energy and entropy around a solute of interest and can also be applied quantitatively. However, the entropy estimates of existing methods have, to date, been almost entirely limited to the first-order terms in the IST’s entropy expansion. These first-order terms account for localization and orientation of water molecules in the field of the solute but not for the modification of water–water correlations by the solute. Here, we present an extension of the Grid Inhomogeneous Solvation Theory (GIST) approach which accounts for water–water translational correlations. The method involves rewriting the two-point density of water in terms of a conditional density and utilizes the efficient nearest-neighbor entropy estimation approach. Spatial maps of this second order term, for water in and around the synthetic host cucurbit[7]uril and in the binding pocket of the enzyme Factor Xa, reveal mainly negative contributions, indicating solute-induced water–water correlations relative to bulk water; particularly strong signals are obtained for sites at the entrances of cavities or pockets. This second-order term thus enters with the same, negative, sign as the first order translational and orientational terms. Numerical and convergence properties of the methodology are examined. PMID:26636620
Entropies from Markov Models as Complexity Measures of Embedded Attractors
Directory of Open Access Journals (Sweden)
Julián D. Arias-Londoño
2015-06-01
Full Text Available This paper addresses the problem of measuring complexity from embedded attractors as a way to characterize changes in the dynamical behavior of different types of systems with a quasi-periodic behavior by observing their outputs. With the aim of measuring the stability of the trajectories of the attractor along time, this paper proposes three new estimations of entropy that are derived from a Markov model of the embedded attractor. The proposed estimators are compared with traditional nonparametric entropy measures, such as approximate entropy, sample entropy and fuzzy entropy, which only take into account the spatial dimension of the trajectory. The method proposes the use of an unsupervised algorithm to find the principal curve, which is considered as the “profile trajectory”, that will serve to adjust the Markov model. The new entropy measures are evaluated using three synthetic experiments and three datasets of physiological signals. In terms of consistency and discrimination capabilities, the results show that the proposed measures perform better than the other entropy measures used for comparison purposes.
Entropy and Multifractality in Relativistic Ion-Ion Collisions
Directory of Open Access Journals (Sweden)
Shaista Khan
2018-01-01
Full Text Available Entropy production in multiparticle systems is investigated by analyzing the experimental data on ion-ion collisions at AGS and SPS energies and comparing the findings with those reported earlier for hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions. It is observed that the entropy produced in limited and full phase space, when normalized to maximum rapidity, exhibits a kind of scaling which is nicely supported by Monte Carlo model HIJING. Using Rényi’s order q information entropy, multifractal characteristics of particle production are examined in terms of generalized dimensions, Dq. Nearly the same values of multifractal specific heat, c, observed in hadronic and ion-ion collisions over a wide range of incident energies suggest that the quantity c might be used as a universal characteristic of multiparticle production in hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions. The analysis is extended to the study of spectrum of scaling indices. The findings reveal that Rényi’s order q information entropy could be another way to investigate the fluctuations in multiplicity distributions in terms of spectral function f(α, which has been argued to be a convenient function for comparison sake not only among different experiments but also between the data and theoretical models.
Two faces of entropy and information in biological systems.
Mitrokhin, Yuriy
2014-10-21
The article attempts to overcome the well-known paradox of contradictions between the emerging biological organization and entropy production in biological systems. It is assumed that quality, speculative correlation between entropy and antientropy processes taking place both in the past and today in the metabolic and genetic cellular systems may be perfectly authorized for adequate description of the evolution of biological organization. So far as thermodynamic entropy itself cannot compensate for the high degree of organization which exists in the cell, we discuss the mode of conjunction of positive entropy events (mutations) in the genetic systems of the past generations and the formation of organized structures of current cells. We argue that only the information which is generated in the conditions of the information entropy production (mutations and other genome reorganization) in genetic systems of the past generations provides the physical conjunction of entropy and antientropy processes separated from each other in time generations. It is readily apparent from the requirements of the Second law of thermodynamics. Copyright © 2014 Elsevier Ltd. All rights reserved.
Entropy and complexity analysis of hydrogenic Rydberg atoms
International Nuclear Information System (INIS)
López-Rosa, S.; Toranzo, I. V.; Dehesa, J. S.; Sánchez-Moreno, P.
2013-01-01
The internal disorder of hydrogenic Rydberg atoms as contained in their position and momentum probability densities is examined by means of the following information-theoretic spreading quantities: the radial and logarithmic expectation values, the Shannon entropy, and the Fisher information. As well, the complexity measures of Crámer-Rao, Fisher-Shannon, and López Ruiz-Mancini-Calvet types are investigated in both reciprocal spaces. The leading term of these quantities is rigorously calculated by use of the asymptotic properties of the concomitant entropic functionals of the Laguerre and Gegenbauer orthogonal polynomials which control the wavefunctions of the Rydberg states in both position and momentum spaces. The associated generalized Heisenberg-like, logarithmic and entropic uncertainty relations are also given. Finally, application to linear (l= 0), circular (l=n− 1), and quasicircular (l=n− 2) states is explicitly done.
International Nuclear Information System (INIS)
Irudayam, Sheeba Jem; Henchman, Richard H
2010-01-01
An equation for the chemical potential of a dilute aqueous solution of noble gases is derived in terms of energies, force and torque magnitudes, and solute and water coordination numbers, quantities which are all measured from an equilibrium molecular dynamics simulation. Also derived are equations for the Gibbs free energy, enthalpy and entropy of hydration for the Henry's law process, the Ostwald process, and a third proposed process going from an arbitrary concentration in the gas phase to the equivalent mole fraction in aqueous solution which has simpler expressions for the enthalpy and entropy changes. Good agreement with experimental hydration free energies is obtained in the TIP4P and SPC/E water models although the solute's force field appears to affect the enthalpies and entropies obtained. In contrast to other methods, the approach gives a complete breakdown of the entropy for every degree of freedom and makes possible a direct structural interpretation of the well-known entropy loss accompanying the hydrophobic hydration of small non-polar molecules under ambient conditions. The noble-gas solutes experience only a small reduction in their vibrational entropy, with larger solutes experiencing a greater loss. The vibrational and librational entropy components of water actually increase but only marginally, negating any idea of water confinement. The term that contributes the most to the hydrophobic entropy loss is found to be water's orientational term which quantifies the number of orientational minima per water molecule and how many ways the whole hydrogen-bond network can form. These findings help resolve contradictory deductions from experiments that water structure around non-polar solutes is similar to bulk water in some ways but different in others. That the entropy loss lies in water's rotational entropy contrasts with other claims that it largely lies in water's translational entropy, but this apparent discrepancy arises because of different
Characterization of time series via Rényi complexity-entropy curves
Jauregui, M.; Zunino, L.; Lenzi, E. K.; Mendes, R. S.; Ribeiro, H. V.
2018-05-01
One of the most useful tools for distinguishing between chaotic and stochastic time series is the so-called complexity-entropy causality plane. This diagram involves two complexity measures: the Shannon entropy and the statistical complexity. Recently, this idea has been generalized by considering the Tsallis monoparametric generalization of the Shannon entropy, yielding complexity-entropy curves. These curves have proven to enhance the discrimination among different time series related to stochastic and chaotic processes of numerical and experimental nature. Here we further explore these complexity-entropy curves in the context of the Rényi entropy, which is another monoparametric generalization of the Shannon entropy. By combining the Rényi entropy with the proper generalization of the statistical complexity, we associate a parametric curve (the Rényi complexity-entropy curve) with a given time series. We explore this approach in a series of numerical and experimental applications, demonstrating the usefulness of this new technique for time series analysis. We show that the Rényi complexity-entropy curves enable the differentiation among time series of chaotic, stochastic, and periodic nature. In particular, time series of stochastic nature are associated with curves displaying positive curvature in a neighborhood of their initial points, whereas curves related to chaotic phenomena have a negative curvature; finally, periodic time series are represented by vertical straight lines.
Quantum statistical entropy corresponding to cosmic horizon in five-dimensional spacetime
Institute of Scientific and Technical Information of China (English)
2008-01-01
The generalized uncertainty relation is introduced to calculate the quantum statis-tical entropy corresponding to cosmic horizon. 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 five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is no divergent logarithmic term in the original brick-wall method. And it is obtained that the quantum statistical en-tropy corresponding to cosmic horizon is proportional to the area of the horizon. Further it is shown that the entropy corresponding to cosmic horizon 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. In our calculation, by using the quantum statistical method, we obtain the partition function of Bose field and Fermi field on the background of five-dimensional spacetime. We provide a way to study the quantum statistical entropy corresponding to cosmic horizon in the higher-dimensional spacetime.
Thermality and excited state Rényi entropy in two-dimensional CFT
Energy Technology Data Exchange (ETDEWEB)
Lin, Feng-Li [Department of Physics, National Taiwan Normal University,Taipei 11677, Taiwan (China); Wang, Huajia [Department of Physics, University of Illinois,Urbana-Champaign, IL 61801 (United States); Zhang, Jia-ju [Dipartimento di Fisica, Università degli Studi di Milano-Bicocca,Piazza della Scienza 3, I-20126 Milano (Italy); Theoretical Physics Division, Institute of High Energy Physics, Chinese Academy of Sciences,19B Yuquan Rd, Beijing 100049 (China); Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences,19B Yuquan Rd, Beijing 100049 (China)
2016-11-21
We evaluate one-interval Rényi entropy and entanglement entropy for the excited states of two-dimensional conformal field theory (CFT) on a cylinder, and examine their differences from the ones for the thermal state. We assume the interval to be short so that we can use operator product expansion (OPE) of twist operators to calculate Rényi entropy in terms of sum of one-point functions of OPE blocks. We find that the entanglement entropy for highly excited state and thermal state behave the same way after appropriate identification of the conformal weight of the state with the temperature. However, there exists no such universal identification for the Rényi entropy in the short-interval expansion. Therefore, the highly excited state does not look thermal when comparing its Rényi entropy to the thermal state one. As the Rényi entropy captures the higher moments of the reduced density matrix but the entanglement entropy only the average, our results imply that the emergence of thermality depends on how refined we look into the entanglement structure of the underlying pure excited state.
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.
Entropy and Compression Capture Different Complexity Features: The Case of Fetal Heart Rate
Directory of Open Access Journals (Sweden)
João Monteiro-Santos
2017-12-01
Full Text Available Entropy and compression have been used to distinguish fetuses at risk of hypoxia from their healthy counterparts through the analysis of Fetal Heart Rate (FHR. Low correlation that was observed between these two approaches suggests that they capture different complexity features. This study aims at characterizing the complexity of FHR features captured by entropy and compression, using as reference international guidelines. Single and multi-scale approaches were considered in the computation of entropy and compression. The following physiologic-based features were considered: FHR baseline; percentage of abnormal long (%abLTV and short (%abSTV term variability; average short term variability; and, number of acceleration and decelerations. All of the features were computed on a set of 68 intrapartum FHR tracings, divided as normal, mildly, and moderately-severely acidemic born fetuses. The correlation between entropy/compression features and the physiologic-based features was assessed. There were correlations between compressions and accelerations and decelerations, but neither accelerations nor decelerations were significantly correlated with entropies. The %abSTV was significantly correlated with entropies (ranging between −0.54 and −0.62, and to a higher extent with compression (ranging between −0.80 and −0.94. Distinction between groups was clearer in the lower scales using entropy and in the higher scales using compression. Entropy and compression are complementary complexity measures.
Entropy of Reissner–Nordström–de Sitter black hole
Energy Technology Data Exchange (ETDEWEB)
Zhang, Li-Chun [Department of Physics, Shanxi Datong University, Datong 037009 (China); Institute of Theoretical Physics, Shanxi Datong University, Datong 037009 (China); Zhao, Ren [Institute of Theoretical Physics, Shanxi Datong University, Datong 037009 (China); Ma, Meng-Sen, E-mail: mengsenma@gmail.com [Department of Physics, Shanxi Datong University, Datong 037009 (China); Institute of Theoretical Physics, Shanxi Datong University, Datong 037009 (China)
2016-10-10
Based on the consideration that the black hole horizon and the cosmological horizon of Reissner–Nordström black hole in de Sitter space are not independent each other, we conjecture the total entropy of the system should have an extra term contributed from the entanglement between the two horizons, except for the sum of the two horizon entropies. Making use of the globally effective first law and the effective thermodynamic quantities, we derive the total entropy and find that it will diverge as the two horizons tend to coincide.
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.
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)
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.
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!
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
Entropy, complexity, and Markov diagrams for random walk cancer models.
Newton, Paul K; Mason, Jeremy; Hurt, Brian; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Kuhn, Peter
2014-12-19
The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential.
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
International Nuclear Information System (INIS)
Baccetti, Valentina; Visser, Matt
2013-01-01
Even if a probability distribution is properly normalizable, its associated Shannon (or von Neumann) entropy can easily be infinite. We carefully analyze conditions under which this phenomenon can occur. Roughly speaking, this happens when arbitrarily small amounts of probability are dispersed into an infinite number of states; we shall quantify this observation and make it precise. We develop several particularly simple, elementary, and useful bounds, and also provide some asymptotic estimates, leading to necessary and sufficient conditions for the occurrence of infinite Shannon entropy. We go to some effort to keep technical computations as simple and conceptually clear as possible. In particular, we shall see that large entropies cannot be localized in state space; large entropies can only be supported on an exponentially large number of states. We are for the time being interested in single-channel Shannon entropy in the information theoretic sense, not entropy in a stochastic field theory or quantum field theory defined over some configuration space, on the grounds that this simple problem is a necessary precursor to understanding infinite entropy in a field theoretic context. (paper)
Entropy Rate Estimates for Natural Language—A New Extrapolation of Compressed Large-Scale Corpora
Directory of Open Access Journals (Sweden)
Ryosuke Takahira
2016-10-01
Full Text Available One of the fundamental questions about human language is whether its entropy rate is positive. The entropy rate measures the average amount of information communicated per unit time. The question about the entropy of language dates back to experiments by Shannon in 1951, but in 1990 Hilberg raised doubt regarding a correct interpretation of these experiments. This article provides an in-depth empirical analysis, using 20 corpora of up to 7.8 gigabytes across six languages (English, French, Russian, Korean, Chinese, and Japanese, to conclude that the entropy rate is positive. To obtain the estimates for data length tending to infinity, we use an extrapolation function given by an ansatz. Whereas some ansatzes were proposed previously, here we use a new stretched exponential extrapolation function that has a smaller error of fit. Thus, we conclude that the entropy rates of human languages are positive but approximately 20% smaller than without extrapolation. Although the entropy rate estimates depend on the script kind, the exponent of the ansatz function turns out to be constant across different languages and governs the complexity of natural language in general. In other words, in spite of typological differences, all languages seem equally hard to learn, which partly confirms Hilberg’s hypothesis.
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.
Landau degeneracy and black hole entropy
International Nuclear Information System (INIS)
Costa, M.S.; Perry, M.J.
1998-01-01
We consider the supergravity solution describing a configuration of intersecting D4-branes with non-vanishing world-volume gauge fields. The entropy of such a black hole is calculated in terms of the D-branes quantised charges. The non-extreme solution is also considered and the corresponding thermodynamical quantities are calculated in terms of a D-brane/anti-D-brane system. To perform the quantum mechanical D-brane analysis we study open strings with their ends on branes with a magnetic condensate. Applying the results to our D-brane system we manage to have a perfect agreement between the D-brane entropy counting and the corresponding semi-classical result. The Landau degeneracy of the open string states describing the excitations of the D-brane system enters in a crucial way. We also derive the near-extreme results which agree with the semi-classical calculations. (orig.)
A New Entropy Formula and Gradient Estimates for the Linear Heat Equation on Static Manifold
Directory of Open Access Journals (Sweden)
Abimbola Abolarinwa
2014-08-01
Full Text Available In this paper we prove a new monotonicity formula for the heat equation via a generalized family of entropy functionals. This family of entropy formulas generalizes both Perelman’s entropy for evolving metric and Ni’s entropy on static manifold. We show that this entropy satisfies a pointwise differential inequality for heat kernel. The consequences of which are various gradient and Harnack estimates for all positive solutions to the heat equation on compact manifold.
Liu, Yong; Shu, Chi-Wang; Zhang, Mengping
2018-02-01
We present a discontinuous Galerkin (DG) scheme with suitable quadrature rules [15] for ideal compressible magnetohydrodynamic (MHD) equations on structural meshes. The semi-discrete scheme is analyzed to be entropy stable by using the symmetrizable version of the equations as introduced by Godunov [32], the entropy stable DG framework with suitable quadrature rules [15], the entropy conservative flux in [14] inside each cell and the entropy dissipative approximate Godunov type numerical flux at cell interfaces to make the scheme entropy stable. The main difficulty in the generalization of the results in [15] is the appearance of the non-conservative "source terms" added in the modified MHD model introduced by Godunov [32], which do not exist in the general hyperbolic system studied in [15]. Special care must be taken to discretize these "source terms" adequately so that the resulting DG scheme satisfies entropy stability. Total variation diminishing / bounded (TVD/TVB) limiters and bound-preserving limiters are applied to control spurious oscillations. We demonstrate the accuracy and robustness of this new scheme on standard MHD examples.
Universal role of correlation entropy in critical phenomena
International Nuclear Information System (INIS)
Gu Shijian; Sun Changpu; Lin Haiqing
2008-01-01
In statistical physics, if we divide successively an equilibrium system into two parts, we will face a situation that, to a certain length ξ, the physics of a subsystem is no longer the same as the original one. The extensive property of the thermal entropy S(A union B) = S(A) + S(B) is then violated. This observation motivates us to introduce a concept of correlation entropy between two points, as measured by the mutual information in information theory, to study the critical phenomena. A rigorous relation is established to display some drastic features of the non-vanishing correlation entropy of a subsystem formed by any two distant particles with long-range correlation. This relation actually indicates a universal role played by the correlation entropy for understanding the critical phenomena. We also verify these analytical studies in terms of two well-studied models for both the thermal and quantum phase transitions: the two-dimensional Ising model and the one-dimensional transverse-field Ising model. Therefore, the correlation entropy provides us with a new physical intuition of the critical phenomena from the point of view of information theory
Large Eddy Simulation of Entropy Generation in a Turbulent Mixing Layer
Sheikhi, Reza H.; Safari, Mehdi; Hadi, Fatemeh
2013-11-01
Entropy transport equation is considered in large eddy simulation (LES) of turbulent flows. The irreversible entropy generation in this equation provides a more general description of subgrid scale (SGS) dissipation due to heat conduction, mass diffusion and viscosity effects. A new methodology is developed, termed the entropy filtered density function (En-FDF), to account for all individual entropy generation effects in turbulent flows. The En-FDF represents the joint probability density function of entropy, frequency, velocity and scalar fields within the SGS. An exact transport equation is developed for the En-FDF, which is modeled by a system of stochastic differential equations, incorporating the second law of thermodynamics. The modeled En-FDF transport equation is solved by a Lagrangian Monte Carlo method. The methodology is employed to simulate a turbulent mixing layer involving transport of passive scalars and entropy. Various modes of entropy generation are obtained from the En-FDF and analyzed. Predictions are assessed against data generated by direct numerical simulation (DNS). The En-FDF predictions are in good agreements with the DNS data.
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
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.
