On the work distribution in quasi-static processes

TL;DR

This paper develops a perturbation expansion for work distribution in quasi-static Langevin processes, revealing its Gaussian nature at first order and its limitations for rare work values, thus clarifying previous conflicting results.

Contribution

It introduces a systematic multiple time-scale perturbation expansion for work distributions and clarifies its applicability and limitations in quasi-static processes.

Findings

First-order expansion yields Gaussian distribution.

Perturbation theory breaks down for tail work values.

Reconciles previous conflicting results on work distribution asymptotics.

Abstract

We derive a systematic, multiple time-scale perturbation expansion for the work distribution in isothermal quasi-static Langevin processes. To first order we find a Gaussian distribution reproducing the result of Speck and Seifert [Phys. Rev. E 70, 066112 (2004)]. Scrutinizing the applicability of perturbation theory we then show that, irrespective of time-scale separation, the expansion breaks down when applied to untypical work values from the tails of the distribution. We thus reconcile the result of Speck and Seifert with apparently conflicting exact expressions for the asymptotics of work distributions in special systems and with an intuitive argument building on the central limit theorem.