Trace inequalities in nonextensive statistical mechanics
Shigeru Furuichi
TL;DR
This paper develops new trace inequalities within nonextensive statistical mechanics, including a variational expression for Tsallis relative entropy and generalized thermodynamic, Peierls-Bogoliubov, and Golden-Thompson inequalities.
Contribution
It introduces novel generalized inequalities and a variational expression specific to Tsallis entropy, expanding the mathematical framework of nonextensive thermodynamics.
Findings
Derived a variational expression for Tsallis relative entropy
Established generalized thermodynamic and Peierls-Bogoliubov inequalities
Proved a generalized Golden-Thompson inequality
Abstract
In this short paper, we establish a variational expression of the Tsallis relative entropy. In addition, we derive a generalized thermodynamic inequality and a generalized Peierls-Bogoliubov inequality. Finally we give a generalized Golden-Thompson inequality.
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Taxonomy
TopicsMathematical Inequalities and Applications · Statistical Mechanics and Entropy · Fractional Differential Equations Solutions