Holographic entanglement entropy for the most general higher derivative gravity
International Nuclear Information System (INIS)
Miao, Rong-Xin; Guo, Wu-zhong
2015-01-01
The holographic entanglement entropy for the most general higher derivative gravity is investigated. We find a new type of Wald entropy, which appears on entangling surface without the rotational symmetry and reduces to usual Wald entropy on Killing horizon. Furthermore, we obtain a formal formula of HEE for the most general higher derivative gravity and work it out exactly for some squashed cones. As an important application, we derive HEE for gravitational action with one derivative of the curvature when the extrinsic curvature vanishes. We also study some toy models with non-zero extrinsic curvature. We prove that our formula yields the correct universal term of entanglement entropy for 4d CFTs. Furthermore, we solve the puzzle raised by Hung, Myers and Smolkin that the logarithmic term of entanglement entropy derived from Weyl anomaly of CFTs does not match the holographic result even if the extrinsic curvature vanishes. We find that such mismatch comes from the ‘anomaly of entropy’ of the derivative of curvature. After considering such contributions carefully, we resolve the puzzle successfully. In general, we need to fix the splitting problem for the conical metrics in order to derive the holographic entanglement entropy. We find that, at least for Einstein gravity, the splitting problem can be fixed by using equations of motion. How to derive the splittings for higher derivative gravity is a non-trivial and open question. For simplicity, we ignore the splitting problem in this paper and find that it does not affect our main results.
Entanglement Entropy in Quantum Spin Chains with Finite Range Interaction
Its, A. R.; Mezzadri, F.; Mo, M. Y.
2008-11-01
We study the entropy of entanglement of the ground state in a wide family of one-dimensional quantum spin chains whose interaction is of finite range and translation invariant. Such systems can be thought of as generalizations of the XY model. The chain is divided in two parts: one containing the first consecutive L spins; the second the remaining ones. In this setting the entropy of entanglement is the von Neumann entropy of either part. At the core of our computation is the explicit evaluation of the leading order term as L → ∞ of the determinant of a block-Toeplitz matrix with symbol Φ(z) = left(begin{array}{cc} iλ & g(z) \\ g^{-1}(z) & i λ right), where g( z) is the square root of a rational function and g(1/ z) = g -1( z). The asymptotics of such determinant is computed in terms of multi-dimensional theta-functions associated to a hyperelliptic curve {mathcal{L}} of genus g ≥ 1, which enter into the solution of a Riemann-Hilbert problem. Phase transitions for these systems are characterized by the branch points of {mathcal{L}} approaching the unit circle. In these circumstances the entropy diverges logarithmically. We also recover, as particular cases, the formulae for the entropy discovered by Jin and Korepin [14] for the XX model and Its, Jin and Korepin [12, 13] for the XY model.
Statistical properties of entropy production derived from fluctuation theorems
International Nuclear Information System (INIS)
Merhav, Neri; Kafri, Yariv
2010-01-01
Several implications of well-known fluctuation theorems, on the statistical properties of entropy production, are studied using various approaches. We begin by deriving a tight lower bound on the variance of the entropy production for a given mean of this random variable. It is shown that the Evans–Searles fluctuation theorem alone imposes a significant lower bound on the variance only when the mean entropy production is very small. It is then nonetheless demonstrated that upon incorporating additional information concerning the entropy production, this lower bound can be significantly improved, so as to capture extensivity properties. Another important aspect of the fluctuation properties of the entropy production is the relationship between the mean and the variance, on the one hand, and the probability of the event where the entropy production is negative, on the other hand. Accordingly, we derive upper and lower bounds on this probability in terms of the mean and the variance. These bounds are tighter than previous bounds that can be found in the literature. Moreover, they are tight in the sense that there exist probability distributions, satisfying the Evans–Searles fluctuation theorem, that achieve them with equality. Finally, we present a general method for generating a wide class of inequalities that must be satisfied by the entropy production. We use this method to derive several new inequalities that go beyond the standard derivation of the second law
High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains
Fisher, Travis C.; Carpenter, Mark H.
2013-01-01
Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.
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.
Black Hole Entropy Calculation in a Modified Thin Film Model Jingyi ...
Indian Academy of Sciences (India)
Abstract. The thin film model is modified to calculate the black hole entropy. The difference from the original method is that the Parikh–. Wilczek tunnelling framework is introduced and the self-gravitation of the emission particles is taken into account. In terms of our improvement, if the entropy is still proportional to the area, ...
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.
Estimating the melting point, entropy of fusion, and enthalpy of ...
The entropies of fusion, enthalies of fusion, and melting points of organic compounds can be estimated through three models developed using the SPARC (SPARC Performs Automated Reasoning in Chemistry) platform. The entropy of fusion is modeled through a combination of interaction terms and physical descriptors. The enthalpy of fusion is modeled as a function of the entropy of fusion, boiling point, and fexibility of the molecule. The melting point model is the enthlapy of fusion divided by the entropy of fusion. These models were developed in part to improve SPARC's vapor pressure and solubility models. These models have been tested on 904 unique compounds. The entropy model has a RMS of 12.5 J mol-1K-1. The enthalpy model has a RMS of 4.87 kJ mol-1. The melting point model has a RMS of 54.4°C. Published in the journal, SAR and QSAR in Environmental Research
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.
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.
Maximum entropy formalism for the analytic continuation of matrix-valued Green's functions
Kraberger, Gernot J.; Triebl, Robert; Zingl, Manuel; Aichhorn, Markus
2017-10-01
We present a generalization of the maximum entropy method to the analytic continuation of matrix-valued Green's functions. To treat off-diagonal elements correctly based on Bayesian probability theory, the entropy term has to be extended for spectral functions that are possibly negative in some frequency ranges. In that way, all matrix elements of the Green's function matrix can be analytically continued; we introduce a computationally cheap element-wise method for this purpose. However, this method cannot ensure important constraints on the mathematical properties of the resulting spectral functions, namely positive semidefiniteness and Hermiticity. To improve on this, we present a full matrix formalism, where all matrix elements are treated simultaneously. We show the capabilities of these methods using insulating and metallic dynamical mean-field theory (DMFT) Green's functions as test cases. Finally, we apply the methods to realistic material calculations for LaTiO3, where off-diagonal matrix elements in the Green's function appear due to the distorted crystal structure.
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.
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 analysis on non-equilibrium two-phase flow models
International Nuclear Information System (INIS)
Karwat, H.; Ruan, Y.Q.
1995-01-01
A method of entropy analysis according to the second law of thermodynamics is proposed for the assessment of a class of practical non-equilibrium two-phase flow models. Entropy conditions are derived directly from a local instantaneous formulation for an arbitrary control volume of a structural two-phase fluid, which are finally expressed in terms of the averaged thermodynamic independent variables and their time derivatives as well as the boundary conditions for the volume. On the basis of a widely used thermal-hydraulic system code it is demonstrated with practical examples that entropy production rates in control volumes can be numerically quantified by using the data from the output data files. Entropy analysis using the proposed method is useful in identifying some potential problems in two-phase flow models and predictions as well as in studying the effects of some free parameters in closure relationships
Entropy analysis on non-equilibrium two-phase flow models
Energy Technology Data Exchange (ETDEWEB)
Karwat, H.; Ruan, Y.Q. [Technische Universitaet Muenchen, Garching (Germany)
1995-09-01
A method of entropy analysis according to the second law of thermodynamics is proposed for the assessment of a class of practical non-equilibrium two-phase flow models. Entropy conditions are derived directly from a local instantaneous formulation for an arbitrary control volume of a structural two-phase fluid, which are finally expressed in terms of the averaged thermodynamic independent variables and their time derivatives as well as the boundary conditions for the volume. On the basis of a widely used thermal-hydraulic system code it is demonstrated with practical examples that entropy production rates in control volumes can be numerically quantified by using the data from the output data files. Entropy analysis using the proposed method is useful in identifying some potential problems in two-phase flow models and predictions as well as in studying the effects of some free parameters in closure relationships.
Directory of Open Access Journals (Sweden)
Mario Faliva
2017-03-01
Full Text Available The paper devises a family of leptokurtic bell-shaped distributions which is based on the hyperbolic secant raised to a positive power, and bridges the Laplace and Gaussian laws on asymptotic arguments. Moment and cumulant generating functions are then derived and represented in terms of polygamma functions. The behaviour of shape parameters, namely kurtosis and entropy, is investigated. In addition, Gram–Charlier-type (GCT expansions, based on the aforementioned distributions and their orthogonal polynomials, are specified, and an operational criterion is provided to meet modelling requirements in a possibly severe kurtosis and skewness environment. The role played by entropy within the kurtosis ranges of GCT expansions is also examined.
Hierarchical Polygamy Inequality for Entanglement of Tsallis q-Entropy
Luo, Yu; Li, Yong-Ming
2018-05-01
In this paper, we study the polygamy inequality of quantum entanglement in terms of Tsallis q-entropy. We first give a lower bound of Tsallis q-entropy entanglement of assistance (TOA) in the 2 ⊗ d systems. The relation-ships between Tsallis q-entropy entanglement (TEE) and TOA are also given. Furthermore, we prove TOA follows a hierarchical polygamy inequality in a 2 ⊗ 2 ⊗ 2 N‑2 systems. Supported by the National Natural Science Foundation of China under Grant No. 11671244, the Higher School Doctoral Subject Foun- dation of Ministry of Education of China under Grant No. 20130202110001, and Fundamental Research Funds for the Central Universities under Grants Nos. 2016TS060 and 2016CBY003
Financial time series analysis based on effective phase transfer entropy
Yang, Pengbo; Shang, Pengjian; Lin, Aijing
2017-02-01
Transfer entropy is a powerful technique which is able to quantify the impact of one dynamic system on another system. In this paper, we propose the effective phase transfer entropy method based on the transfer entropy method. We use simulated data to test the performance of this method, and the experimental results confirm that the proposed approach is capable of detecting the information transfer between the systems. We also explore the relationship between effective phase transfer entropy and some variables, such as data size, coupling strength and noise. The effective phase transfer entropy is positively correlated with the data size and the coupling strength. Even in the presence of a large amount of noise, it can detect the information transfer between systems, and it is very robust to noise. Moreover, this measure is indeed able to accurately estimate the information flow between systems compared with phase transfer entropy. In order to reflect the application of this method in practice, we apply this method to financial time series and gain new insight into the interactions between systems. It is demonstrated that the effective phase transfer entropy can be used to detect some economic fluctuations in the financial market. To summarize, the effective phase transfer entropy method is a very efficient tool to estimate the information flow between systems.
Giant onsite electronic entropy enhances the performance of ceria for water splitting.
Naghavi, S Shahab; Emery, Antoine A; Hansen, Heine A; Zhou, Fei; Ozolins, Vidvuds; Wolverton, Chris
2017-08-18
Previous studies have shown that a large solid-state entropy of reduction increases the thermodynamic efficiency of metal oxides, such as ceria, for two-step thermochemical water splitting cycles. In this context, the configurational entropy arising from oxygen off-stoichiometry in the oxide, has been the focus of most previous work. Here we report a different source of entropy, the onsite electronic configurational entropy, arising from coupling between orbital and spin angular momenta in lanthanide f orbitals. We find that onsite electronic configurational entropy is sizable in all lanthanides, and reaches a maximum value of ≈4.7 k B per oxygen vacancy for Ce 4+ /Ce 3+ reduction. This unique and large positive entropy source in ceria explains its excellent performance for high-temperature catalytic redox reactions such as water splitting. Our calculations also show that terbium dioxide has a high electronic entropy and thus could also be a potential candidate for solar thermochemical reactions.Solid-state entropy of reduction increases the thermodynamic efficiency of ceria for two-step thermochemical water splitting. Here, the authors report a large and different source of entropy, the onsite electronic configurational entropy arising from coupling between orbital and spin angular momenta in f orbitals.
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.
Third law of thermodynamics as a key test of generalized entropies.
Bento, E P; Viswanathan, G M; da Luz, M G E; Silva, R
2015-02-01
The laws of thermodynamics constrain the formulation of statistical mechanics at the microscopic level. The third law of thermodynamics states that the entropy must vanish at absolute zero temperature for systems with nondegenerate ground states in equilibrium. Conversely, the entropy can vanish only at absolute zero temperature. Here we ask whether or not generalized entropies satisfy this fundamental property. We propose a direct analytical procedure to test if a generalized entropy satisfies the third law, assuming only very general assumptions for the entropy S and energy U of an arbitrary N-level classical system. Mathematically, the method relies on exact calculation of β=dS/dU in terms of the microstate probabilities p(i). To illustrate this approach, we present exact results for the two best known generalizations of statistical mechanics. Specifically, we study the Kaniadakis entropy S(κ), which is additive, and the Tsallis entropy S(q), which is nonadditive. We show that the Kaniadakis entropy correctly satisfies the third law only for -1law for q<1. Finally, we give a concrete example of the power of our proposed method by applying it to a paradigmatic system: the one-dimensional ferromagnetic Ising model with nearest-neighbor interactions.
Monte Carlo power iteration: Entropy and spatial correlations
International Nuclear Information System (INIS)
Nowak, Michel; Miao, Jilang; Dumonteil, Eric; Forget, Benoit; Onillon, Anthony; Smith, Kord S.; Zoia, Andrea
2016-01-01
Highlights: • We show that the entropy function might be misleading in criticality simulations. • We interpret the spatial fluctuations of the fission chains in terms of the key parameters of the simulated system. • We show that the behavior of the entropy function is related to the theory of neutron clustering. - Abstract: The behavior of Monte Carlo criticality simulations is often assessed by examining the convergence of the so-called entropy function. In this work, we shall show that the entropy function may lead to a misleading interpretation, and that potential issues occur when spatial correlations induced by fission events are important. We will support our analysis by examining the higher-order moments of the entropy function and the center of mass of the neutron population. Within the framework of a simplified model based on branching processes, we will relate the behavior of the spatial fluctuations of the fission chains to the key parameters of the simulated system, namely, the number of particles per generation, the reactor size and the migration area. Numerical simulations of a fuel rod and of a whole core suggest that the obtained results are quite general and hold true also for real-world applications.
Institute of Scientific and Technical Information of China (English)
XU Dian-Yan
2003-01-01
The free energy and entropy of Reissner-Nordstrom black holes in higher-dimensional space-time are calculated by the quantum statistic method with a brick wall model. The space-time of the black holes is divided into three regions: region 1, (r > r0); region 2, (r0 > r > n); and region 3, (T-J > r > 0), where r0 is the radius of the outer event horizon, and r, is the radius of the inner event horizon. Detailed calculation shows that the entropy contributed by region 2 is zero, the entropy contributed by region 1 is positive and proportional to the outer event horizon area, the entropy contributed by region 3 is negative and proportional to the inner event horizon area. The total entropy contributed by all the three regions is positive and proportional to the area difference between the outer and inner event horizons. As rt approaches r0 in the nearly extreme case, the total quantum statistical entropy approaches zero.
Relative entropy of excited states in two dimensional conformal field theories
Energy Technology Data Exchange (ETDEWEB)
Sárosi, Gábor [Department of Theoretical Physics, Institute of Physics, Budapest University of Technology,Budapest, H-1521 (Hungary); Ugajin, Tomonori [Kavli Institute for Theoretical Physics, University of California,Santa Barbara,CA 93106 (United States)
2016-07-21
We study the relative entropy and the trace square distance, both of which measure the distance between reduced density matrices of two excited states in two dimensional conformal field theories. We find a general formula for the relative entropy between two primary states with the same conformal dimension in the limit of a single small interval and find that in this case the relative entropy is proportional to the trace square distance. We check our general formulae by calculating the relative entropy between two generalized free fields and the trace square distance between the spin and disorder operators of the critical Ising model. We also give the leading term of the relative entropy in the small interval expansion when the two operators have different conformal dimensions. This turns out to be universal when the CFT has no primaires lighter than the stress tensor. The result reproduces the previously known special cases.
Free Energy, Enthalpy and Entropy from Implicit Solvent End-Point Simulations.
Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro
2018-01-01
Free energy is the key quantity to describe the thermodynamics of biological systems. In this perspective we consider the calculation of free energy, enthalpy and entropy from end-point molecular dynamics simulations. Since the enthalpy may be calculated as the ensemble average over equilibrated simulation snapshots the difficulties related to free energy calculation are ultimately related to the calculation of the entropy of the system and in particular of the solvent entropy. In the last two decades implicit solvent models have been used to circumvent the problem and to take into account solvent entropy implicitly in the solvation terms. More recently outstanding advancement in both implicit solvent models and in entropy calculations are making the goal of free energy estimation from end-point simulations more feasible than ever before. We review briefly the basic theory and discuss the advancements in light of practical applications.
Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2014-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
Free Energy, Enthalpy and Entropy from Implicit Solvent End-Point Simulations
Directory of Open Access Journals (Sweden)
Federico Fogolari
2018-02-01
Full Text Available Free energy is the key quantity to describe the thermodynamics of biological systems. In this perspective we consider the calculation of free energy, enthalpy and entropy from end-point molecular dynamics simulations. Since the enthalpy may be calculated as the ensemble average over equilibrated simulation snapshots the difficulties related to free energy calculation are ultimately related to the calculation of the entropy of the system and in particular of the solvent entropy. In the last two decades implicit solvent models have been used to circumvent the problem and to take into account solvent entropy implicitly in the solvation terms. More recently outstanding advancement in both implicit solvent models and in entropy calculations are making the goal of free energy estimation from end-point simulations more feasible than ever before. We review briefly the basic theory and discuss the advancements in light of practical applications.
Entropy lower bounds of quantum decision tree complexity
Shi, Yaoyun
2000-01-01
We prove a general lower bound of quantum decision tree complexity in terms of some entropy notion. We regard the computation as a communication process in which the oracle and the computer exchange several rounds of messages, each round consisting of O(log(n)) bits. Let E(f) be the Shannon entropy of the random variable f(X), where X is uniformly random in f's domain. Our main result is that it takes \\Omega(E(f)) queries to compute any \\emph{total} function f. It is interesting to contrast t...
Extremal Black Holes in Supergravity and the Bekenstein-Hawking Entropy
Directory of Open Access Journals (Sweden)
R. D'Auria
2002-03-01
Full Text Available Abstract: We review some results on the connection among supergravity central charges, BPS states and Bekenstein-Hawking entropy. In particular, N = 2 super-gravity in four dimensions is studied in detail. For higher N supergravities we just give an account of the general theory specializing the discussion to the N = 8 case when one half of supersymmetry is preserved. We stress the fact that for extremal supergravity black holes the entropy formula is topological, that is the entropy turns out to be a moduli independent quantity and can be written in terms of invariants of the duality group of the supergravity theory.
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
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
Configurational entropy change of netropsin and distamycin upon DNA minor-groove binding.
Dolenc, Jozica; Baron, Riccardo; Oostenbrink, Chris; Koller, Joze; van Gunsteren, Wilfred F
2006-08-15
Binding of a small molecule to a macromolecular target reduces its conformational freedom, resulting in a negative entropy change that opposes the binding. The goal of this study is to estimate the configurational entropy change of two minor-groove-binding ligands, netropsin and distamycin, upon binding to the DNA duplex d(CGCGAAAAACGCG).d(CGCGTTTTTCGCG). Configurational entropy upper bounds based on 10-ns molecular dynamics simulations of netropsin and distamycin in solution and in complex with DNA in solution were estimated using the covariance matrix of atom-positional fluctuations. The results suggest that netropsin and distamycin lose a significant amount of configurational entropy upon binding to the DNA minor groove. The estimated changes in configurational entropy for netropsin and distamycin are -127 J K(-1) mol(-1) and -104 J K(-1) mol(-1), respectively. Estimates of the configurational entropy contributions of parts of the ligands are presented, showing that the loss of configurational entropy is comparatively more pronounced for the flexible tails than for the relatively rigid central body.
