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...

By recourse to (i) the Hellmann–Feynman theorem and (ii) the virial one, the information-optimizing principle based on Fisher’s information measure uncovers a Legendre-transform structure associated with Schrödinger’s equation, in close analogy with the structure that lies behind the...

An approach to formulating the Hellmann–Feynman theorem within the “second choice” formalism of non-extensive statistical mechanics is considered. For the state of thermal equilibrium, we derive a relation of Hellmann–Feynman type between the derivative of the non-extensive free energy...

This paper investigates the dualities of two-parameter entropies, Sk,r Kaniadakis et al. (2005). Two kinds of dualities are found, namely inverse (r→−r) and inverse-scaling (r→−rs,k→ks) which recovers the additive (q→2−q) and multiplicative (q→1/q) dualities in the Tsallis limit.

We derive the multiplicative duality “q↔1/q” and other typical mathematical structures as the special cases of the (μ,ν,q)-relation behind Tsallis statistics by means of the (μ,ν)-multinomial coefficient. Recently the additive duality “q↔2-q” in Tsallis statistics is derived in...