Variational principles for the rate distortion (RD) theory in lossy compression are formulated within the ambit of the generalized nonextensive statistics of Tsallis, for values of the nonextensivity parameter satisfying 0<q<1 and q>1. Alternating minimization numerical schemes to evaluate the nonextensive...</q<1>

There exist two different versions of the Kullback–Leibler divergence (K–Ld) in Tsallis statistics, namely the usual generalized K–Ld and the generalized Bregman K–Ld. Problems have been encountered in trying to reconcile them. A condition for consistency between these two generalized...

The study of conditional q-entropies in composite quantum systems has recently been the focus of considerable interest, particularly in connection with the problem of separability. The q-entropies depend on the density matrix <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$\rho$</EquationSource> </InlineEquation> through the quantity <InlineEquation ID="Equ3"> <EquationSource Format="TEX">$\omega_q={\rm Tr}\rho^q$</EquationSource> </InlineEquation>, and admit...</equationsource></inlineequation></equationsource></inlineequation>

This work analyzes the classical statistical mechanics associated to phase-space curves in three dimensions. Special attention is paid to the entropic force. Strange effects like confinement, hard core, and asymptotic freedom are uncovered.

Our protagonists are (i) the Cressie–Read family of divergences (characterized by the parameter γ), (ii) Tsallis’ generalized relative entropies (characterized by the q one), and, as a particular instance of both, (iii) the Kullback–Leibler (KL) relative entropy. In their normalized...

We generate a family of phase space, thermal coherent-state’s representations, within the framework of Tsallis’ Generalized Statistical Mechanics and study their properties. Our protagonists are q-gaussian distributions. We obtain analytical expressions for the most important...

Escort distributions are a well established but (for physicists) a relatively new concept that is rapidly gaining wide acceptance in world. In this work we wish to revisit the concept within the strictures of the celebrated semiclassical Husimi distributions (HDs) and thereby investigate the...

In this paper, we present some geometric properties of the maximum entropy Tsallis-distributions under energy constraint. In the case q1, these distributions are proved to be marginals of uniform distributions on the sphere; in the case q1, they can be constructed as conditional distributions of...

Information concerning important details of an ecosystem's evolution are shown to be contained in an appropriately constructed power spectrum. In particular, it provides an answer to the question of just why power-law behavior vanishes in the absence of Darwinian competition.

We discuss here the use of generalized forms of entropy, taken as information measures, to characterize phase transitions and critical behavior in thermodynamic systems. Our study is based on geometric considerations pertaining to the space of parameters that describe statistical mechanics...