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
Memory behaviors of entropy production rates in heat conduction
Li, Shu-Nan; Cao, Bing-Yang
2018-02-01
Based on the relaxation time approximation and first-order expansion, memory behaviors in heat conduction are found between the macroscopic and Boltzmann-Gibbs-Shannon (BGS) entropy production rates with exponentially decaying memory kernels. In the frameworks of classical irreversible thermodynamics (CIT) and BGS statistical mechanics, the memory dependency on the integrated history is unidirectional, while for the extended irreversible thermodynamics (EIT) and BGS entropy production rates, the memory dependences are bidirectional and coexist with the linear terms. When macroscopic and microscopic relaxation times satisfy a specific relationship, the entropic memory dependences will be eliminated. There also exist initial effects in entropic memory behaviors, which decay exponentially. The second-order term are also discussed, which can be understood as the global non-equilibrium degree. The effects of the second-order term are consisted of three parts: memory dependency, initial value and linear term. The corresponding memory kernels are still exponential and the initial effects of the global non-equilibrium degree also decay exponentially.
An alternative expression to the Sackur-Tetrode entropy formula for an ideal gas
Nagata, Shoichi
2018-03-01
An expression for the entropy of a monoatomic classical ideal gas is known as the Sackur-Tetrode equation. This pioneering investigation about 100 years ago incorporates quantum considerations. The purpose of this paper is to provide an alternative expression for the entropy in terms of the Heisenberg uncertainty relation. The analysis is made on the basis of fluctuation theory, for a canonical system in thermal equilibrium at temperature T. This new formula indicates manifestly that the entropy of macroscopic world is recognized as a measure of uncertainty in microscopic quantum world. The entropy in the Sackur-Tetrode equation can be re-interpreted from a different perspective viewpoint. The emphasis is on the connection between the entropy and the uncertainty relation in quantum consideration.
International Nuclear Information System (INIS)
Magagnin, Valentina; Bassani, Tito; Bari, Vlasta; Turiel, Maurizio; Porta, Alberto; Maestri, Roberto; Pinna, Gian Domenico
2011-01-01
The autonomic regulation is non-invasively estimated from heart rate variability (HRV). Many methods utilized to assess autonomic regulation require stationarity of HRV recordings. However, non-stationarities are frequently present even during well-controlled experiments, thus potentially biasing HRV indices. The aim of our study is to quantify the potential bias of spectral, symbolic and entropy HRV indices due to non-stationarities. We analyzed HRV series recorded in healthy subjects during uncontrolled daily life activities typical of 24 h Holter recordings and during predetermined levels of robotic-assisted treadmill-based physical exercise. A stationarity test checking the stability of the mean and variance over short HRV series (about 300 cardiac beats) was utilized to distinguish stationary periods from non-stationary ones. Spectral, symbolic and entropy indices evaluated solely over stationary periods were contrasted with those derived from all the HRV segments. When indices were calculated solely over stationary series, we found that (i) during both uncontrolled daily life activities and controlled physical exercise, the entropy-based complexity indices were significantly larger; (ii) during uncontrolled daily life activities, the spectral and symbolic indices linked to sympathetic modulation were significantly smaller and those associated with vagal modulation were significantly larger; (iii) while during uncontrolled daily life activities, the variance of spectral, symbolic and entropy rate indices was significantly larger, during controlled physical exercise, it was smaller. The study suggests that non-stationarities increase the likelihood to overestimate the contribution of sympathetic control and affect the power of statistical tests utilized to discriminate conditions and/or groups
Practical device-independent quantum cryptography via entropy accumulation.
Arnon-Friedman, Rotem; Dupuis, Frédéric; Fawzi, Omar; Renner, Renato; Vidick, Thomas
2018-01-31
Device-independent cryptography goes beyond conventional quantum cryptography by providing security that holds independently of the quality of the underlying physical devices. Device-independent protocols are based on the quantum phenomena of non-locality and the violation of Bell inequalities. This high level of security could so far only be established under conditions which are not achievable experimentally. Here we present a property of entropy, termed "entropy accumulation", which asserts that the total amount of entropy of a large system is the sum of its parts. We use this property to prove the security of cryptographic protocols, including device-independent quantum key distribution, while achieving essentially optimal parameters. Recent experimental progress, which enabled loophole-free Bell tests, suggests that the achieved parameters are technologically accessible. Our work hence provides the theoretical groundwork for experimental demonstrations of device-independent cryptography.
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 ...
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.
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.
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Weber, Gernot (Dr. Gernot Weber, Energie-Gebaeudetechnik, Kleinostheim)
2011-07-01
Thermodynamics generally is regarded as one of the most difficult fields of knowledge. This may be particularly due to the difficulties and due to the often very complicated described correlations between the terms energy, entropy and exergy in the technical literature. The contribution under consideration tries to explain these correlations to the (scientifically trained) technically interested readers understandable.
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.
Absence of log correction in entropy of large black holes
Energy Technology Data Exchange (ETDEWEB)
Ghosh, A., E-mail: amit.ghosh@saha.ac.in; Mitra, P., E-mail: parthasarathi.mitra@saha.ac.in
2014-06-27
Earlier calculations of black hole entropy in loop quantum gravity led to a dominant term proportional to the area, but there was a correction involving the logarithm of the area, the Chern–Simons level being assumed to be large. We find that the calculations yield an entropy proportional to the area eigenvalue with no such correction if the Chern–Simons level is finite, so that the area eigenvalue can be relatively large.
Maximizing Entropy of Pickard Random Fields for 2x2 Binary Constraints
DEFF Research Database (Denmark)
Søgaard, Jacob; Forchhammer, Søren
2014-01-01
This paper considers the problem of maximizing the entropy of two-dimensional (2D) Pickard Random Fields (PRF) subject to constraints. We consider binary Pickard Random Fields, which provides a 2D causal finite context model and use it to define stationary probabilities for 2x2 squares, thus...... allowing us to calculate the entropy of the field. All possible binary 2x2 constraints are considered and all constraints are categorized into groups according to their properties. For constraints which can be modeled by a PRF approach and with positive entropy, we characterize and provide statistics...... of the maximum PRF entropy. As examples, we consider the well known hard square constraint along with a few other constraints....
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)
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.
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.
Editorial: Entropy in Landscape Ecology
Directory of Open Access Journals (Sweden)
Samuel A. Cushman
2018-04-01
Full Text Available Entropy and the second law of thermodynamics are the central organizing principles of nature, but the ideas and implications of the second law are poorly developed in landscape ecology. The purpose of this Special Issue “Entropy in Landscape Ecology” in Entropy is to bring together current research on applications of thermodynamics in landscape ecology, to consolidate current knowledge and identify key areas for future research. The special issue contains six articles, which cover a broad range of topics including relationships between entropy and evolution, connections between fractal geometry and entropy, new approaches to calculate configurational entropy of landscapes, example analyses of computing entropy of landscapes, and using entropy in the context of optimal landscape planning. Collectively these papers provide a broad range of contributions to the nascent field of ecological thermodynamics. Formalizing the connections between entropy and ecology are in a very early stage, and that this special issue contains papers that address several centrally important ideas, and provides seminal work that will be a foundation for the future development of ecological and evolutionary thermodynamics.
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
Entropy Filtered Density Function for Large Eddy Simulation of Turbulent Reacting Flows
Safari, Mehdi
Analysis of local entropy generation is an effective means to optimize the performance of energy and combustion systems by minimizing the irreversibilities in transport processes. Large eddy simulation (LES) is employed to describe entropy transport and generation in turbulent reacting flows. The entropy transport equation in LES contains several unclosed terms. These are the subgrid scale (SGS) entropy flux and entropy generation caused by irreversible processes: heat conduction, mass diffusion, chemical reaction and viscous dissipation. The SGS effects are taken into account using a novel methodology based on the filtered density function (FDF). This methodology, entitled entropy FDF (En-FDF), is developed and utilized in the form of joint entropy-velocity-scalar-turbulent frequency FDF and the marginal scalar-entropy FDF, both of which contain the chemical reaction effects in a closed form. The former constitutes the most comprehensive form of the En-FDF and provides closure for all the unclosed filtered moments. This methodology is applied for LES of a turbulent shear layer involving transport of passive scalars. Predictions show favor- able agreements with the data generated by direct numerical simulation (DNS) of the same layer. The marginal En-FDF accounts for entropy generation effects as well as scalar and entropy statistics. This methodology is applied to a turbulent nonpremixed jet flame (Sandia Flame D) and predictions are validated against experimental data. In both flows, sources of irreversibility are predicted and analyzed.
Identifying Student Resources in Reasoning about Entropy and the Approach to Thermal Equilibrium
Loverude, Michael
2015-01-01
As part of an ongoing project to examine student learning in upper-division courses in thermal and statistical physics, we have examined student reasoning about entropy and the second law of thermodynamics. We have examined reasoning in terms of heat transfer, entropy maximization, and statistical treatments of multiplicity and probability. In…
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...
International Nuclear Information System (INIS)
Sun Guohua; Dong Shihai
2013-01-01
Shannon entropy for the position and momentum eigenstates of the symmetrically trigonometric Rosen–Morse potential for the lower states n = 1–4 is evaluated. The position information entropies S x for n = 1,2 are presented analytically. Some interesting features of the information entropy densities ρ s (x) and ρ s (p) are demonstrated graphically. We find that the ρ s (p) is inversely proportional to the range of potential a and the S x decreases with increasing the potential depth D. In particular, we note that the S x might become negative for some given parameters a and D. The Bialynicki-Birula–Mycielski inequality is also tested for a number of states and is found to generally hold well. (paper)
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.
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
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
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
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
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…
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 (§
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.
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.
Position-momentum uncertainty relations in the presence of quantum memory
DEFF Research Database (Denmark)
Furrer, Fabian; Berta, Mario; Tomamichel, Marco
2014-01-01
A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are thereby measured in terms of entropies providing a clear oper....... As an illustration, we evaluate the uncertainty relations for position and momentum measurements, which is operationally significant in that it implies security of a quantum key distribution scheme based on homodyne detection of squeezed Gaussian states....
Psychoacoustic entropy theory and its implications for performance practice
Strohman, Gregory J.
This dissertation attempts to motivate, derive and imply potential uses for a generalized perceptual theory of musical harmony called psychoacoustic entropy theory. This theory treats the human auditory system as a physical system which takes acoustic measurements. As a result, the human auditory system is subject to all the appropriate uncertainties and limitations of other physical measurement systems. This is the theoretic basis for defining psychoacoustic entropy. Psychoacoustic entropy is a numerical quantity which indexes the degree to which the human auditory system perceives instantaneous disorder within a sound pressure wave. Chapter one explains the importance of harmonic analysis as a tool for performance practice. It also outlines the critical limitations for many of the most influential historical approaches to modeling harmonic stability, particularly when compared to available scientific research in psychoacoustics. Rather than analyze a musical excerpt, psychoacoustic entropy is calculated directly from sound pressure waves themselves. This frames psychoacoustic entropy theory in the most general possible terms as a theory of musical harmony, enabling it to be invoked for any perceivable sound. Chapter two provides and examines many widely accepted mathematical models of the acoustics and psychoacoustics of these sound pressure waves. Chapter three introduces entropy as a precise way of measuring perceived uncertainty in sound pressure waves. Entropy is used, in combination with the acoustic and psychoacoustic models introduced in chapter two, to motivate the mathematical formulation of psychoacoustic entropy theory. Chapter four shows how to use psychoacoustic entropy theory to analyze the certain types of musical harmonies, while chapter five applies the analytical tools developed in chapter four to two short musical excerpts to influence their interpretation. Almost every form of harmonic analysis invokes some degree of mathematical reasoning
Directory of Open Access Journals (Sweden)
Henriette Elvang
2015-10-01
Full Text Available In the presence of a sharp corner in the boundary of the entanglement region, the entanglement entropy (EE and Rényi entropies for 3d CFTs have a logarithmic term whose coefficient, the corner function, is scheme-independent. In the limit where the corner becomes smooth, the corner function vanishes quadratically with coefficient σ for the EE and σn for the Rényi entropies. For a free real scalar and a free Dirac fermion, we evaluate analytically the integral expressions of Casini, Huerta, and Leitao to derive exact results for σ and σn for all n=2,3,… . The results for σ agree with a recent universality conjecture of Bueno, Myers, and Witczak-Krempa that σ/CT=π2/24 in all 3d CFTs, where CT is the central charge. For the Rényi entropies, the ratios σn/CT do not indicate similar universality. However, in the limit n→∞, the asymptotic values satisfy a simple relationship and equal 1/(4π2 times the asymptotic values of the free energy of free scalars/fermions on the n-covered 3-sphere.
Black Hole Entropy with and without Log Correction in Loop Quantum Gravity
International Nuclear Information System (INIS)
Mitra, P.
2014-01-01
Earlier calculations of black hole entropy in loop quantum gravity have given a term proportional to the area with a correction involving the logarithm of the area when the area eigenvalue is close to the classical area. However the calculations yield an entropy proportional to the area eigenvalue with no such correction when the area eigenvalue is large compared to the classical area
Institute of Scientific and Technical Information of China (English)
吴金平
1991-01-01
The relation between the excess entropy production criterion of thermodynamic stabilityfor nonequilibrium states and kinetic linear stability principle is discussed. It is shown thatthe condition required by the excess entropy production criterion generally is sufficient, butnot necessary to judge the system stability. The condition required by the excess entropyproduction criterion is stronger than that of the linear stability principle. Only when theproduct matrix between the linearized matrix of kinetic equations and matrix of quadraticform of second-order excess entropy is symmetric, is the condition required by the excessentropy production criterion that the steady steate is asymptotically stable (δ_xP>0) necessaryand sufficient. The counterexample given by Fox to prove that the excess entropy, (δ~2S)ss,is not a Liapunov function is incorrect. Contradictory to his conclusion, the counterexampleis just a positive one that proves that the excess entropy is a Liapunov function. Moreover,the excess entropy production criterion is not limited by symmetric conditions of the linear-ized matrix of kinetic equations. The excess entropy around nonequilibrium steady states,(δ~2S)ss, is a Liapunov function of thermodynamic system.
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.
Directory of Open Access Journals (Sweden)
Donghai Wang
2011-01-01
Full Text Available The concept of entropy and its relevant principles, mainly the principle of maximum entropy production (MEP, the effect of negative entropy flow (NEF on the organization of atmospheric systems and the principle of the Second Law of thermodynamics, as well as their applications to atmospheric sciences, are reviewed. Some formulations of sub-grid processes such as diffusion parameterization schemes in computational geophysical fluid dynamics that can be improved based on full-irreversibility are also discussed, although they have not yet been systematically subjected to scrutiny from the perspective of the entropy budgets. A comparative investigation shows that the principle of MEP applies to the entropy production of macroscopic fluxes and determines the most probable state, that is, a system may choose a development meta-stable trajectory with a smaller production since entropy production behavior involves many specific dynamical and thermodynamic processes in the atmosphere and the extremal principles only provide a general insight into the overall configuration of the atmosphere. In contrast to the principle of MEP, the analysis of NEF is able to provide a new insight into the mechanism responsible for the evolution of a weather system as well as a new approach to predicting its track and intensity trend.
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.
The maximization of Tsallis entropy with complete deformed functions and the problem of constraints
International Nuclear Information System (INIS)
Oikonomou, Thomas; Bagci, G. Baris
2010-01-01
By only requiring the q deformed logarithms (q exponentials) to possess arguments chosen from the entire set of positive real numbers (all real numbers), we show that the q-logarithm (q exponential) can be written in such a way that its argument varies between 0 and 1 (among negative real numbers) for 1≤q<2, while the interval 0< q≤1 corresponds to any real argument greater than 1 (positive real numbers). These two distinct intervals of the nonextensivity index q, also the expressions of the deformed functions associated with them, are related to one another through the relation (2-q), which is so far used to obtain the ordinary stationary distributions from the corresponding escort distributions, and vice versa in an almost ad hoc manner. This shows that the escort distributions are only a means of extending the interval of validity of the deformed functions to the one of ordinary, undeformed ones. Moreover, we show that, since the Tsallis entropy is written in terms of the q-logarithm and its argument, being the inverse of microstate probabilities, takes values equal to or greater than 1, the resulting stationary solution is uniquely described by the one obtained from the ordinary constraint. Finally, we observe that even the escort stationary distributions can be obtained through the use of the ordinary averaging procedure if the argument of the q-exponential lies in (-∞,0]. However, this case corresponds to, although related, a different entropy expression than the Tsallis entropy.
Li, Shu-Nan; Cao, Bing-Yang
2017-09-01
The second law of thermodynamics governs the direction of heat transport, which provides the foundational definition of thermodynamic Clausius entropy. The definitions of entropy are further generalized for the phenomenological heat transport models in the frameworks of classical irreversible thermodynamics and extended irreversible thermodynamics (EIT). In this work, entropic functions from mathematics are combined with phenomenological heat conduction models and connected to several information-geometrical conceptions. The long-time behaviors of these mathematical entropies exhibit a wide diversity and physical pictures in phenomenological heat conductions, including the tendency to thermal equilibrium, and exponential decay of nonequilibrium and asymptotics, which build a bridge between the macroscopic and microscopic modelings. In contrast with the EIT entropies, the mathematical entropies expressed in terms of the internal energy function can avoid singularity paired with nonpositive local absolute temperature caused by non-Fourier heat conduction models.
Entropy generation in natural convection in a symmetrically and uniformly heated vertical channel
Energy Technology Data Exchange (ETDEWEB)
Andreozzi, Assunta [Dipartimento di Energetica, Termofluidodinamica applicata e Condizionamenti ambientali, Universita degli Studi di Napoli Federico II, Piazzale Tecchio 80, 80125 Napoli (Italy); Auletta, Antonio [CIRA - Centro Italiano Ricerche Aerospaziali, Via Maiorise 1, 81043 Capua (CE) (Italy); Manca, Oronzio [Dipartimento di Ingegneria Aerospaziale e Meccanica, Seconda Universita degli Studi di Napoli, Real Casa dell' Annunziata, Via Roma 29, 81031 Aversa (CE) (Italy)
2006-08-15
In this study numerical predictions of local and global entropy generation rates in natural convection in air in a vertical channel symmetrically heated at uniform heat flux are reported. Results of entropy generation analysis are obtained by solving the entropy generation equation based on the velocity and temperature data. The analyzed regime is two-dimensional, laminar and steady state. The numerical procedure expands an existing computer code on natural convection in vertical channels. Results in terms of fields and profiles of local entropy generation, for various Rayleigh number, Ra, and aspect ratio values, L/b, are given. The distributions of local values show different behaviours for the different Ra values. A correlation between global entropy generation rates, Rayleigh number and aspect ratio is proposed in the ranges 10{sup 3}=
An improved thin film brick-wall model of black hole entropy
Liu Wen Biao
2001-01-01
The authors improve the brick-wall model to take only the contribution of a thin film near the event horizon into account. This improvement not only gives them a satisfactory result, but also avoids some drawbacks in the original brick-wall method such as the little mass approximation, neglecting logarithm term, and taking the term L/sup 3/ as the contribution of the vacuum surrounding a black hole. It is found that there is an intrinsic relation between the event horizon and the entropy. The event horizon is the characteristic of a black hole, so the entropy calculating of a black hole is also naturally related to its horizon. (12 refs).
Entropy Viscosity Method for High-Order Approximations of Conservation Laws
Guermond, J. L.
