Tsallis statistics generalization of non-equilibrium work relations

TL;DR

This paper extends non-equilibrium work relations like Jarzynski and Crooks theorems using Tsallis statistics, providing a generalized framework for systems described by non-extensive entropy.

Contribution

It introduces a q-statistics generalization of key fluctuation theorems using the third constraint formulation of Tsallis statistics.

Findings

Derived q-generalized Jarzynski equality

Established q-generalized Crooks fluctuation theorem

Links free energy differences with non-equilibrium work in non-extensive systems

Abstract

We use third constraint formulation of Tsallis statistics and derive the $q$-statistics generalization of non-equilibrium work relations such as the Jarzynski equality and the Crooks fluctuation theorem which relate the free energy differences between two equilibrium states and the work distribution of the non-equilibrium processes.