Information-theoretic structure for the Tsallis q-entropy in statistical physics
Mathematical Physics
2026-03-31 v3 math.MP
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.
Cite
@article{arxiv.2603.23257,
title = {Information-theoretic structure for the Tsallis q-entropy in statistical physics},
author = {Marco A. S. Trindade},
journal= {arXiv preprint arXiv:2603.23257},
year = {2026}
}