Quasi-additivity of Tsallis entropies and correlated subsystems

TL;DR

This paper investigates how the Tsallis entropy's entropic index q approaches 1 as system size increases, extending the concept from independent to correlated subsystems, indicating a move towards additivity.

Contribution

It generalizes the quasi-additivity property of Tsallis entropies to correlated subsystems, showing q approaches 1 with increasing system size.

Findings

q approaches 1 for large independent systems

q approaches a specific value for correlated systems as size increases

extension of quasi-additivity to correlated subsystems

Abstract

We use Beck's quasi-additivity of Tsallis entropies for $n$ independent subsystems to show that like the case of $n=2$, the entropic index $q$ approaches 1 by increasing system size. Then, we will generalize that concept to correlated subsystems to find that in the case of correlated subsystems, when system size increases, $q$ also approaches a value corresponding to the additive case.