2010-09-17
A stabilization technique for conservation laws is presented. It introduces in the governing equations a nonlinear dissipation function of the residual of the associated entropy equation and bounded from above by a first order viscous term. Different two-dimensional test cases are simulated - a 2D Burgers problem, the "KPP rotating wave" and the Euler system - using high order methods: spectral elements or Fourier expansions. Details on the tuning of the parameters controlling the entropy viscosity are given. © 2011 Springer.
Entropy Viscosity Method for High-Order Approximations of Conservation Laws
Guermond, J. L.; Pasquetti, R.
2010-01-01
A stabilization technique for conservation laws is presented. It introduces in the governing equations a nonlinear dissipation function of the residual of the associated entropy equation and bounded from above by a first order viscous term. Different two-dimensional test cases are simulated - a 2D Burgers problem, the "KPP rotating wave" and the Euler system - using high order methods: spectral elements or Fourier expansions. Details on the tuning of the parameters controlling the entropy viscosity are given. © 2011 Springer.
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-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.
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.
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
Directory of Open Access Journals (Sweden)
Beretta, Gian Paolo
2008-02-01
Full Text Available What is the physical significance of entropy? What is the physical origin of irreversibility? Do entropy and irreversibility exist only for complex and macroscopic systems? Most physicists still accept and teach that the rationalization of these fundamental questions is given by Statistical Mechanics. Indeed, for everyday laboratory physics, the mathematical formalism of Statistical Mechanics (canonical and grand-canonical, Boltzmann, Bose-Einstein and Fermi-Dirac distributions allows a successful description of the thermodynamic equilibrium properties of matter, including entropy values. However, as already recognized by Schrodinger in 1936, Statistical Mechanics is impaired by conceptual ambiguities and logical inconsistencies, both in its explanation of the meaning of entropy and in its implications on the concept of state of a system. An alternative theory has been developed by Gyftopoulos, Hatsopoulos and the present author to eliminate these stumbling conceptual blocks while maintaining the mathematical formalism so successful in applications. To resolve both the problem of the meaning of entropy and that of the origin of irreversibility we have built entropy and irreversibility into the laws of microscopic physics. The result is a theory, that we call Quantum Thermodynamics, that has all the necessary features to combine Mechanics and Thermodynamics uniting all the successful results of both theories, eliminating the logical inconsistencies of Statistical Mechanics and the paradoxes on irreversibility, and providing an entirely new perspective on the microscopic origin of irreversibility, nonlinearity (therefore including chaotic behavior and maximal-entropy-generation nonequilibrium dynamics. In this paper we discuss the background and formalism of Quantum Thermodynamics including its nonlinear equation of motion and the main general results. Our objective is to show in a not-too-technical manner that this theory provides indeed a
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.
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.
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)
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
Uncertainty relations for information entropy in wave mechanics
International Nuclear Information System (INIS)
Bialynicki-Birula, I.; Pittsburgh Univ., Pa.; Mycielski, J.
1975-01-01
New uncertainty relations in quantum mechanics are derived. They express restrictions imposed by quantum theory on probability distributions of canonically conjugate variables in terms of corresponding information entropies. The Heisenberg uncertainty relation follows from those inequalities and so does the Gross-Nelson inequality. (orig.) [de
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.)
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)
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.
Cellular network entropy as the energy potential in Waddington's differentiation landscape
Banerji, Christopher R. S.; Miranda-Saavedra, Diego; Severini, Simone; Widschwendter, Martin; Enver, Tariq; Zhou, Joseph X.; Teschendorff, Andrew E.
2013-01-01
Differentiation is a key cellular process in normal tissue development that is significantly altered in cancer. Although molecular signatures characterising pluripotency and multipotency exist, there is, as yet, no single quantitative mark of a cellular sample's position in the global differentiation hierarchy. Here we adopt a systems view and consider the sample's network entropy, a measure of signaling pathway promiscuity, computable from a sample's genome-wide expression profile. We demonstrate that network entropy provides a quantitative, in-silico, readout of the average undifferentiated state of the profiled cells, recapitulating the known hierarchy of pluripotent, multipotent and differentiated cell types. Network entropy further exhibits dynamic changes in time course differentiation data, and in line with a sample's differentiation stage. In disease, network entropy predicts a higher level of cellular plasticity in cancer stem cell populations compared to ordinary cancer cells. Importantly, network entropy also allows identification of key differentiation pathways. Our results are consistent with the view that pluripotency is a statistical property defined at the cellular population level, correlating with intra-sample heterogeneity, and driven by the degree of signaling promiscuity in cells. In summary, network entropy provides a quantitative measure of a cell's undifferentiated state, defining its elevation in Waddington's landscape. PMID:24154593
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
Renormalized thermodynamic entropy of black holes in higher dimensions
International Nuclear Information System (INIS)
Kim, S.P.; Kim, S.K.; Soh, K.; Yee, J.H.
1997-01-01
We study the ultraviolet divergent structures of the matter (scalar) field in a higher D-dimensional Reissner-Nordstroem black hole and compute the matter field contribution to the Bekenstein-Hawking entropy by using the Pauli-Villars regularization method. We find that the matter field contribution to the black hole entropy does not, in general, yield the correct renormalization of the gravitational coupling constants. In particular, we show that the matter field contribution in odd dimensions does not give the term proportional to the area of the black hole event horizon. copyright 1997 The American Physical Society
Efficient Computation of Entropy Gradient for Semi-Supervised Conditional Random Fields
National Research Council Canada - National Science Library
Mann, Gideon S; McCallum, Andrew
2007-01-01
Entropy regularization is a straightforward and successful method of semi-supervised learning that augments the traditional conditional likelihood objective function with an additional term that aims...
Kinetics of the Dynamical Information Shannon Entropy for Complex Systems
International Nuclear Information System (INIS)
Yulmetyev, R.M.; Yulmetyeva, D.G.
1999-01-01
Kinetic behaviour of dynamical information Shannon entropy is discussed for complex systems: physical systems with non-Markovian property and memory in correlation approximation, and biological and physiological systems with sequences of the Markovian and non-Markovian random noises. For the stochastic processes, a description of the information entropy in terms of normalized time correlation functions is given. The influence and important role of two mutually dependent channels of the entropy change, correlation (creation or generation of correlations) and anti-correlation (decay or annihilation of correlation) is discussed. The method developed here is also used in analysis of the density fluctuations in liquid cesium obtained from slow neutron scattering data, fractal kinetics of the long-range fluctuation in the short-time human memory and chaotic dynamics of R-R intervals of human ECG. (author)
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.
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.
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...
CoFea: A Novel Approach to Spam Review Identification Based on Entropy and Co-Training
Directory of Open Access Journals (Sweden)
Wen Zhang
2016-11-01
Full Text Available With the rapid development of electronic commerce, spam reviews are rapidly growing on the Internet to manipulate online customers’ opinions on goods being sold. This paper proposes a novel approach, called CoFea (Co-training by Features, to identify spam reviews, based on entropy and the co-training algorithm. After sorting all lexical terms of reviews by entropy, we produce two views on the reviews by dividing the lexical terms into two subsets. One subset contains odd-numbered terms and the other contains even-numbered terms. Using SVM (support vector machine as the base classifier, we further propose two strategies, CoFea-T and CoFea-S, embedded with the CoFea approach. The CoFea-T strategy uses all terms in the subsets for spam review identification by SVM. The CoFea-S strategy uses a predefined number of terms with small entropy for spam review identification by SVM. The experiment results show that the CoFea-T strategy produces better accuracy than the CoFea-S strategy, while the CoFea-S strategy saves more computing time than the CoFea-T strategy with acceptable accuracy in spam review identification.
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.
Bayesian Maximum Entropy Based Algorithm for Digital X-ray Mammogram Processing
Directory of Open Access Journals (Sweden)
Radu Mutihac
2009-06-01
Full Text Available Basics of Bayesian statistics in inverse problems using the maximum entropy principle are summarized in connection with the restoration of positive, additive images from various types of data like X-ray digital mammograms. An efficient iterative algorithm for image restoration from large data sets based on the conjugate gradient method and Lagrange multipliers in nonlinear optimization of a specific potential function was developed. The point spread function of the imaging system was determined by numerical simulations of inhomogeneous breast-like tissue with microcalcification inclusions of various opacities. The processed digital and digitized mammograms resulted superior in comparison with their raw counterparts in terms of contrast, resolution, noise, and visibility of details.
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
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.
Epoch-based Entropy for Early Screening of Alzheimer's Disease.
Houmani, N; Dreyfus, G; Vialatte, F B
2015-12-01
In this paper, we introduce a novel entropy measure, termed epoch-based entropy. This measure quantifies disorder of EEG signals both at the time level and spatial level, using local density estimation by a Hidden Markov Model on inter-channel stationary epochs. The investigation is led on a multi-centric EEG database recorded from patients at an early stage of Alzheimer's disease (AD) and age-matched healthy subjects. We investigate the classification performances of this method, its robustness to noise, and its sensitivity to sampling frequency and to variations of hyperparameters. The measure is compared to two alternative complexity measures, Shannon's entropy and correlation dimension. The classification accuracies for the discrimination of AD patients from healthy subjects were estimated using a linear classifier designed on a development dataset, and subsequently tested on an independent test set. Epoch-based entropy reached a classification accuracy of 83% on the test dataset (specificity = 83.3%, sensitivity = 82.3%), outperforming the two other complexity measures. Furthermore, it was shown to be more stable to hyperparameter variations, and less sensitive to noise and sampling frequency disturbances than the other two complexity measures.
Surface single-molecule dynamics controlled by entropy at low temperatures
Gehrig, J. C.; Penedo, M.; Parschau, M.; Schwenk, J.; Marioni, M. A.; Hudson, E. W.; Hug, H. J.
2017-02-01
Configuration transitions of individual molecules and atoms on surfaces are traditionally described using an Arrhenius equation with energy barrier and pre-exponential factor (attempt rate) parameters. Characteristic parameters can vary even for identical systems, and pre-exponential factors sometimes differ by orders of magnitude. Using low-temperature scanning tunnelling microscopy (STM) to measure an individual dibutyl sulfide molecule on Au(111), we show that the differences arise when the relative position of tip apex and molecule changes by a fraction of the molecule size. Altering the tip position on that scale modifies the transition's barrier and attempt rate in a highly correlated fashion, which results in a single-molecular enthalpy-entropy compensation. Conversely, appropriately positioning the STM tip allows selecting the operating point on the compensation line and modifying the transition rates. The results highlight the need to consider entropy in transition rates of single molecules, even at low temperatures.
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.
Rényi entropy, stationarity, and entanglement of the conformal scalar
Energy Technology Data Exchange (ETDEWEB)
Lee, Jeongseog; Lewkowycz, Aitor [Department of Physics, Princeton University,Princeton, NJ 08544 (United States); Perlmutter, Eric [DAMTP, Centre for Mathematical Sciences, University of Cambridge,Cambridge, CB3 0WA (United Kingdom); Safdi, Benjamin R. [Department of Physics, Princeton University,Princeton, NJ 08544 (United States)
2015-03-16
We extend previous work on the perturbative expansion of the Rényi entropy, S{sub q}, around q=1 for a spherical entangling surface in a general CFT. Applied to conformal scalar fields in various spacetime dimensions, the results appear to conflict with the known conformal scalar Rényi entropies. On the other hand, the perturbative results agree with known Rényi entropies in a variety of other theories, including theories of free fermions and vector fields and theories with Einstein gravity duals. We propose a resolution stemming from a careful consideration of boundary conditions near the entangling surface. This is equivalent to a proper treatment of total-derivative terms in the definition of the modular Hamiltonian. As a corollary, we are able to resolve an outstanding puzzle in the literature regarding the Rényi entropy of N=4 super-Yang-Mills near q=1. A related puzzle regards the question of stationarity of the renormalized entanglement entropy (REE) across a circle for a (2+1)-dimensional massive scalar field. We point out that the boundary contributions to the modular Hamiltonian shed light on the previously-observed non-stationarity. Moreover, IR divergences appear in perturbation theory about the massless fixed point that inhibit our ability to reliably calculate the REE at small non-zero mass.
Rényi entropy, stationarity, and entanglement of the conformal scalar
Lee, Jeongseog; Lewkowycz, Aitor; Perlmutter, Eric; Safdi, Benjamin R.
2015-03-01
We extend previous work on the perturbative expansion of the Rényi entropy, S q , around q = 1 for a spherical entangling surface in a general CFT. Applied to conformal scalar fields in various spacetime dimensions, the results appear to conflict with the known conformal scalar Rényi entropies. On the other hand, the perturbative results agree with known Rényi entropies in a variety of other theories, including theories of free fermions and vector fields and theories with Einstein gravity duals. We propose a resolution stemming from a careful consideration of boundary conditions near the entangling surface. This is equivalent to a proper treatment of total-derivative terms in the definition of the modular Hamiltonian. As a corollary, we are able to resolve an outstanding puzzle in the literature regarding the Rényi entropy of super-Yang-Mills near q = 1. A related puzzle regards the question of stationarity of the renormalized entanglement entropy (REE) across a circle for a (2+1)-dimensional massive scalar field. We point out that the boundary contributions to the modular Hamiltonian shed light on the previously-observed non-stationarity. Moreover, IR divergences appear in perturbation theory about the massless fixed point that inhibit our ability to reliably calculate the REE at small non-zero mass.
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.
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.
Expansion, thermalization, and entropy production in high-energy nuclear collisions
International Nuclear Information System (INIS)
Heiselberg, H.; Wang, X.
1996-01-01
The thermalization process is studied in an expanding parton gas using the Boltzmann equation with two types of collision terms. In the relaxation time approximation we determine the criteria under which a time-dependent relaxation time leads to thermalization of the partons. We calculate the entropy production due to collisions for the general time-dependent relaxation time. In a perturbative QCD approach on the other hand, we can, given the initial conditions, estimate the effective relaxation time due to elastic collisions; this will be an upper limit only since radiative processes will also contribute to thermalization. We find that the parton gas does thermalize eventually but only after having undergone a phase of free streaming and gradual equilibration where considerable entropy is produced (open-quote open-quote after burning close-quote close-quote). The final entropy and thus particle density depends on the collision time as well as the initial conditions (a open-quote open-quote memory effect close-quote close-quote). Results for entropy production are presented based upon various model estimates of early parton production. copyright 1996 The American Physical Society
Giant onsite electronic entropy enhances the performance of ceria for water splitting
DEFF Research Database (Denmark)
Naghavi, S. Shahab; Emery, Antoine A.; Hansen, Heine Anton
2017-01-01
lanthanides, and reaches a maximum value of ≈4.7 kB per oxygen vacancy for Ce4+/Ce3+ reduction. This unique and large positive entropy source in ceria explains its excellent performance for high-temperature catalytic redox reactions such as water splitting. Our calculations also show that terbium dioxide has...... a high electronic entropy and thus could also be a potential candidate for solar thermochemical reactions....
Pedagogical introduction to the entropy of entanglement for Gaussian states
Demarie, Tommaso F.
2018-05-01
In quantum information theory, the entropy of entanglement is a standard measure of bipartite entanglement between two partitions of a composite system. For a particular class of continuous variable quantum states, the Gaussian states, the entropy of entanglement can be expressed elegantly in terms of symplectic eigenvalues, elements that characterise a Gaussian state and depend on the correlations of the canonical variables. We give a rigorous step-by-step derivation of this result and provide physical insights, together with an example that can be useful in practice for calculations.
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 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.
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 ...
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2015-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
The Elusive Nature of Entropy and Its Physical Meaning
Directory of Open Access Journals (Sweden)
Milivoje M. Kostic
2014-02-01
Full Text Available Entropy is the most used and often abused concept in science, but also in philosophy and society. Further confusions are produced by some attempts to generalize entropy with similar but not the same concepts in other disciplines. The physical meaning of phenomenological, thermodynamic entropy is reasoned and elaborated by generalizing Clausius definition with inclusion of generated heat, since it is irrelevant if entropy is changed due to reversible heat transfer or irreversible heat generation. Irreversible, caloric heat transfer is introduced as complementing reversible heat transfer. It is also reasoned and thus proven why entropy cannot be destroyed but is always generated (and thus over-all increased locally and globally, at every space and time scales, without any exception. It is concluded that entropy is a thermal displacement (dynamic thermal-volume of thermal energy due to absolute temperature as a thermal potential (dQ = TdS, and thus associated with thermal heat and absolute temperature, i.e., distribution of thermal energy within thermal micro-particles in space. Entropy is an integral measure of (random thermal energy redistribution (due to heat transfer and/or irreversible heat generation within a material system structure in space, per absolute temperature level: dS = dQSys/T = mCSysdT/T, thus logarithmic integral function, with J/K unit. It may be also expressed as a measure of “thermal disorder”, being related to logarithm of number of all thermal, dynamic microstates W (their position and momenta, S = kBlnW, or to the sum of their logarithmic probabilities S = −kB∑pilnpi, that correspond to, or are consistent with the given thermodynamic macro-state. The number of thermal microstates W, is correlated with macro-properties temperature T and volume V for ideal gases. A system form and/or functional order or disorder are not (thermal energy order/disorder and the former is not related to Thermodynamic entropy. Expanding
A simple expression for the entropy of a fireball from experimental strange particle ratios
International Nuclear Information System (INIS)
Levai, P.; Lukacs, B.; Zimanyi, J.; Heinz, U.
1989-04-01
An expression is derived for the specific entropy S/N B in a non-interacting, non-relativistic Boltzmann gas mixture in terms of strange particle ratios. Then the influences of relativistic and quantum statistical effects and the role of hadronic interactions on reconstructing the specific entropy from the particle ratios are studied. Since neglect of the relativistic effects causes the largest correction, they are included in an improved expression. The resulting formula gives the specific entropy from the observed particle ratios with less than 20% error. (author) 24 refs.; 3 figs
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.
Simple regular black hole with logarithmic entropy correction
Energy Technology Data Exchange (ETDEWEB)
Morales-Duran, Nicolas; Vargas, Andres F.; Hoyos-Restrepo, Paulina; Bargueno, Pedro [Universidad de los Andes, Departamento de Fisica, Bogota, Distrito Capital (Colombia)
2016-10-15
A simple regular black hole solution satisfying the weak energy condition is obtained within Einstein-non-linear electrodynamics theory. We have computed the thermodynamic properties of this black hole by a careful analysis of the horizons and we have found that the usual Bekenstein-Hawking entropy gets corrected by a logarithmic term. Therefore, in this sense our model realises some quantum gravity predictions which add this kind of correction to the black hole entropy. In particular, we have established some similitudes between our model and a quadratic generalised uncertainty principle. This similitude has been confirmed by the existence of a remnant, which prevents complete evaporation, in agreement with the quadratic generalised uncertainty principle case. (orig.)
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
Entropy Generation and Human Aging: Lifespan Entropy and Effect of Physical Activity Level
Directory of Open Access Journals (Sweden)
Kalyan Annamalai
2008-06-01
Full Text Available The first and second laws of thermodynamics were applied to biochemical reactions typical of human metabolism. An open-system model was used for a human body. Energy conservation, availability and entropy balances were performed to obtain the entropy generated for the main food components. Quantitative results for entropy generation were obtained as a function of age using the databases from the U.S. Food and Nutrition Board (FNB and Centers for Disease Control and Prevention (CDC, which provide energy requirements and food intake composition as a function of age, weight and stature. Numerical integration was performed through human lifespan for different levels of physical activity. Results were presented and analyzed. Entropy generated over the lifespan of average individuals (natural death was found to be 11,404 kJ/Ã‚ÂºK per kg of body mass with a rate of generation three times higher on infants than on the elderly. The entropy generated predicts a life span of 73.78 and 81.61 years for the average U.S. male and female individuals respectively, which are values that closely match the average lifespan from statistics (74.63 and 80.36 years. From the analysis of the effect of different activity levels, it is shown that entropy generated increases with physical activity, suggesting that exercise should be kept to a Ã¢Â€Âœhealthy minimumÃ¢Â€Â if entropy generation is to be minimized.
