Factorization and escorting in the game-theoretical approach to non-extensive entropy measures

TL;DR

This paper explores the game-theoretical framework for non-extensive entropy in statistical physics, focusing on complexity measures and their factorization properties, revealing that only Tsallis entropy-related measures exhibit this property.

Contribution

It identifies the specific class of complexity measures linked to Tsallis entropy that possess the factorization property, clarifying their role in the observer-system separation.

Findings

Only Tsallis entropy-related measures have the factorization property.

Factorization reflects the separation between observer and system.

Escort measures are related to the factorization property.

Abstract

The game-theoretical approach to non-extensive entropy measures of statistical physics is based on an abstract measure of complexity from which the entropy measure is derived in a natural way. A wide class of possible complexity measures is considered and a property of factorization investigated. The property reflects a separation between the system being observed and the observer. Apparently, the property is also related to escorting. It is shown that only those complexity measures which are connected with Tsallis entropy have the factorization property.