Related papers: Pairwise interactions origin of entropy functions
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
$H$-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…
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…
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…
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…
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…
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…
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,…
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…