Finite Bath Fluctuation Theorem

TL;DR

This paper derives a fluctuation theorem applicable to systems coupled with finite heat baths, bridging canonical and microcanonical cases, and demonstrates its validity through a 2D hard disk simulation.

Contribution

It introduces a finite bath fluctuation theorem that generalizes existing theorems for systems with finite heat baths, connecting canonical and microcanonical limits.

Findings

The theorem reduces to known fluctuation theorems in limiting cases.

Simulation confirms the theorem's validity for a 2D hard disk system.

Provides a unified framework for finite and infinite heat bath scenarios.

Abstract

We demonstrate that a Finite Bath Fluctuation Theorem of the Crooks type holds for systems that have been thermalized via weakly coupling it to a bath with energy independent finite specific heat. We show that this theorem reduces to the known canonical and microcanonical fluctuation theorems in the two respective limiting cases of infinite and vanishing specific heat of the bath. The result is elucidated by applying it to a 2D hard disk colliding elastically with few other hard disks in a rectangular box with perfectly reflecting walls.