Toward Generalized Entropy Composition with Different q Indices and H-Theorem

TL;DR

This paper explores constructing composite entropy with varying q indices for subsystems and investigates conditions under which the H-theorem holds, especially in near-equilibrium and weakly interacting states.

Contribution

It introduces a framework for generalized entropy composition with different q indices and analyzes the conditions for the H-theorem to be valid in such systems.

Findings

Some composite entropies do not decrease over time in near-equilibrium states.

The H-theorem approximately holds in factorized states with weak interactions.

The study extends understanding of entropy behavior in complex systems with multiple q indices.

Abstract

An attempt is made to construct composable composite entropy with different $q$ indices of subsystems and address the H-theorem problem of the composite system. Though the H-theorem does not hold in general situations, it is shown that some composite entropies do not decrease in time in near-equilibrium states and factorized states with negligibly weak interaction between the subsystems.