相关论文: Classical and Nonextensive Information Theory

We address the problem of quantifying the information content of a source for an arbitrary information theory, where the information content is defined in terms of the asymptotic achievable compression rate. The functions that solve this…

Gibbs-Boltzmann entropy leads to systems that have a strong dependence on initial conditions. In reality, most materials behave quite independently of initial conditions. Nonextensive entropy or Tsallis entropy leads to nonextensive…

It is shown that there is a mapping of the replica approach to disordered systems with finite replica index $n$ on the Tsallis non-extensive statistics, if the average thermodynamic entropy differs from the information entropy for the…

It is shown how, among a class of generalized entropies, the Tsallis entropy can uniquely be identified by the principles of thermodynamics, the concept of stability and the axiomatic foundation.

Using known entropic and information inequalities new inequalities for some classical polynomials are obtained. Examples of Jacobi and Legendre polynomials are considered.

Tsallis has suggested a nonextensive generalization of the Boltzmann-Gibbs entropy, the maximization of which gives a generalized canonical distribution under special constraints. In this brief report we show that the generalized canonical…

We formulate and solve the diffusion equation over a previously studied field $\mathcal{R}$, whose construction was motivated by the Tsallis entropy composition property. We compare this solution with the solutions of the diffusion and of…

In this thesis I present a short review of ideas in quantum information theory. The first chapter contains introductory material, sketching the central ideas of probability and information theory. Quantum mechanics is presented at the level…

We give several inequalities on generalized entropies involving Tsallis entropies, using some inequalities obtained by improvements of Young's inequality. We also give a generalized Han's inequality.

This is a review on entropy in various fields of mathematics and science. Its scope is to convey a unified vision of the classical as well as some newer entropy notions to a broad audience with an intermediate background in dynamical…

A lower bound of the reduced relative entropy is given by the use of a variational expression. The reduced Tsallis relative entropy is defined and some results are given. In particular, the convexity of the reduced Tsallis relative entropy…

A density matrix formulation of classical bipartite correlations is constructed. This leads to an understanding of the appearance of classical statistical correlations intertwined with the quantum correlations as well as a physical…

The framework of non-extensive statistical mechanics, proposed by Tsallis, has been used to describe a variety of systems. The non-extensive statistical mechanics is usually introduced in a formal way, using the maximization of entropy. In…

The formalism of statistical mechanics can be generalized by starting from more general measures of information than the Shannon entropy and maximizing those subject to suitable constraints. We discuss some of the most important examples of…

A large class of technically non-chaotic systems, involving scatterings of light particles by flat surfaces with sharp boundaries, is nonetheless characterized by complex random looking motion in phase space. For these systems one may…

We consider the computability of entropy and information in classical Hamiltonian systems. We define the information part and total information capacity part of entropy in classical Hamiltonian systems using relative information under a…

The Tsallis entropy and Fisher information entropy (matrix) are very important quantities expressing information measures in nonextensive systems. Stationary and dynamical properties of the information entropies have been investigated in…

Given the constant rise in quantity and quality of data obtained from neural systems on many scales ranging from molecular to systems', information-theoretic analyses became increasingly necessary during the past few decades in the…

Kullback-Leibler relative-entropy has unique properties in cases involving distributions resulting from relative-entropy minimization. Tsallis relative-entropy is a one parameter generalization of Kullback-Leibler relative-entropy in the…

We review the properties of the quantum relative entropy function and discuss its application to problems of classical and quantum information transfer and to quantum data compression. We then outline further uses of relative entropy to…