Matrix trace inequalities on the Tsallis entropies

TL;DR

This paper explores matrix trace inequalities related to Tsallis relative entropy within nonextensive statistical physics, providing new insights into entropy measures for non-negative matrices.

Contribution

It introduces new matrix trace inequalities associated with Tsallis relative entropy, expanding the mathematical framework for nonextensive statistical physics.

Findings

Derived novel matrix trace inequalities for Tsallis entropy

Linked Tsallis relative entropy to matrix analysis techniques

Enhanced understanding of entropy measures in nonextensive systems

Abstract

Maximum entropy principles in nonextensive statistical physics are revisited as an application of the Tsallis relative entropy defined for non-negative matrices in the framework of matrix analysis. In addtition, some matrix trace inequalities related to the Tsallis relative entropy are studied.