Information-theoretic structure for the Tsallis q-entropy in statistical physics

TL;DR

This paper develops an information-theoretic framework for Tsallis q-entropy, establishing new properties, inequalities, and theorems, and explores their implications in nonextensive statistical physics.

Contribution

It introduces novel information measures and inequalities for q-entropy, including a Tsallis version of the Shannon-McMillan-Breiman theorem, advancing the theoretical foundation of nonextensive physics.

Findings

Derived properties of joint, conditional, and relative q-entropy.

Proved a Tsallis version of the Shannon-McMillan-Breiman theorem.

Established inequalities analogous to classical information theory.

Abstract

In this work, we derive information-theoretic properties for a modified Tsallis entropy, hereinafter referred to as q-entropy. We introduce the notions of joint q-entropy, conditional q-entropy, relative q-entropy, conditional mutual q-information, and establish several inequalities analogous to those of classical information theory. Within the context of Markov chains, these results are employed to prove a version of the second law of thermodynamics. Furthermore, we investigate the maximum entropy method in this setting. Finally, we prove a Tsallis version of the Shannon-McMillan-Breiman theorem and discuss the implications of these results in nonextensive statistical physics.