Entropy 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.
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.
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.
Kuramochi, Yui; Ueda, Masahito
2015-03-01
We consider the information flow on a system observable X corresponding to a positive-operator-valued measure under a quantum measurement process Y described by a completely positive instrument from the viewpoint of the relative entropy. We establish a sufficient condition for the relative-entropy conservation law which states that the average decrease in the relative entropy of the system observable X equals the relative entropy of the measurement outcome of Y , i.e., the information gain due to measurement. This sufficient condition is interpreted as an assumption of classicality in the sense that there exists a sufficient statistic in a joint successive measurement of Y followed by X such that the probability distribution of the statistic coincides with that of a single measurement of X for the premeasurement state. We show that in the case when X is a discrete projection-valued measure and Y is discrete, the classicality condition is equivalent to the relative-entropy conservation for arbitrary states. The general theory on the relative-entropy conservation is applied to typical quantum measurement models, namely, quantum nondemolition measurement, destructive sharp measurements on two-level systems, a photon counting, a quantum counting, homodyne and heterodyne measurements. These examples except for the nondemolition and photon-counting measurements do not satisfy the known Shannon-entropy conservation law proposed by Ban [M. Ban, J. Phys. A: Math. Gen. 32, 1643 (1999), 10.1088/0305-4470/32/9/012], implying that our approach based on the relative entropy is applicable to a wider class of quantum measurements.
Single-cell entropy for accurate estimation of differentiation potency from a cell's transcriptome
Teschendorff, Andrew E.; Enver, Tariq
2017-01-01
The ability to quantify differentiation potential of single cells is a task of critical importance. Here we demonstrate, using over 7,000 single-cell RNA-Seq profiles, that differentiation potency of a single cell can be approximated by computing the signalling promiscuity, or entropy, of a cell's transcriptome in the context of an interaction network, without the need for feature selection. We show that signalling entropy provides a more accurate and robust potency estimate than other entropy-based measures, driven in part by a subtle positive correlation between the transcriptome and connectome. Signalling entropy identifies known cell subpopulations of varying potency and drug resistant cancer stem-cell phenotypes, including those derived from circulating tumour cells. It further reveals that expression heterogeneity within single-cell populations is regulated. In summary, signalling entropy allows in silico estimation of the differentiation potency and plasticity of single cells and bulk samples, providing a means to identify normal and cancer stem-cell phenotypes. PMID:28569836
On the Possibility of Calculating Entropy, Free Energy, and Enthalpy of Vitreous Substances
Directory of Open Access Journals (Sweden)
Sergei V. Nemilov
2018-03-01
Full Text Available A critical analysis for the arguments in support of, and against, the traditional approach to thermodynamics of vitreous state is provided. In this approach one presumes that there is a continuous variation of the entropy in the glass-liquid transition temperature range, or a “continuous entropy approach” towards 0 K which produces a positive value of the entropy at T → 0 K. I find that arguments given against this traditional approach use a different understanding of the thermodynamics of glass transition on cooling a liquid, because it suggests a discontinuity or “entropy loss approach” in the variation of entropy in the glass-liquid transition range. That is based on: (1 an unjustifiable use of the classical Boltzmann statistics for interpreting the value of entropy at absolute zero; (2 the rejection of thermodynamic analysis of systems with broken ergodicity, even though the possibility of analogous analysis was proposed already by Gibbs; (3 the possibility of a finite change in entropy of a system without absorption or release of heat; and, (4 describing the thermodynamic properties of glasses in the framework of functions, instead of functionals. The last one is necessary because for glasses the entropy and enthalpy are not functions of the state, but functionals, as defined by Gibbs’ in his classification.
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)
Directory of Open Access Journals (Sweden)
Mathias Baumert
2014-12-01
Full Text Available Autonomic activity affects beat-to-beat variability of heart rate and QT interval. The aim of this study was to explore whether entropy measures are suitable to detect changes in neural outflow to the heart elicited by two different stress paradigms. We recorded short-term ECG in 11 normal subjects during an experimental protocol that involved head-up tilt and mental arithmetic stress and computed sample entropy, cross-sample entropy and causal interactions based on conditional entropy from RR and QT interval time series. Head-up tilt resulted in a significant reduction in sample entropy of RR intervals and cross-sample entropy, while mental arithmetic stress resulted in a significant reduction in coupling directed from RR to QT. In conclusion, measures of entropy are suitable to detect changes in neural outflow to the heart and decoupling of repolarisation variability from heart rate variability elicited by orthostatic or mental arithmetic stress.
Testing the mutual information expansion of entropy with multivariate Gaussian distributions.
Goethe, Martin; Fita, Ignacio; Rubi, J Miguel
2017-12-14
The mutual information expansion (MIE) represents an approximation of the configurational entropy in terms of low-dimensional integrals. It is frequently employed to compute entropies from simulation data of large systems, such as macromolecules, for which brute-force evaluation of the full configurational integral is intractable. Here, we test the validity of MIE for systems consisting of more than m = 100 degrees of freedom (dofs). The dofs are distributed according to multivariate Gaussian distributions which were generated from protein structures using a variant of the anisotropic network model. For the Gaussian distributions, we have semi-analytical access to the configurational entropy as well as to all contributions of MIE. This allows us to accurately assess the validity of MIE for different situations. We find that MIE diverges for systems containing long-range correlations which means that the error of consecutive MIE approximations grows with the truncation order n for all tractable n ≪ m. This fact implies severe limitations on the applicability of MIE, which are discussed in the article. For systems with correlations that decay exponentially with distance, MIE represents an asymptotic expansion of entropy, where the first successive MIE approximations approach the exact entropy, while MIE also diverges for larger orders. In this case, MIE serves as a useful entropy expansion when truncated up to a specific truncation order which depends on the correlation length of the system.
Entanglement temperature with Gauss–Bonnet term
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Shesansu Sekhar Pal
2015-09-01
Full Text Available We compute the entanglement temperature using the first law-like of thermodynamics, ΔE=TentΔSEE, up to Gauss–Bonnet term in the Jacobson–Myers entropy functional in any arbitrary spacetime dimension. The computation is done when the entangling region is the geometry of a slab. We also show that such a Gauss–Bonnet term, which becomes a total derivative, when the co-dimension two hypersurface is four dimensional, does not contribute to the finite term in the entanglement entropy. We observe that the Weyl-squared term does not contribute to the entanglement entropy. It is important to note that the calculations are performed when the entangling region is very small and the energy is calculated using the normal Hamiltonian.
Local Entropy Production in Turbulent Shear Flows: A Tool for Evaluating Heat Transfer Performance
Institute of Scientific and Technical Information of China (English)
H. HERWIG; F. KOCK
2006-01-01
Performance evaluation of heat transfer devices can be based on the overall entropy production in these devices.In our study we therefore provide equations for the systematic and detailed determination of local entropy production due to dissipation of mechanical energy and due to heat conduction, both in turbulent flows. After turbulence modeling has been incorporated for the fluctuating parts the overall entropy production can be determined by integration with respect to the whole flow domain. Since, however, entropy production rates show very steep gradients close to the wall, numerical solutions are far more effective with wall functions for the entropy production terms. These wall functions are mandatory when high Reynolds number turbulence models are used. For turbulent flow in a pipe with an inserted twisted tape as heat transfer promoter it is shown that based on the overall entropy production rate a clear statement from a thermodynamic point of view is possible. For a certain range of twist strength there is a decrease in overall entropy production compared to the case without insert. Also, the optimum twist strength can be determined. This information is unavailable when only pressure drop and heat transfer data are given.
International Nuclear Information System (INIS)
Papaioannou, V E; Pneumatikos, I A; Chouvarda, I G; Maglaveras, N K; Baltopoulos, G I
2013-01-01
A few studies estimating temperature complexity have found decreased Shannon entropy, during severe stress. In this study, we measured both Shannon and Tsallis entropy of temperature signals in a cohort of critically ill patients and compared these measures with the sequential organ failure assessment (SOFA) score, in terms of intensive care unit (ICU) mortality. Skin temperature was recorded in 21 mechanically ventilated patients, who developed sepsis and septic shock during the first 24 h of an ICU-acquired infection. Shannon and Tsallis entropies were calculated in wavelet-based decompositions of the temperature signal. Statistically significant differences of entropy features were tested between survivors and non-survivors and classification models were built, for predicting final outcome. Significantly reduced Tsallis and Shannon entropies were found in non-survivors (seven patients, 33%) as compared to survivors. Wavelet measurements of both entropy metrics were found to predict ICU mortality better than SOFA, according to a combination of area under the curve, sensitivity and specificity values. Both entropies exhibited similar prognostic accuracy. Combination of SOFA and entropy presented improved the outcome of univariate models. We suggest that reduced wavelet Shannon and Tsallis entropies of temperature signals may complement SOFA in mortality prediction, during the first 24 h of an ICU-acquired infection. (paper)
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)
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 ...
Entropies of negative incomes, Pareto-distributed loss, and financial crises.
Gao, Jianbo; Hu, Jing; Mao, Xiang; Zhou, Mi; Gurbaxani, Brian; Lin, Johnny
2011-01-01
Health monitoring of world economy is an important issue, especially in a time of profound economic difficulty world-wide. The most important aspect of health monitoring is to accurately predict economic downturns. To gain insights into how economic crises develop, we present two metrics, positive and negative income entropy and distribution analysis, to analyze the collective "spatial" and temporal dynamics of companies in nine sectors of the world economy over a 19 year period from 1990-2008. These metrics provide accurate predictive skill with a very low false-positive rate in predicting downturns. The new metrics also provide evidence of phase transition-like behavior prior to the onset of recessions. Such a transition occurs when negative pretax incomes prior to or during economic recessions transition from a thin-tailed exponential distribution to the higher entropy Pareto distribution, and develop even heavier tails than those of the positive pretax incomes. These features propagate from the crisis initiating sector of the economy to other sectors.
Entropies of negative incomes, Pareto-distributed loss, and financial crises.
Directory of Open Access Journals (Sweden)
Jianbo Gao
Full Text Available Health monitoring of world economy is an important issue, especially in a time of profound economic difficulty world-wide. The most important aspect of health monitoring is to accurately predict economic downturns. To gain insights into how economic crises develop, we present two metrics, positive and negative income entropy and distribution analysis, to analyze the collective "spatial" and temporal dynamics of companies in nine sectors of the world economy over a 19 year period from 1990-2008. These metrics provide accurate predictive skill with a very low false-positive rate in predicting downturns. The new metrics also provide evidence of phase transition-like behavior prior to the onset of recessions. Such a transition occurs when negative pretax incomes prior to or during economic recessions transition from a thin-tailed exponential distribution to the higher entropy Pareto distribution, and develop even heavier tails than those of the positive pretax incomes. These features propagate from the crisis initiating sector of the economy to other sectors.
N{sup 3} entropy of M5 branes from dielectric effect
Energy Technology Data Exchange (ETDEWEB)
Hatefi, E., E-mail: ehatefi@ictp.it [International Centre for Theoretical Physics, Strada Costiera 11, Trieste (Italy); Nurmagambetov, A.J., E-mail: ajn@kipt.kharkov.ua [A.I. Akhiezer Institute for Theoretical Physics of NSC KIPT, 1 Akademicheskaya St., Kharkov, UA 61108 (Ukraine); Park, I.Y., E-mail: inyongpark05@gmail.com [Department of Natural and physical Sciences, Philander Smith College, Little Rock, AR 72223 (United States)
2013-01-01
We observe that the N{sup 3} entropy behavior of near-extremal M5 branes can be reproduced from SYM side with the role of Myers' terms. We start by generalizing the Klebanov-Tseytlin (KT) supergravity solution that displays the N{sup 3} entropy behavior. The new feature of the general solution is visibility of the 'internal' degrees of the M5 branes, i.e., the M0 branes and the M2 branes. With the rationale provided by the supergravity analysis, we consider a D0 brane quantum mechanical setup with Myers' terms. Using localization technique, we show that the leading N{sup 3} behavior of the free energy comes from the 'classical contribution' with the rest subleading.
von Neumann entropy associated with the haldane exclusion statistics
International Nuclear Information System (INIS)
Rajagopal, A.K.
1995-01-01
We obtain the von Neumann entropy per state of the Haldane exclusion statistics with parameter g in terms of the mean occupation number bar n{wlnw-(1+w)ln(1+w)}, where w=(1-bar n). This reduces correctly to the well known expressions in the limiting cases of Bose (g=0) and Fermi (g=1) statistics. We have derived the second and third order fluctuations in the occupation numbers for arbitrary g. An elegant general duality relationship between the w factor associated with the particle and that associated with the hole at the reciprocal g is deduced along with the attendant relationship between the two respective entropies
Numerical analysis of entropy generation in an annular microcombustor using multistep kinetics
International Nuclear Information System (INIS)
Jejurkar, Swarup Y.; Mishra, D.P.
2013-01-01
Entropy generation by combustion and additional irreversibility due to heat loss was studied numerically for a premixed flame based microcombustor. Detailed axisymmetric reactive flow model employing a 21 step–9 species reaction mechanism for hydrogen–air mixture was considered. The analysis identified reactions contributing most of the entropy generated in combustion. These reactions are removed from thermodynamic equilibrium in the low temperature region between 400 and 700 K of the flame and a combination of their high affinity and low temperature induces entropy generation in this region. Single step kinetics and a reduced scheme neglecting HO 2 is consequently incapable of accurately calculating the entropy generation and second law performance. Overall entropy generation rates increased from lean to rich mixtures in the range Φ = 0.5–1.4 and were dominated by combustion reactions. Characterization of combustor performance in terms of second law efficiency showed that availability reduction by wall heat losses and combustion irreversibility were of the same order for stoichiometric and both decreased for rich flames. On the other hand, near-quenching fuel lean flames (Φ≤0.75) suffered mostly from combustion irreversibility. These trends caused the minimum efficiency (maximum thermodynamic irreversibility) point to locate near stoichiometric fuel–air composition. -- Highlights: ► Reaction set dominating heat release and entropy generation involve HO 2 . ► Entropy generation increased from lean to rich Φ. ► Second law efficiency is minimum at stoichiometric Φ. ► Post-flame heat loss, transport processes needed in microcombustor entropy analysis
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
Nearest Neighbor Estimates of Entropy for Multivariate Circular Distributions
Directory of Open Access Journals (Sweden)
Neeraj Misra
2010-05-01
Full Text Available In molecular sciences, the estimation of entropies of molecules is important for the understanding of many chemical and biological processes. Motivated by these applications, we consider the problem of estimating the entropies of circular random vectors and introduce non-parametric estimators based on circular distances between n sample points and their k th nearest neighbors (NN, where k (≤ n – 1 is a fixed positive integer. The proposed NN estimators are based on two different circular distances, and are proven to be asymptotically unbiased and consistent. The performance of one of the circular-distance estimators is investigated and compared with that of the already established Euclidean-distance NN estimator using Monte Carlo samples from an analytic distribution of six circular variables of an exactly known entropy and a large sample of seven internal-rotation angles in the molecule of tartaric acid, obtained by a realistic molecular-dynamics simulation.
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
Sonnino, Giorgio; Steinbrecher, György; Cardinali, Alessandro; Sonnino, Alberto; Tlidi, Mustapha
2013-01-01
Using statistical thermodynamics, we derive a general expression of the stationary probability distribution for thermodynamic systems driven out of equilibrium by several thermodynamic forces. The local equilibrium is defined by imposing the minimum entropy production and the maximum entropy principle under the scale invariance restrictions. The obtained probability distribution presents a singularity that has immediate physical interpretation in terms of the intermittency models. The derived reference probability distribution function is interpreted as time and ensemble average of the real physical one. A generic family of stochastic processes describing noise-driven intermittency, where the stationary density distribution coincides exactly with the one resulted from entropy maximization, is presented.
Field’s entropy in the atom–field interaction: Statistical mixture of coherent states
Energy Technology Data Exchange (ETDEWEB)
Zúñiga-Segundo, Arturo [Instituto Politécnico Nacional. ESFM Departamento de Física, Edificio 9 Unidad Profesional Adolfo López Mateos, CP 07738 CDMX (Mexico); Juárez-Amaro, Raúl [Universidad Tecnológica de la Mixteca, Apdo. Postal 71, Huajuapan de León, Oax., 69000 (Mexico); Aguilar-Loreto, Omar [Departamento de Ingenierías, CUCSur, Universidad de Guadalajara CP 48900, Autlán de Navarro, Jal. (Mexico); Moya-Cessa, Héctor M., E-mail: hmmc@inaoep.mx [Instituto Nacional de Astrofísica, Óptica y Electrónica, Calle Luis Enrique Erro No. 1, Sta. Ma. Tonantzintla, Pue. CP 72840 (Mexico)
2017-04-15
We study the atom–field interaction when the field is in a mixture of coherent states. We show that in this case it is possible to calculate analytically the field entropy for times of the order of twice the collapse time. Such analytical results are done with the help of numerical analysis. We also give an expression in terms of Chebyshev polynomials for power of density matrices. - Highlights: • We calculate the field entropy for times of the order of twice the collapse time. • We give a relation between powers of the density matrices of the subsystems. • Entropy operators for both subsystems are obtained.
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
Energy Technology Data Exchange (ETDEWEB)
Papoular, R
1997-07-01
The Fourier Transform is of central importance to Crystallography since it allows the visualization in real space of tridimensional scattering densities pertaining to physical systems from diffraction data (powder or single-crystal diffraction, using x-rays, neutrons, electrons or else). In turn, this visualization makes it possible to model and parametrize these systems, the crystal structures of which are eventually refined by Least-Squares techniques (e.g., the Rietveld method in the case of Powder Diffraction). The Maximum Entropy Method (sometimes called MEM or MaxEnt) is a general imaging technique, related to solving ill-conditioned inverse problems. It is ideally suited for tackling undetermined systems of linear questions (for which the number of variables is much larger than the number of equations). It is already being applied successfully in Astronomy, Radioastronomy and Medical Imaging. The advantages of using MAXIMUM Entropy over conventional Fourier and `difference Fourier` syntheses stem from the following facts: MaxEnt takes the experimental error bars into account; MaxEnt incorporate Prior Knowledge (e.g., the positivity of the scattering density in some instances); MaxEnt allows density reconstructions from incompletely phased data, as well as from overlapping Bragg reflections; MaxEnt substantially reduces truncation errors to which conventional experimental Fourier reconstructions are usually prone. The principles of Maximum Entropy imaging as applied to Crystallography are first presented. The method is then illustrated by a detailed example specific to Neutron Diffraction: the search for proton in solids. (author). 17 refs.
Entropies of the Chinese Land Use/Cover Change from 1990 to 2010 at a County Level
Directory of Open Access Journals (Sweden)
Yong Fan
2017-01-01
Full Text Available Land Use/Cover Change (LUCC has gradually became an important direction in the research of global changes. LUCC is a complex system, and entropy is a measure of the degree of disorder of a system. According to land use information entropy, this paper analyzes changes in land use from the perspective of the system. Research on the entropy of LUCC structures has a certain “guiding role” for the optimization and adjustment of regional land use structure. Based on the five periods of LUCC data from the year of 1990 to 2010, this paper focuses on analyzing three types of LUCC entropies among counties in China—namely, Shannon, Renyi, and Tsallis entropies. The findings suggest that: (1 Shannon entropy can reflect the volatility of the LUCC, that Renyi and Tsallis entropies also have this function when their parameter has a positive value, and that Renyi and Tsallis entropies can reflect the extreme case of the LUCC when their parameter has a negative value.; (2 The entropy of China’s LUCC is uneven in time and space distributions, and that there is a large trend during 1990–2010, the central region generally has high entropy in space.
