Thermodynamic non-additivity in disordered systems

TL;DR

This paper explores the connection between the replica approach in disordered systems and Tsallis non-extensive statistics, revealing how incomplete information affects thermodynamic entropy and relates to the entropic index q.

Contribution

It establishes a mapping between replica approach with finite n and Tsallis statistics, linking entropy differences to information loss.

Findings

Entropic index q relates to the degree of lost information.

Mapping exists between replica approach and Tsallis statistics.

Incomplete information influences thermodynamic entropy.

Abstract

It is shown that there is a mapping of the replica approach to disordered systems with finite replica index $n$ on the Tsallis non-extensive statistics, if the average thermodynamic entropy differs from the information entropy for the probability distribution. In the case of incomplete information the entropic index $q=1-n$ is shown to be related to the degree of lost information.