Work relations for a system governed by Tsallis statistics

TL;DR

This paper extends fundamental nonequilibrium work relations, like Jarzynski and Crooks, to systems described by Tsallis statistics, specifically for an overdamped oscillator in a spatially varying temperature profile.

Contribution

It derives new work relations expressed with q-exponentials for systems governed by Tsallis statistics, broadening the scope of nonequilibrium thermodynamics.

Findings

Derived Tsallis-based Jarzynski equality and Crooks relation.

Showed these relations apply to systems with spatially varying temperature.

Indicated potential universality of these identities in Tsallis-distributed systems.

Abstract

We derive analogues of the Jarzynski equality and Crooks relation to characterise the nonequilibrium work associated with changes in the spring constant of an overdamped oscillator in a quadratically varying spatial temperature profile. The stationary state of such an oscillator is described by Tsallis statistics, and the work relations for certain processes may be expressed in terms of q-exponentials. We suggest that these identities might be a feature of nonequilibrium processes in circumstances where Tsallis distributions are found.