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)
Marwaha, Puneeta; Sunkaria, Ramesh Kumar
2017-02-01
Multiscale entropy (MSE) and refined multiscale entropy (RMSE) techniques are being widely used to evaluate the complexity of a time series across multiple time scales 't'. Both these techniques, at certain time scales (sometimes for the entire time scales, in the case of RMSE), assign higher entropy to the HRV time series of certain pathologies than that of healthy subjects, and to their corresponding randomized surrogate time series. This incorrect assessment of signal complexity may be due to the fact that these techniques suffer from the following limitations: (1) threshold value 'r' is updated as a function of long-term standard deviation and hence unable to explore the short-term variability as well as substantial variability inherited in beat-to-beat fluctuations of long-term HRV time series. (2) In RMSE, entropy values assigned to different filtered scaled time series are the result of changes in variance, but do not completely reflect the real structural organization inherited in original time series. In the present work, we propose an improved RMSE (I-RMSE) technique by introducing a new procedure to set the threshold value by taking into account the period-to-period variability inherited in a signal and evaluated it on simulated and real HRV database. The proposed I-RMSE assigns higher entropy to the age-matched healthy subjects than that of patients suffering from atrial fibrillation, congestive heart failure, sudden cardiac death and diabetes mellitus, for the entire time scales. The results strongly support the reduction in complexity of HRV time series in female group, old-aged, patients suffering from severe cardiovascular and non-cardiovascular diseases, and in their corresponding surrogate time series.
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.
Topological Rényi entropy after a quantum quench.
Halász, Gábor B; Hamma, Alioscia
2013-04-26
We present an analytical study on the resilience of topological order after a quantum quench. The system is initially prepared in the ground state of the toric-code model, and then quenched by switching on an external magnetic field. During the subsequent time evolution, the variation in topological order is detected via the topological Rényi entropy of order 2. We consider two different quenches: the first one has an exact solution, while the second one requires perturbation theory. In both cases, we find that the long-term time average of the topological Rényi entropy in the thermodynamic limit is the same as its initial value. Based on our results, we argue that topological order is resilient against a wide range of quenches.
Rényi-Fisher entropy product as a marker of topological phase transitions
Bolívar, J. C.; Nagy, Ágnes; Romera, Elvira
2018-05-01
The combined Rényi-Fisher entropy product of electrons plus holes displays a minimum at the charge neutrality points. The Stam-Rényi difference and the Stam-Rényi uncertainty product of the electrons plus holes, show maxima at the charge neutrality points. Topological quantum numbers capable of detecting the topological insulator and the band insulator phases, are defined. Upper and lower bounds for the position and momentum space Rényi-Fisher entropy products are derived.
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
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
Subleading contributions to the black hole entropy in the brick wall approach
International Nuclear Information System (INIS)
Sarkar, Sudipta; Shankaranarayanan, S.; Sriramkumar, L.
2008-01-01
The brick wall model is a semiclassical approach to understand the microscopic origin of black hole entropy. In this approach, the black hole geometry is assumed to be a fixed classical background on which matter fields propagate, and the entropy of black holes supposedly arises due to the canonical entropy of matter fields outside the black hole event horizon, evaluated at the Hawking temperature. Apart from certain lower dimensional cases, the density of states of the matter fields around black holes cannot be evaluated exactly. As a result, often, in the brick wall model, the density of states and the resulting canonical entropy of the matter fields are evaluated at the leading order (in terms of (ℎ/2π)) in the WKB approximation. The success of the approach is reflected by the fact that the Bekenstein-Hawking area law - viz. that the entropy of black holes is equal to one-quarter the area of their event horizon, say, A H - has been recovered using this model in a variety of black hole spacetimes. In this work, we compute the canonical entropy of a quantum scalar field around static and spherically symmetric black holes through the brick wall approach at the higher orders (in fact, up to the sixth order in (ℎ/2π)) in the WKB approximation. We explicitly show that the brick wall model generally predicts corrections to the Bekenstein-Hawking entropy in all spacetime dimensions. In four dimensions, we find that the corrections to the Bekenstein-Hawking entropy are of the form [A H n logA H ], while, in six dimensions, the corrections behave as [A H m +A H n logA H ], where (m,n)<1. We compare our results with the corrections to the Bekenstein-Hawking entropy that have been obtained through the other approaches in the literature, and discuss the implications.
Computing algebraic transfer entropy and coupling directions via transcripts
Amigó, José M.; Monetti, Roberto; Graff, Beata; Graff, Grzegorz
2016-11-01
Most random processes studied in nonlinear time series analysis take values on sets endowed with a group structure, e.g., the real and rational numbers, and the integers. This fact allows to associate with each pair of group elements a third element, called their transcript, which is defined as the product of the second element in the pair times the first one. The transfer entropy of two such processes is called algebraic transfer entropy. It measures the information transferred between two coupled processes whose values belong to a group. In this paper, we show that, subject to one constraint, the algebraic transfer entropy matches the (in general, conditional) mutual information of certain transcripts with one variable less. This property has interesting practical applications, especially to the analysis of short time series. We also derive weak conditions for the 3-dimensional algebraic transfer entropy to yield the same coupling direction as the corresponding mutual information of transcripts. A related issue concerns the use of mutual information of transcripts to determine coupling directions in cases where the conditions just mentioned are not fulfilled. We checked the latter possibility in the lowest dimensional case with numerical simulations and cardiovascular data, and obtained positive results.
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)
Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains
Directory of Open Access Journals (Sweden)
Rodrigo Cofré
2018-01-01
Full Text Available The spiking activity of neuronal networks follows laws that are not time-reversal symmetric; the notion of pre-synaptic and post-synaptic neurons, stimulus correlations and noise correlations have a clear time order. Therefore, a biologically realistic statistical model for the spiking activity should be able to capture some degree of time irreversibility. We use the thermodynamic formalism to build a framework in the context maximum entropy models to quantify the degree of time irreversibility, providing an explicit formula for the information entropy production of the inferred maximum entropy Markov chain. We provide examples to illustrate our results and discuss the importance of time irreversibility for modeling the spike train statistics.
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.
The Entropy of Co-Compact Open Covers
Directory of Open Access Journals (Sweden)
Steven Bourquin
2013-06-01
Full Text Available Co-compact entropy is introduced as an invariant of topological conjugation for perfect mappings defined on any Hausdorff space (compactness and metrizability are not necessarily required. This is achieved through the consideration of co-compact covers of the space. The advantages of co-compact entropy include: (1 it does not require the space to be compact and, thus, generalizes Adler, Konheim and McAndrew’s topological entropy of continuous mappings on compact dynamical systems; and (2 it is an invariant of topological conjugation, compared to Bowen’s entropy, which is metric-dependent. Other properties of co-compact entropy are investigated, e.g., the co-compact entropy of a subsystem does not exceed that of the whole system. For the linear system, (R; f, defined by f(x = 2x, the co-compact entropy is zero, while Bowen’s entropy for this system is at least log 2. More generally, it is found that co-compact entropy is a lower bound of Bowen’s entropies, and the proof of this result also generates the Lebesgue Covering Theorem to co-compact open covers of non-compact metric spaces.
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.
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)
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.
Winning market positioning strategies for long term care facilities.
Higgins, L F; Weinstein, K; Arndt, K
1997-01-01
The decision to develop an aggressive marketing strategy for its long term care facility has become a priority for the management of a one-hundred bed facility in the Rocky Mountain West. Financial success and lasting competitiveness require that the facility in question (Deer Haven) establish itself as the preferred provider of long term care for its target market. By performing a marketing communications audit, Deer Haven evaluated its present market position and created a strategy for solidifying and dramatizing this position. After an overview of present conditions in the industry, we offer a seven step process that provides practical guidance for positioning a long term care facility. We conclude by providing an example application.
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.
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.
Thomas, David; Finan, Chris; Newport, Melanie J; Jones, Susan
2015-10-01
The complexity of DNA can be quantified using estimates of entropy. Variation in DNA complexity is expected between the promoters of genes with different transcriptional mechanisms; namely housekeeping (HK) and tissue specific (TS). The former are transcribed constitutively to maintain general cellular functions, and the latter are transcribed in restricted tissue and cells types for specific molecular events. It is known that promoter features in the human genome are related to tissue specificity, but this has been difficult to quantify on a genomic scale. If entropy effectively quantifies DNA complexity, calculating the entropies of HK and TS gene promoters as profiles may reveal significant differences. Entropy profiles were calculated for a total dataset of 12,003 human gene promoters and for 501 housekeeping (HK) and 587 tissue specific (TS) human gene promoters. The mean profiles show the TS promoters have a significantly lower entropy (pentropy distributions for the 3 datasets show that promoter entropies could be used to identify novel HK genes. Functional features comprise DNA sequence patterns that are non-random and hence they have lower entropies. The lower entropy of TS gene promoters can be explained by a higher density of positive and negative regulatory elements, required for genes with complex spatial and temporary expression. Copyright © 2015 Elsevier Ltd. All rights reserved.
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.
Entanglement entropy of two disjoint blocks in XY chains
International Nuclear Information System (INIS)
Fagotti, Maurizio; Calabrese, Pasquale
2010-01-01
We study the Rényi entanglement entropies of two disjoint intervals in XY chains. We exploit the exact solution of the model in terms of free Majorana fermions and we show how to construct the reduced density matrix in the spin variables by taking the Jordan–Wigner string between the two blocks properly into account. From this we can evaluate any Rényi entropy of finite integer order. We study in detail critical XX and Ising chains and we show that the asymptotic results for large blocks agree with recent conformal field theory predictions if corrections to the scaling are included in the analysis correctly. We also report results for the gapped phase and after a quantum quench
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 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.
Holographic entanglement for Chern-Simons terms
International Nuclear Information System (INIS)
Azeyanagi, Tatsuo; Loganayagam, R.; Ng, Gim Seng
2017-01-01
We derive the holographic entanglement entropy contribution from pure and mixed gravitational Chern-Simons(CS) terms in AdS 2k+1 . This is done through two different methods: first, by a direct evaluation of CS action in a holographic replica geometry and second by a descent of Dong’s derivation applied to the corresponding anomaly polynomial. In lower dimensions (k=1,2), the formula coincides with the Tachikawa formula for black hole entropy from gravitational CS terms. New extrinsic curvature corrections appear for k≥3: we give explicit and concise expressions for the two pure gravitational CS terms in AdS 7 and present various consistency checks, including agreements with the black hole entropy formula when evaluated at the bifurcation surface.
Holographic entanglement for Chern-Simons terms
Energy Technology Data Exchange (ETDEWEB)
Azeyanagi, Tatsuo [Département de Physique, Ecole Normale Supérieure, CNRS,24 rue Lhomond, 75005 Paris (France); Loganayagam, R. [School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States); Ng, Gim Seng [Department of Physics, McGill University,Montréal, QC H3A 2T8 (Canada)
2017-02-01
We derive the holographic entanglement entropy contribution from pure and mixed gravitational Chern-Simons(CS) terms in AdS{sub 2k+1}. This is done through two different methods: first, by a direct evaluation of CS action in a holographic replica geometry and second by a descent of Dong’s derivation applied to the corresponding anomaly polynomial. In lower dimensions (k=1,2), the formula coincides with the Tachikawa formula for black hole entropy from gravitational CS terms. New extrinsic curvature corrections appear for k≥3: we give explicit and concise expressions for the two pure gravitational CS terms in AdS{sub 7} and present various consistency checks, including agreements with the black hole entropy formula when evaluated at the bifurcation surface.
Holographic entanglement for Chern-Simons terms
Azeyanagi, Tatsuo; Loganayagam, R.; Ng, Gim Seng
2017-02-01
We derive the holographic entanglement entropy contribution from pure and mixed gravitational Chern-Simons(CS) terms in AdS2 k+1. This is done through two different methods: first, by a direct evaluation of CS action in a holographic replica geometry and second by a descent of Dong's derivation applied to the corresponding anomaly polynomial. In lower dimensions ( k = 1 , 2), the formula coincides with the Tachikawa formula for black hole entropy from gravitational CS terms. New extrinsic curvature corrections appear for k ≥ 3: we give explicit and concise expressions for the two pure gravitational CS terms in AdS7 and present various consistency checks, including agreements with the black hole entropy formula when evaluated at the bifurcation surface.
Ugarte, Juan P.; Orozco-Duque, Andrés; Tobón, Catalina; Kremen, Vaclav; Novak, Daniel; Saiz, Javier; Oesterlein, Tobias; Schmitt, Clauss; Luik, Armin; Bustamante, John
2014-01-01
There is evidence that rotors could be drivers that maintain atrial fibrillation. Complex fractionated atrial electrograms have been located in rotor tip areas. However, the concept of electrogram fractionation, defined using time intervals, is still controversial as a tool for locating target sites for ablation. We hypothesize that the fractionation phenomenon is better described using non-linear dynamic measures, such as approximate entropy, and that this tool could be used for locating the rotor tip. The aim of this work has been to determine the relationship between approximate entropy and fractionated electrograms, and to develop a new tool for rotor mapping based on fractionation levels. Two episodes of chronic atrial fibrillation were simulated in a 3D human atrial model, in which rotors were observed. Dynamic approximate entropy maps were calculated using unipolar electrogram signals generated over the whole surface of the 3D atrial model. In addition, we optimized the approximate entropy calculation using two real multi-center databases of fractionated electrogram signals, labeled in 4 levels of fractionation. We found that the values of approximate entropy and the levels of fractionation are positively correlated. This allows the dynamic approximate entropy maps to localize the tips from stable and meandering rotors. Furthermore, we assessed the optimized approximate entropy using bipolar electrograms generated over a vicinity enclosing a rotor, achieving rotor detection. Our results suggest that high approximate entropy values are able to detect a high level of fractionation and to locate rotor tips in simulated atrial fibrillation episodes. We suggest that dynamic approximate entropy maps could become a tool for atrial fibrillation rotor mapping. PMID:25489858
Ugarte, Juan P; Orozco-Duque, Andrés; Tobón, Catalina; Kremen, Vaclav; Novak, Daniel; Saiz, Javier; Oesterlein, Tobias; Schmitt, Clauss; Luik, Armin; Bustamante, John
2014-01-01
There is evidence that rotors could be drivers that maintain atrial fibrillation. Complex fractionated atrial electrograms have been located in rotor tip areas. However, the concept of electrogram fractionation, defined using time intervals, is still controversial as a tool for locating target sites for ablation. We hypothesize that the fractionation phenomenon is better described using non-linear dynamic measures, such as approximate entropy, and that this tool could be used for locating the rotor tip. The aim of this work has been to determine the relationship between approximate entropy and fractionated electrograms, and to develop a new tool for rotor mapping based on fractionation levels. Two episodes of chronic atrial fibrillation were simulated in a 3D human atrial model, in which rotors were observed. Dynamic approximate entropy maps were calculated using unipolar electrogram signals generated over the whole surface of the 3D atrial model. In addition, we optimized the approximate entropy calculation using two real multi-center databases of fractionated electrogram signals, labeled in 4 levels of fractionation. We found that the values of approximate entropy and the levels of fractionation are positively correlated. This allows the dynamic approximate entropy maps to localize the tips from stable and meandering rotors. Furthermore, we assessed the optimized approximate entropy using bipolar electrograms generated over a vicinity enclosing a rotor, achieving rotor detection. Our results suggest that high approximate entropy values are able to detect a high level of fractionation and to locate rotor tips in simulated atrial fibrillation episodes. We suggest that dynamic approximate entropy maps could become a tool for atrial fibrillation rotor mapping.
On the computation of black hole entropy in loop quantum gravity
International Nuclear Information System (INIS)
Fernando Barbero G, J; Villasenor, Eduardo J S
2009-01-01
We discuss some issues related to the computation of black hole entropy in loop quantum gravity from the novel point of view provided by the recent number-theoretical methods introduced by the authors and their collaborators. In particular we give exact expressions, in the form of integral transforms, for the black hole entropy in terms of the area. We do this by following several approaches based both on our combinatorial techniques and on functional equations similar to those employed by Meissner in his pioneering work on this subject. To put our results in perspective, we compare them with those of Meissner. We will show how our methods confirm some of his findings, extend the validity of others and correct some mistakes. At the end of the paper, we will discuss the delicate issue of the asymptotics of black hole entropy.
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)
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...
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.
General H-theorem and Entropies that Violate the Second Law
Directory of Open Access Journals (Sweden)
Alexander N. Gorban
2014-04-01
Full Text Available H-theorem states that the entropy production is nonnegative and, therefore, the entropy of a closed system should monotonically change in time. In information processing, the entropy production is positive for random transformation of signals (the information processing lemma. Originally, the H-theorem and the information processing lemma were proved for the classical Boltzmann-Gibbs-Shannon entropy and for the correspondent divergence (the relative entropy. Many new entropies and divergences have been proposed during last decades and for all of them the H-theorem is needed. This note proposes a simple and general criterion to check whether the H-theorem is valid for a convex divergence H and demonstrates that some of the popular divergences obey no H-theorem. We consider systems with n states Ai that obey first order kinetics (master equation. A convex function H is a Lyapunov function for all master equations with given equilibrium if and only if its conditional minima properly describe the equilibria of pair transitions Ai ⇌ Aj . This theorem does not depend on the principle of detailed balance and is valid for general Markov kinetics. Elementary analysis of pair equilibria demonstrate that the popular Bregman divergences like Euclidian distance or Itakura-Saito distance in the space of distribution cannot be the universal Lyapunov functions for the first-order kinetics and can increase in Markov processes. Therefore, they violate the second law and the information processing lemma. In particular, for these measures of information (divergences random manipulation with data may add information to data. The main results are extended to nonlinear generalized mass action law kinetic equations.
Holographic entanglement entropy for hollow cones and banana shaped regions
Energy Technology Data Exchange (ETDEWEB)
Dorn, Harald [Institut für Physik und IRIS Adlershof, Humboldt-Universität zu Berlin,Zum Großen Windkanal 6, D-12489 Berlin (Germany)
2016-06-09
We consider banana shaped regions as examples of compact regions, whose boundary has two conical singularities. Their regularised holographic entropy is calculated with all divergent as well as finite terms. The coefficient of the squared logarithmic divergence, also in such a case with internally curved boundary, agrees with that calculated in the literature for infinite circular cones with their internally flat boundary. For the otherwise conformally invariant coefficient of the ordinary logarithmic divergence an anomaly under exceptional conformal transformations is observed. The construction of minimal submanifolds, needed for the entanglement entropy of cones, requires fine-tuning of Cauchy data. Perturbations of such fine-tuning leads to solutions relevant for hollow cones. The divergent parts for the entanglement entropy of hollow cones are calculated. Increasing the difference between the opening angles of their outer and inner boundary, one finds a transition between connected solutions for small differences to disconnected solutions for larger ones.
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
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
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
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
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.
