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This paper develops systematic approaches to obtain $f$-divergence inequalities, dealing with pairs of probability measures defined on arbitrary alphabets. Functional domination is one such approach, where special emphasis is placed on…

Information Theory · Computer Science 2016-12-06 Igal Sason , Sergio Verdú

We developed a perturbative calculation for entropy dynamics considering a sudden coupling between a system and a bath. The theory we developed can work in general environment without Markovian approximation. A perturbative formula is given…

High Energy Physics - Theory · Physics 2021-05-12 Yu Chen

We consider nonclassical entropy solutions to scalar conservation laws with concave-convex flux functions, whose set of left- and right-hand admissible states across undercompressive shocks is selected by a kinetic function \phi. We…

Analysis of PDEs · Mathematics 2008-12-23 Marc Laforest , Philippe G. LeFloch

In this paper we review various information-theoretic characterizations of the approach to equilibrium in biological systems. The replicator equation, evolutionary game theory, Markov processes and chemical reaction networks all describe…

Information Theory · Computer Science 2017-08-22 John C. Baez , Blake S. Pollard

A consistent generalization of statistical mechanics is obtained by applying the maximum entropy principle to a trace-form entropy and by requiring that physically motivated mathematical properties are preserved. The emerging…

Statistical Mechanics · Physics 2009-11-10 G. Kaniadakis , M. Lissia , A. M. Scarfone

We show that a proper expression of the uncertainty relation for a pair of canonically-conjugate continuous variables relies on entropy power, a standard notion in Shannon information theory for real-valued signals. The resulting…

Quantum Physics · Physics 2018-01-16 Anaelle Hertz , Michael G. Jabbour , Nicolas J. Cerf

In the recent [3], Cesbron and Herda study a Vlasov-Fokker-Planck (VFP) equation with non-symmetric interaction, introduced in physics to model the distribution of electrons in a synchrotron particle accelerator. We make four remarks in…

Probability · Mathematics 2023-11-13 Pierre Monmarché

A restricted form of Landauer's Principle, independent of computational considerations, is shown to hold for thermal systems by reference to the joint entropy associated with conjugate observables. It is shown that the source of the…

Quantum Physics · Physics 2024-01-15 R. E. Kastner , Andreas Schlatter

The Kullback-Leibler divergence or relative entropy is an information-theoretic measure between statistical models that play an important role in measuring a distance between random variables. In the study of complex systems, random fields…

Information Theory · Computer Science 2022-03-25 Alexandre L. M. Levada

We show that, in 't Hooft's large N limit, matrix models can be formulated as a classical theory whose equations of motion are the factorized Schwinger--Dyson equations. We discover an action principle for this classical theory. This action…

High Energy Physics - Theory · Physics 2014-11-18 L. Akant , G. S. Krishnaswami , S. G. Rajeev

The purpose of the present effort is threefold. Firstly, it is shown that there exists a principle, that we call Kinetical Interaction Principle (KIP), underlying the non linear kinetics in particle systems, independently on the picture…

Statistical Mechanics · Physics 2009-11-07 G. Kaniadakis

We introduce a new generalization of relative entropy to non-negative vectors with sums $\gt 1$. We show in a purely combinatorial setting, with no probabilistic considerations, that in the presence of linear constraints defining a convex…

Information Theory · Computer Science 2024-05-08 Kostas N. Oikonomou

$H$-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…

Statistical Mechanics · Physics 2014-10-10 Alexander N. Gorban

We study the entanglement entropy of random partitions in one- and two-dimensional critical fermionic systems. In an infinite system we consider a finite, connected (hypercubic) domain of linear extent $L$, the points of which with…

Disordered Systems and Neural Networks · Physics 2022-02-18 Gergö Roósz , István A. Kovács , Ferenc Iglói

For statistical systems that violate one of the four Shannon-Khinchin axioms, entropy takes a more general form than the Boltzmann-Gibbs entropy. The framework of superstatistics allows one to formulate a maximum entropy principle with…

Classical Physics · Physics 2012-11-13 Rudolf Hanel , Stefan Thurner , Murray Gell-Mann

Entanglement entropy (EE) in interacting field theories has two important issues: renormalization of UV divergences and non-Gaussianity of the vacuum. In this letter, we investigate them in the framework of the two-particle irreducible…

High Energy Physics - Theory · Physics 2021-05-21 Satoshi Iso , Takato Mori , Katsuta Sakai

Product probability property, known in the literature as statistical independence, is examined first. Then generalized entropies are introduced, all of which give generalizations to Shannon entropy. It is shown that the nature of the…

Statistics Theory · Mathematics 2009-11-13 A. M. Mathai , H. J. Haubold

We generalize the recently introduced dual fermion (DF) formalism for disordered fermion systems by including the effect of interactions. For an interacting disordered system the contributions to the full vertex function have to be…

Strongly Correlated Electrons · Physics 2014-05-21 S. -X. Yang , P. Haase , H. Terletska , Z. Y. Meng , T. Pruschke , J. Moreno , M. Jarrell

The entropy definition is deduced by means of (re)deriving the generalized non-linear Langevin equation using Zwanzig projector operator formalism. It is shown to be necessarily related to an invariant measure which, in classical mechanics,…

Statistical Mechanics · Physics 2007-05-23 E. A. J. F. Peters

The role of symmetries in what concerns entanglement entropy has been extensively explored in the last years and revealed a profound connection with the quantum field theory's algebraic structure. Recently, it was found that some universal…

High Energy Physics - Theory · Physics 2022-07-13 Marina Huerta , Guido van der Velde