Nonextensive triangle equality and other properties of Tsallis relative-entropy minimization

TL;DR

This paper explores the properties of Tsallis relative-entropy minimization, highlighting differences from classical cases and introducing a generalized triangle equality within the nonextensive thermostatistics framework.

Contribution

It introduces the nonextensive triangle equality and analyzes properties of Tsallis relative-entropy minimization, expanding the theoretical understanding of nonextensive statistics.

Findings

Generalization of triangle equality for Tsallis relative-entropy

Use of q-product operator in distribution representation

Differences identified between Tsallis and classical relative-entropy

Abstract

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 nonextensive thermostatistics. In this paper, we present the properties of Tsallis relative-entropy minimization and present some differences with the classical case. In the representation of such a minimum relative-entropy distribution, we highlight the use of the q-product, an operator that has been recently introduced to derive the mathematical structure behind the Tsallis statistics. One of our main results is generalization of triangle equality of relative-entropy minimization to the nonextensive case.