Gravitational entropy and the cosmological no-hair conjecture
Bolejko, Krzysztof
2018-04-01
The gravitational entropy and no-hair conjectures seem to predict contradictory future states of our Universe. The growth of the gravitational entropy is associated with the growth of inhomogeneity, while the no-hair conjecture argues that a universe dominated by dark energy should asymptotically approach a homogeneous and isotropic de Sitter state. The aim of this paper is to study these two conjectures. The investigation is based on the Simsilun simulation, which simulates the universe using the approximation of the Silent Universe. The Silent Universe is a solution to the Einstein equations that assumes irrotational, nonviscous, and insulated dust, with vanishing magnetic part of the Weyl curvature. The initial conditions for the Simsilun simulation are sourced from the Millennium simulation, which results with a realistically appearing but relativistic at origin simulation of a universe. The Simsilun simulation is evolved from the early universe (t =25 Myr ) until far future (t =1000 Gyr ). The results of this investigation show that both conjectures are correct. On global scales, a universe with a positive cosmological constant and nonpositive spatial curvature does indeed approach the de Sitter state. At the same time it keeps generating the gravitational entropy.
A Real-Time Analysis Method for Pulse Rate Variability Based on Improved Basic Scale Entropy
Directory of Open Access Journals (Sweden)
Yongxin Chou
2017-01-01
Full Text Available Base scale entropy analysis (BSEA is a nonlinear method to analyze heart rate variability (HRV signal. However, the time consumption of BSEA is too long, and it is unknown whether the BSEA is suitable for analyzing pulse rate variability (PRV signal. Therefore, we proposed a method named sliding window iterative base scale entropy analysis (SWIBSEA by combining BSEA and sliding window iterative theory. The blood pressure signals of healthy young and old subjects are chosen from the authoritative international database MIT/PhysioNet/Fantasia to generate PRV signals as the experimental data. Then, the BSEA and the SWIBSEA are used to analyze the experimental data; the results show that the SWIBSEA reduces the time consumption and the buffer cache space while it gets the same entropy as BSEA. Meanwhile, the changes of base scale entropy (BSE for healthy young and old subjects are the same as that of HRV signal. Therefore, the SWIBSEA can be used for deriving some information from long-term and short-term PRV signals in real time, which has the potential for dynamic PRV signal analysis in some portable and wearable medical devices.
Directory of Open Access Journals (Sweden)
Lina Zhao
2015-09-01
Full Text Available Entropy provides a valuable tool for quantifying the regularity of physiological time series and provides important insights for understanding the underlying mechanisms of the cardiovascular system. Before any entropy calculation, certain common parameters need to be initialized: embedding dimension m, tolerance threshold r and time series length N. However, no specific guideline exists on how to determine the appropriate parameter values for distinguishing congestive heart failure (CHF from normal sinus rhythm (NSR subjects in clinical application. In the present study, a thorough analysis on the selection of appropriate values of m, r and N for sample entropy (SampEn and recently proposed fuzzy measure entropy (FuzzyMEn is presented for distinguishing two group subjects. 44 long-term NRS and 29 long-term CHF RR interval recordings from http://www.physionet.org were used as the non-pathological and pathological data respectively. Extreme (>2 s and abnormal heartbeat RR intervals were firstly removed from each RR recording and then the recording was segmented with a non-overlapping segment length N of 300 and 1000, respectively. SampEn and FuzzyMEn were performed for each RR segment under different parameter combinations: m of 1, 2, 3 and 4, and r of 0.10, 0.15, 0.20 and 0.25 respectively. The statistical significance between NSR and CHF groups under each combination of m, r and N was observed. The results demonstrated that the selection of m, r and N plays a critical role in determining the SampEn and FuzzyMEn outputs. Compared with SampEn, FuzzyMEn shows a better regularity when selecting the parameters m and r. In addition, FuzzyMEn shows a better relative consistency for distinguishing the two groups, that is, the results of FuzzyMEn in the NSR group were consistently lower than those in the CHF group while SampEn were not. The selections of m of 2 and 3 and r of 0.10 and 0.15 for SampEn and the selections of m of 1 and 2 whenever r (herein
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.
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 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.
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.
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.
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.
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...
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
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."
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.
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.
Efficient Transfer Entropy Analysis of Non-Stationary Neural Time Series
Vicente, Raul; Díaz-Pernas, Francisco J.; Wibral, Michael
2014-01-01
Information theory allows us to investigate information processing in neural systems in terms of information transfer, storage and modification. Especially the measure of information transfer, transfer entropy, has seen a dramatic surge of interest in neuroscience. Estimating transfer entropy from two processes requires the observation of multiple realizations of these processes to estimate associated probability density functions. To obtain these necessary observations, available estimators typically assume stationarity of processes to allow pooling of observations over time. This assumption however, is a major obstacle to the application of these estimators in neuroscience as observed processes are often non-stationary. As a solution, Gomez-Herrero and colleagues theoretically showed that the stationarity assumption may be avoided by estimating transfer entropy from an ensemble of realizations. Such an ensemble of realizations is often readily available in neuroscience experiments in the form of experimental trials. Thus, in this work we combine the ensemble method with a recently proposed transfer entropy estimator to make transfer entropy estimation applicable to non-stationary time series. We present an efficient implementation of the approach that is suitable for the increased computational demand of the ensemble method's practical application. In particular, we use a massively parallel implementation for a graphics processing unit to handle the computationally most heavy aspects of the ensemble method for transfer entropy estimation. We test the performance and robustness of our implementation on data from numerical simulations of stochastic processes. We also demonstrate the applicability of the ensemble method to magnetoencephalographic data. While we mainly evaluate the proposed method for neuroscience data, we expect it to be applicable in a variety of fields that are concerned with the analysis of information transfer in complex biological, social, and
Jennings, Robert C; Zucchelli, Giuseppe
2014-01-01
We examine ergodicity and configurational entropy for a dilute pigment solution and for a suspension of plant photosystem particles in which both ground and excited state pigments are present. It is concluded that the pigment solution, due to the extreme brevity of the excited state lifetime, is non-ergodic and the configurational entropy approaches zero. Conversely, due to the rapid energy transfer among pigments, each photosystem is ergodic and the configurational entropy is positive. This decreases the free energy of the single photosystem pigment array by a small amount. On the other hand, the suspension of photosystems is non-ergodic and the configurational entropy approaches zero. The overall configurational entropy which, in principle, includes contributions from both the single excited photosystems and the suspension which contains excited photosystems, also approaches zero. Thus the configurational entropy upon photon absorption by either a pigment solution or a suspension of photosystem particles is approximately zero. Copyright © 2014 Elsevier B.V. All rights reserved.
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. ...
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.
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.
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.
The High Temperature Tensile and Creep Behaviors of High Entropy Superalloy.
Tsao, Te-Kang; Yeh, An-Chou; Kuo, Chen-Ming; Kakehi, Koji; Murakami, Hideyuki; Yeh, Jien-Wei; Jian, Sheng-Rui
2017-10-04
This article presents the high temperature tensile and creep behaviors of a novel high entropy alloy (HEA). The microstructure of this HEA resembles that of advanced superalloys with a high entropy FCC matrix and L1 2 ordered precipitates, so it is also named as "high entropy superalloy (HESA)". The tensile yield strengths of HESA surpass those of the reported HEAs from room temperature to elevated temperatures; furthermore, its creep resistance at 982 °C can be compared to those of some Ni-based superalloys. Analysis on experimental results indicate that HESA could be strengthened by the low stacking-fault energy of the matrix, high anti-phase boundary energy of the strengthening precipitate, and thermally stable microstructure. Positive misfit between FCC matrix and precipitate has yielded parallel raft microstructure during creep at 982 °C, and the creep curves of HESA were dominated by tertiary creep behavior. To the best of authors' knowledge, this article is the first to present the elevated temperature tensile creep study on full scale specimens of a high entropy alloy, and the potential of HESA for high temperature structural application is discussed.
The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems
Di Francesco, M.; Fellner, K.; Markowich, P. A
2008-01-01
and reaction terms and admit fewer conservation laws than the size of the system. In particular, we successfully apply the entropy approach to general linear systems and to a nonlinear example of a reaction-diffusion-convection system arising in solid
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.
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 production and rectification efficiency in colloid transport along a pulsating channel
Florencia Carusela, M.; Rubi, J. Miguel
2018-06-01
We study the current rectification of particles moving in a pulsating channel under the influence of an applied force. We have shown the existence of different rectification scenarios in which entropic and energetic effects compete. The effect can be quantified by means of a rectification coefficient that is analyzed in terms of the force, the frequency and the diffusion coefficient. The energetic cost of the motion of the particles expressed in terms of the entropy production depends on the importance of the entropic contribution to the total force. Rectification is more important at low values of the applied force when entropic effects become dominant. In this regime, the entropy production is not invariant under reversal of the applied force. The phenomenon observed could be used to optimize transport in microfluidic devices or in biological channels.
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.
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.
Mixed memory, (non) Hurst effect, and maximum entropy of rainfall in the tropical Andes
Poveda, Germán
2011-02-01
Diverse linear and nonlinear statistical parameters of rainfall under aggregation in time and the kind of temporal memory are investigated. Data sets from the Andes of Colombia at different resolutions (15 min and 1-h), and record lengths (21 months and 8-40 years) are used. A mixture of two timescales is found in the autocorrelation and autoinformation functions, with short-term memory holding for time lags less than 15-30 min, and long-term memory onwards. Consistently, rainfall variance exhibits different temporal scaling regimes separated at 15-30 min and 24 h. Tests for the Hurst effect evidence the frailty of the R/ S approach in discerning the kind of memory in high resolution rainfall, whereas rigorous statistical tests for short-memory processes do reject the existence of the Hurst effect. Rainfall information entropy grows as a power law of aggregation time, S( T) ˜ Tβ with = 0.51, up to a timescale, TMaxEnt (70-202 h), at which entropy saturates, with β = 0 onwards. Maximum entropy is reached through a dynamic Generalized Pareto distribution, consistently with the maximum information-entropy principle for heavy-tailed random variables, and with its asymptotically infinitely divisible property. The dynamics towards the limit distribution is quantified. Tsallis q-entropies also exhibit power laws with T, such that Sq( T) ˜ Tβ( q) , with β( q) ⩽ 0 for q ⩽ 0, and β( q) ≃ 0.5 for q ⩾ 1. No clear patterns are found in the geographic distribution within and among the statistical parameters studied, confirming the strong variability of tropical Andean rainfall.
The concept of entropy in landscape evolution
Leopold, Luna Bergere; Langbein, Walter Basil
1962-01-01
The concept of entropy is expressed in terms of probability of various states. Entropy treats of the distribution of energy. The principle is introduced that the most probable condition exists when energy in a river system is as uniformly distributed as may be permitted by physical constraints. From these general considerations equations for the longitudinal profiles of rivers are derived that are mathematically comparable to those observed in the field. The most probable river profiles approach the condition in which the downstream rate of production of entropy per unit mass is constant. Hydraulic equations are insufficient to determine the velocity, depths, and slopes of rivers that are themselves authors of their own hydraulic geometries. A solution becomes possible by introducing the concept that the distribution of energy tends toward the most probable. This solution leads to a theoretical definition of the hydraulic geometry of river channels that agrees closely with field observations. The most probable state for certain physical systems can also be illustrated by random-walk models. Average longitudinal profiles and drainage networks were so derived and these have the properties implied by the theory. The drainage networks derived from random walks have some of the principal properties demonstrated by the Horton analysis; specifically, the logarithms of stream length and stream numbers are proportional to stream order.
Directory of Open Access Journals (Sweden)
Hou Hucan
2017-01-01
Full Text Available Inspired by wide application of the second law of thermodynamics to flow and heat transfer devices, local entropy production analysis method was creatively introduced into energy assessment system of centrifugal water pump. Based on Reynolds stress turbulent model and energy equation model, the steady numerical simulation of the whole flow passage of one IS centrifugal pump was carried out. The local entropy production terms were calculated by user defined functions, mainly including wall entropy production, turbulent entropy production, and viscous entropy production. The numerical results indicated that the irreversible energy loss calculated by the local entropy production method agreed well with that calculated by the traditional method but with some deviations which were probably caused by high rotatability and high curvature of impeller and volute. The wall entropy production and turbulent entropy production took up large part of the whole entropy production about 48.61% and 47.91%, respectively, which indicated that wall friction and turbulent fluctuation were the major factors in affecting irreversible energy loss. Meanwhile, the entropy production rate distribution was discussed and compared with turbulent kinetic energy dissipation rate distribution, it showed that turbulent entropy production rate increased sharply at the near wall regions and both distributed more uniformly. The blade region in leading edge near suction side, trailing edge and volute tongue were the main regions to generate irreversible exergy loss. This research broadens a completely new view in evaluating energy loss and further optimizes pump using entropy production minimization.
Interface Enthalpy-Entropy Competition in Nanoscale Metal Hydrides
Directory of Open Access Journals (Sweden)
Nicola Patelli
2018-01-01
Full Text Available We analyzed the effect of the interfacial free energy on the thermodynamics of hydrogen sorption in nano-scaled materials. When the enthalpy and entropy terms are the same for all interfaces, as in an isotropic bi-phasic system, one obtains a compensation temperature, which does not depend on the system size nor on the relative phase abundance. The situation is different and more complex in a system with three or more phases, where the interfaces have different enthalpy and entropy. We also consider the possible effect of elastic strains on the stability of the hydride phase and on hysteresis. We compare a simple model with experimental data obtained on two different systems: (1 bi-phasic nanocomposites where ultrafine TiH2 crystallite are dispersed within a Mg nanoparticle and (2 Mg nanodots encapsulated by different phases.
Directory of Open Access Journals (Sweden)
Francesco Oliveri
2016-01-01
Full Text Available The exploitation of second law of thermodynamics for a mixture of two fluids with a scalar internal variable and a first order nonlocal state space is achieved by using the extended Liu approach. This method requires to insert as constraints in the entropy inequality either the field equations or their gradient extensions. Consequently, the thermodynamic restrictions imposed by the entropy principle are derived without introducing extra terms neither in the energy balance equation nor in the entropy inequality.
Liang, Yingjie; Chen, Wen; Magin, Richard L.
2016-07-01
Analytical solutions to the fractional diffusion equation are often obtained by using Laplace and Fourier transforms, which conveniently encode the order of the time and the space derivatives (α and β) as non-integer powers of the conjugate transform variables (s, and k) for the spectral and the spatial frequencies, respectively. This study presents a new solution to the fractional diffusion equation obtained using the Laplace transform and expressed as a Fox's H-function. This result clearly illustrates the kinetics of the underlying stochastic process in terms of the Laplace spectral frequency and entropy. The spectral entropy is numerically calculated by using the direct integration method and the adaptive Gauss-Kronrod quadrature algorithm. Here, the properties of spectral entropy are investigated for the cases of sub-diffusion and super-diffusion. We find that the overall spectral entropy decreases with the increasing α and β, and that the normal or Gaussian case with α = 1 and β = 2, has the lowest spectral entropy (i.e., less information is needed to describe the state of a Gaussian process). In addition, as the neighborhood over which the entropy is calculated increases, the spectral entropy decreases, which implies a spatial averaging or coarse graining of the material properties. Consequently, the spectral entropy is shown to provide a new way to characterize the temporal correlation of anomalous diffusion. Future studies should be designed to examine changes of spectral entropy in physical, chemical and biological systems undergoing phase changes, chemical reactions and tissue regeneration.
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)
Johannessen, Eivind; Rosjorde, Audun
2007-01-01
We show that the theorem of equipartition of entropy production is important for the understanding of the state of minimum entropy production in diabatic distillation. The theorem is not valid in a strictly mathematical sense. We explain why, when and in what sense this theorem is a good approximation to the optimal state in diabatic distillation. In order to make these predictions, we use a hypothesis for the state of minimum entropy production of an optimally controlled system, which was formulated on the basis of results of entropy production minimisation in chemical reactors. The hypothesis says that the state of minimum entropy production is characterised by approximately constant local entropy production and thermodynamic forces, given that there is sufficient freedom in the system. We present numerical results which are in agreement with the predictions. The results show that a column with constant tray entropy production in the stripping section and in the rectifying section is a good approximation to the optimal column, except when the total heat transfer area is low. The agreement between the two columns becomes better and better as the total heat transfer area and the number of trays increase. The fact that the predictions and the numerical results agree very well gives support to the validity of the hypothesis
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.
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)
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.
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.
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 ...
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
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.
Directory of Open Access Journals (Sweden)
Hang Liu
2016-08-01
Full Text Available In this paper, we investigate the angular momentum independence of the entropy sum and product for AdS rotating black holes based on the first law of thermodynamics and a mathematical lemma related to Vandermonde determinant. The advantage of this method is that the explicit forms of the spacetime metric, black hole mass and charge are not needed but the Hawking temperature and entropy formula on the horizons are necessary for static black holes, while our calculations require the expressions of metric and angular velocity formula. We find that the entropy sum is always independent of angular momentum for all dimensions and the angular momentum-independence of entropy product only holds for the dimensions d>4 with at least one rotation parameter ai=0, while the mass-free of entropy sum and entropy product for rotating black holes only stand for higher dimensions (d>4 and for all dimensions, respectively. On the other hand, we find that the introduction of a negative cosmological constant does not affect the angular momentum-free of entropy sum and product but the criterion for angular momentum-independence of entropy product will be affected.
GONOME: measuring correlations between GO terms and genomic positions
Directory of Open Access Journals (Sweden)
Bailey Timothy L
2006-02-01
Full Text Available Abstract Background: Current methods to find significantly under- and over-represented gene ontology (GO terms in a set of genes consider the genes as equally probable "balls in a bag", as may be appropriate for transcripts in micro-array data. However, due to the varying length of genes and intergenic regions, that approach is inappropriate for deciding if any GO terms are correlated with a set of genomic positions. Results: We present an algorithm – GONOME – that can determine which GO terms are significantly associated with a set of genomic positions given a genome annotated with (at least the starts and ends of genes. We show that certain GO terms may appear to be significantly associated with a set of randomly chosen positions in the human genome if gene lengths are not considered, and that these same terms have been reported as significantly over-represented in a number of recent papers. This apparent over-representation disappears when gene lengths are considered, as GONOME does. For example, we show that, when gene length is taken into account, the term "development" is not significantly enriched in genes associated with human CpG islands, in contradiction to a previous report. We further demonstrate the efficacy of GONOME by showing that occurrences of the proteosome-associated control element (PACE upstream activating sequence in the S. cerevisiae genome associate significantly to appropriate GO terms. An extension of this approach yields a whole-genome motif discovery algorithm that allows identification of many other promoter sequences linked to different types of genes, including a large group of previously unknown motifs significantly associated with the terms 'translation' and 'translational elongation'. Conclusion: GONOME is an algorithm that correctly extracts over-represented GO terms from a set of genomic positions. By explicitly considering gene size, GONOME avoids a systematic bias toward GO terms linked to large genes
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.
Entropy for the Complexity of Physiological Signal Dynamics.
Zhang, Xiaohua Douglas
2017-01-01
Recently, the rapid development of large data storage technologies, mobile network technology, and portable medical devices makes it possible to measure, record, store, and track analysis of biological dynamics. Portable noninvasive medical devices are crucial to capture individual characteristics of biological dynamics. The wearable noninvasive medical devices and the analysis/management of related digital medical data will revolutionize the management and treatment of diseases, subsequently resulting in the establishment of a new healthcare system. One of the key features that can be extracted from the data obtained by wearable noninvasive medical device is the complexity of physiological signals, which can be represented by entropy of biological dynamics contained in the physiological signals measured by these continuous monitoring medical devices. Thus, in this chapter I present the major concepts of entropy that are commonly used to measure the complexity of biological dynamics. The concepts include Shannon entropy, Kolmogorov entropy, Renyi entropy, approximate entropy, sample entropy, and multiscale entropy. I also demonstrate an example of using entropy for the complexity of glucose dynamics.
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)
Value at risk estimation with entropy-based wavelet analysis in exchange markets
He, Kaijian; Wang, Lijun; Zou, Yingchao; Lai, Kin Keung
2014-08-01
In recent years, exchange markets are increasingly integrated together. Fluctuations and risks across different exchange markets exhibit co-moving and complex dynamics. In this paper we propose the entropy-based multivariate wavelet based approaches to analyze the multiscale characteristic in the multidimensional domain and improve further the Value at Risk estimation reliability. Wavelet analysis has been introduced to construct the entropy-based Multiscale Portfolio Value at Risk estimation algorithm to account for the multiscale dynamic correlation. The entropy measure has been proposed as the more effective measure with the error minimization principle to select the best basis when determining the wavelet families and the decomposition level to use. The empirical studies conducted in this paper have provided positive evidence as to the superior performance of the proposed approach, using the closely related Chinese Renminbi and European Euro exchange market.
Entropy as a measure of the noise extent in a two-level quantum feedback controlled system
Institute of Scientific and Technical Information of China (English)
Wang Tao-Bo; Fang Mao-Fa; Hu Yao-Hua
2007-01-01
By introducing the von Neumann entropy as a measure of the extent of noise, this paper discusses the entropy evolution in a two-level quantum feedback controlled system. The results show that the feedback control can induce the reduction of the degree of noise, and different control schemes exhibit different noise controlling ability, the extent of the reduction also related with the position of the target state on the Bloch sphere. It is shown that the evolution of entropy can provide a real time noise observation and a systematic guideline to make reasonable choice of control strategy.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type’s Langevin equation in 6N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or
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.
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 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
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.
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
Left-right entanglement entropy of Dp-branes
Energy Technology Data Exchange (ETDEWEB)
Zayas, Leopoldo A. Pando [The Abdus Salam International Centre for Theoretical Physics,Strada Costiera 11, 34014 Trieste (Italy); Michigan Center for Theoretical Physics, Randall Laboratory of Physics,The University of Michigan,450 Church Street, Ann Arbor, MI 48109-1120 (United States); Quiroz, Norma [Departamento de Ciencias Exactas, Tecnología y Metodología,Centro Universitario del Sur, Universidad de Guadalajara,Enrique Arreola Silva 883, C.P. 49000, Cd. Guzmán, Jalisco (Mexico)
2016-11-04
We compute the left-right entanglement entropy for Dp-branes in string theory. We employ the CFT approach to string theory Dp-branes, in particular, its presentation as coherent states of the closed string sector. The entanglement entropy is computed as the von Neumann entropy for a density matrix resulting from integration over the left-moving degrees of freedom. We discuss various crucial ambiguities related to sums over spin structures and argue that different choices capture different physics; however, we advance a themodynamic argument that seems to favor a particular choice of replica. We also consider Dp branes on compact dimensions and verify that the effects of T-duality act covariantly on the Dp brane entanglement entropy. We find that generically the left-right entanglement entropy provides a suitable generalization of boundary entropy and of the D-brane tension.
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.
Entropy Applications to Water Monitoring Network Design: A Review
Directory of Open Access Journals (Sweden)
Jongho Keum
2017-11-01
Full Text Available Having reliable water monitoring networks is an essential component of water resources and environmental management. A standardized process for the design of water monitoring networks does not exist with the exception of the World Meteorological Organization (WMO general guidelines about the minimum network density. While one of the major challenges in the design of optimal hydrometric networks has been establishing design objectives, information theory has been successfully adopted to network design problems by providing measures of the information content that can be deliverable from a station or a network. This review firstly summarizes the common entropy terms that have been used in water monitoring network designs. Then, this paper deals with the recent applications of the entropy concept for water monitoring network designs, which are categorized into (1 precipitation; (2 streamflow and water level; (3 water quality; and (4 soil moisture and groundwater networks. The integrated design method for multivariate monitoring networks is also covered. Despite several issues, entropy theory has been well suited to water monitoring network design. However, further work is still required to provide design standards and guidelines for operational use.
Entanglement entropy of non-unitary integrable quantum field theory
Directory of Open Access Journals (Sweden)
Davide Bianchini
2015-07-01
Full Text Available In this paper we study the simplest massive 1+1 dimensional integrable quantum field theory which can be described as a perturbation of a non-unitary minimal conformal field theory: the Lee–Yang model. We are particularly interested in the features of the bi-partite entanglement entropy for this model and on building blocks thereof, namely twist field form factors. Non-unitarity selects out a new type of twist field as the operator whose two-point function (appropriately normalized yields the entanglement entropy. We compute this two-point function both from a form factor expansion and by means of perturbed conformal field theory. We find good agreement with CFT predictions put forward in a recent work involving the present authors. In particular, our results are consistent with a scaling of the entanglement entropy given by ceff3logℓ where ceff is the effective central charge of the theory (a positive number related to the central charge and ℓ is the size of the region. Furthermore the form factor expansion of twist fields allows us to explore the large region limit of the entanglement entropy and find the next-to-leading order correction to saturation. We find that this correction is very different from its counterpart in unitary models. Whereas in the latter case, it had a form depending only on few parameters of the model (the particle spectrum, it appears to be much more model-dependent for non-unitary models.
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
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)
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)
Biosemiotic Entropy of the Genome: Mutations and Epigenetic Imbalances Resulting in Cancer
Directory of Open Access Journals (Sweden)
Samuel S. Shepard
2013-01-01
Full Text Available Biosemiotic entropy involves the deterioration of biological sign systems. The genome is a coded sign system that is connected to phenotypic outputs through the interpretive functions of the tRNA/ribosome machinery. This symbolic sign system (semiosis at the core of all biology has been termed “biosemiosis”. Layers of biosemiosis and cellular information management are analogous in varying degrees to the semiotics of computer programming, spoken, and written human languages. Biosemiotic entropy — an error or deviation from a healthy state — results from errors in copying functional information (mutations and errors in the appropriate context or quantity of gene expression (epigenetic imbalance. The concept of biosemiotic entropy is a deeply imbedded assumption in the study of cancer biology. Cells have a homeostatic, preprogrammed, ideal or healthy state that is rooted in genomics, strictly orchestrated by epigenetic regulation, and maintained by DNA repair mechanisms. Cancer is an eminent illustration of biosemiotic entropy, in which the corrosion of genetic information via substitutions, deletions, insertions, fusions, and aberrant regulation results in malignant phenotypes. However, little attention has been given to explicitly outlining the paradigm of biosemiotic entropy in the context of cancer. Herein we distill semiotic theory (from the familiar and well understood spheres of human language and computer code to draw analogies useful for understanding the operation of biological semiosis at the genetic level. We propose that the myriad checkpoints, error correcting mechanisms, and immunities are all systems whose primary role is to defend against the constant pressure of biosemiotic entropy, which malignancy must shut down in order to achieve advanced stages. In lieu of the narrower tumor suppressor/oncogene model, characterization of oncogenesis into the biosemiotic framework of sign, index, or object entropy may allow for more
Excess entropy scaling for the segmental and global dynamics of polyethylene melts.
Voyiatzis, Evangelos; Müller-Plathe, Florian; Böhm, Michael C
2014-11-28
The range of validity of the Rosenfeld and Dzugutov excess entropy scaling laws is analyzed for unentangled linear polyethylene chains. We consider two segmental dynamical quantities, i.e. the bond and the torsional relaxation times, and two global ones, i.e. the chain diffusion coefficient and the viscosity. The excess entropy is approximated by either a series expansion of the entropy in terms of the pair correlation function or by an equation of state for polymers developed in the context of the self associating fluid theory. For the whole range of temperatures and chain lengths considered, the two estimates of the excess entropy are linearly correlated. The scaled bond and torsional relaxation times fall into a master curve irrespective of the chain length and the employed scaling scheme. Both quantities depend non-linearly on the excess entropy. For a fixed chain length, the reduced diffusion coefficient and viscosity scale linearly with the excess entropy. An empirical reduction to a chain length-independent master curve is accessible for both dynamic quantities. The Dzugutov scheme predicts an increased value of the scaled diffusion coefficient with increasing chain length which contrasts physical expectations. The origin of this trend can be traced back to the density dependence of the scaling factors. This finding has not been observed previously for Lennard-Jones chain systems (Macromolecules, 2013, 46, 8710-8723). Thus, it limits the applicability of the Dzugutov approach to polymers. In connection with diffusion coefficients and viscosities, the Rosenfeld scaling law appears to be of higher quality than the Dzugutov approach. An empirical excess entropy scaling is also proposed which leads to a chain length-independent correlation. It is expected to be valid for polymers in the Rouse regime.
Stock Selection for Portfolios Using Expected Utility-Entropy Decision Model
Directory of Open Access Journals (Sweden)
Jiping Yang
2017-09-01
Full Text Available Yang and Qiu proposed and then recently improved an expected utility-entropy (EU-E measure of risk and decision model. When segregation holds, Luce et al. derived an expected utility term, plus a constant multiplies the Shannon entropy as the representation of risky choices, further demonstrating the reasonability of the EU-E decision model. In this paper, we apply the EU-E decision model to selecting the set of stocks to be included in the portfolios. We first select 7 and 10 stocks from the 30 component stocks of Dow Jones Industrial Average index, and then derive and compare the efficient portfolios in the mean-variance framework. The conclusions imply that efficient portfolios composed of 7(10 stocks selected using the EU-E model with intermediate intervals of the tradeoff coefficients are more efficient than that composed of the sets of stocks selected using the expected utility model. Furthermore, the efficient portfolio of 7(10 stocks selected by the EU-E decision model have almost the same efficient frontier as that of the sample of all stocks. This suggests the necessity of incorporating both the expected utility and Shannon entropy together when taking risky decisions, further demonstrating the importance of Shannon entropy as the measure of uncertainty, as well as the applicability of the EU-E model as a decision-making model.
Time-evolution of the entropy of fluctuations in some biological systems as investigated by NMR
International Nuclear Information System (INIS)
Lenk, R.
1979-01-01
A simple expression for the entropy of fluctuations has been developed, using the tunnelling-effect model. This gives the possibility to estimate the changes and evolution of entropy in non-crystalline and biological samples by NMR investigations. On the other hand, the oscillatory character of the time-evolution of some properties, experimentally found in the investigated samples of plants, is interpreted in terms of the generalized master equation with an exponential memory function. (Auth.)
Directory of Open Access Journals (Sweden)
Jacques Demongeot
2018-01-01
Full Text Available Networks used in biological applications at different scales (molecule, cell and population are of different types: neuronal, genetic, and social, but they share the same dynamical concepts, in their continuous differential versions (e.g., non-linear Wilson-Cowan system as well as in their discrete Boolean versions (e.g., non-linear Hopfield system; in both cases, the notion of interaction graph G(J associated to its Jacobian matrix J, and also the concepts of frustrated nodes, positive or negative circuits of G(J, kinetic energy, entropy, attractors, structural stability, etc., are relevant and useful for studying the dynamics and the robustness of these systems. We will give some general results available for both continuous and discrete biological networks, and then study some specific applications of three new notions of entropy: (i attractor entropy, (ii isochronal entropy and (iii entropy centrality; in three domains: a neural network involved in the memory evocation, a genetic network responsible of the iron control and a social network accounting for the obesity spread in high school environment.
Saccadic entropy of head impulses in acute unilateral vestibular loss.
Hsieh, Li-Chun; Lin, Hung-Ching; Lee, Guo-She
2017-10-01
To evaluate the complexity of vestibular-ocular reflex (VOR) in patients with acute unilateral vestibular loss (AUVL) via entropy analysis of head impulses. Horizontal head impulse test (HIT) with high-velocity alternating directions was used to evaluate 12 participants with AUVL and 16 healthy volunteers. Wireless electro-oculography and electronic gyrometry were used to acquire eye positional signals and head velocity signals. The eye velocity signals were then obtained through differentiation, band-pass filtering. The approximate entropy of eye velocity to head velocity (R ApEn ) was used to evaluate chaos property. VOR gain, gain asymmetry ratio, and R ApEn asymmetry ratio were also used to compare the groups. For the lesion-side HIT of the patient group, the mean VOR gain was significantly lower and the mean R ApEn was significantly greater compared with both nonlesion-side HIT and healthy controls (p Entropy and gain analysis of HIT using wireless electro-oculography system could be used to detect the VOR dysfunctions of AUVL and may become effective methods for evaluating vestibular disorders. Copyright © 2017. Published by Elsevier B.V.
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
International Nuclear Information System (INIS)
Sun Fengrui; Qin Xiaoyong; Chen Lingen; Wu Chih
2005-01-01
For an endoreversible four-heat-reservoir absorption heat-transformer cycle, for which a linear (Newtonian) heat-transfer law applies, an ecological optimization criterion is proposed for the best mode of operation of the cycle. This involves maximizing a function representing the compromise between the heating load and the entropy-production rate. The optimal relation between the ecological criterion and the COP (coefficient of performance), the maximum ecological criterion and the corresponding COP, heating load and entropy production rate, as well as the ecological criterion and entropy-production rate at the maximum heating load are derived using finite-time thermodynamics. Moreover, compared with the heating-load criterion, the effects of the cycle parameters on the ecological performance are studied by numerical examples. These show that achieving the maximum ecological criterion makes the entropy-production rate decrease by 77.0% and the COP increase by 55.4% with only 27.3% heating-load losses compared with the maximum heating-load objective. The results reflect that the ecological criterion has long-term significance for optimal design of absorption heat-transformers
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.)
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.
International Nuclear Information System (INIS)
Green, James A.; Irudayam, Sheeba Jem; Henchman, Richard H.
2011-01-01
Research highlights: → A method to calculate a liquid's entropy of vaporization is proposed. → The entropy of vaporisation depends on force magnitudes from computer simulation. → Calculated values agree with experiment, Trouton's rule and Hildebrand's rule. → Free volumes decrease for larger molecules or those with stronger interactions. - Abstract: The entropy of vaporization at a liquid's boiling point is well approximated by Trouton's rule and even more accurately by Hildebrand's rule. A cell method is used here to calculate the entropy of vaporization for a range of liquids by subtracting the entropy of the gas from that of the liquid. The liquid's entropy is calculated from the force magnitudes measured in a molecular dynamics simulation based on the harmonic approximation. The change in rotational entropy is not accounted for except in the case of liquid water. The predicted entropies of vaporization agree well with experiment and Trouton's and Hildebrand's rules for most liquids and for water except other liquids with hydrogen bonds. This supports the idea that molecular rotation is close to ideal at a liquid's boiling point if hydrogen bonds are absent; if they are present, then the rotational entropy gain must be included. The method provides a molecular interpretation of those rules by providing an equation in terms of a molecule's free volume in a liquid which depends on the force magnitudes. Free volumes at each liquid's boiling point are calculated to be ∼1 A 3 for liquids lacking hydrogen bonds, lower at ∼0.3 A 3 for those with hydrogen bonds, and they decrease weakly with increasing molecular size.
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)
Teschendorff, Andrew E.; Banerji, Christopher R. S.; Severini, Simone; Kuehn, Reimer; Sollich, Peter
2015-01-01
One of the key characteristics of cancer cells is an increased phenotypic plasticity, driven by underlying genetic and epigenetic perturbations. However, at a systems-level it is unclear how these perturbations give rise to the observed increased plasticity. Elucidating such systems-level principles is key for an improved understanding of cancer. Recently, it has been shown that signaling entropy, an overall measure of signaling pathway promiscuity, and computable from integrating a sample's gene expression profile with a protein interaction network, correlates with phenotypic plasticity and is increased in cancer compared to normal tissue. Here we develop a computational framework for studying the effects of network perturbations on signaling entropy. We demonstrate that the increased signaling entropy of cancer is driven by two factors: (i) the scale-free (or near scale-free) topology of the interaction network, and (ii) a subtle positive correlation between differential gene expression and node connectivity. Indeed, we show that if protein interaction networks were random graphs, described by Poisson degree distributions, that cancer would generally not exhibit an increased signaling entropy. In summary, this work exposes a deep connection between cancer, signaling entropy and interaction network topology. PMID:25919796
Entropy Generation Analysis of Desalination Technologies
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John H. Lienhard V
2011-09-01
Full Text Available Increasing global demand for fresh water is driving the development and implementation of a wide variety of seawater desalination technologies. Entropy generation analysis, and specifically, Second Law efficiency, is an important tool for illustrating the influence of irreversibilities within a system on the required energy input. When defining Second Law efficiency, the useful exergy output of the system must be properly defined. For desalination systems, this is the minimum least work of separation required to extract a unit of water from a feed stream of a given salinity. In order to evaluate the Second Law efficiency, entropy generation mechanisms present in a wide range of desalination processes are analyzed. In particular, entropy generated in the run down to equilibrium of discharge streams must be considered. Physical models are applied to estimate the magnitude of entropy generation by component and individual processes. These formulations are applied to calculate the total entropy generation in several desalination systems including multiple effect distillation, multistage flash, membrane distillation, mechanical vapor compression, reverse osmosis, and humidification-dehumidification. Within each technology, the relative importance of each source of entropy generation is discussed in order to determine which should be the target of entropy generation minimization. As given here, the correct application of Second Law efficiency shows which systems operate closest to the reversible limit and helps to indicate which systems have the greatest potential for improvement.
International Nuclear Information System (INIS)
Cavouras, D.; Kandarakis, I.; Maris, T.; Panayiotakis, G.S.; Nomicos, C.D.
2001-01-01
In information theory, entropy expresses the information gain obtained after detection of a signal concerning the state of a parameter of interest. In this study, entropy has been expressed in terms of physical quantities (emitted optical fluence and MTF) related to the imaging performance of phosphor materials, which are employed in medical imaging radiation detectors. Four phosphor materials, used in the form of laboratory-prepared fluorescent layers (screens), were compared on the basis of their entropy performance. Measurements were performed using 30- and 80-kVp X-ray beams often employed in X-ray imaging. Results showed that phosphor materials with high density and effective atomic number exhibit high entropy performance, especially at the higher X-ray tube voltage of 80 kVp. Entropy values are also affected by the type of activator, which determines the intrinsic X-ray-to-light conversion efficiency, and the spectrum of emitted light. The proximity of the incident X-ray quanta energy to the energy of the K-shell threshold for photoelectric absorption is an additional important factor which increases entropy. This effect was more apparent in the performance of yttrium-based phosphors at the lower voltage of 30 kVp. (orig.)
Entropy of a rotating and charged black string to all orders in the Planck length
International Nuclear Information System (INIS)
Ren, Zhao; Yue-Qin, Wu; Li-Chun, Zhang
2009-01-01
By using the entanglement entropy method, this paper calculates the statistical entropy of the Bose and Fermi fields in thin films, and derives the Bekenstein–Hawking entropy and its correction term on the background of a rotating and charged black string. Here, the quantum field is entangled with quantum states in the black string and thin film to the event horizon from outside the rotating and charged black string. Taking into account the effect of the generalized uncertainty principle on quantum state density, it removes the difficulty of the divergence of state density near the event horizon in the brick-wall model. These calculations and discussions imply that high density quantum states near the event horizon of a black string are strongly correlated with the quantum states in a black string and that black string entropy is a quantum effect. The ultraviolet cut-off in the brick-wall model is not reasonable. The generalized uncertainty principle should be considered in the high energy quantum field near the event horizon. From the viewpoint of quantum statistical mechanics, the correction value of Bekenstein–Hawking entropy is obtained. This allows the fundamental recognition of the correction value of black string entropy at nonspherical coordinates