Distribution of work in isothermal non-equilibrium processes

TL;DR

This paper investigates the distribution of work in isothermal non-equilibrium processes, revealing Gaussian behavior under slow driving and highlighting potential limitations of perturbative methods in more complex scenarios.

Contribution

It introduces a projection method to analyze work distribution in driven diffusive systems and uncovers non-analytic behaviors in higher-order expansions.

Findings

Work distribution is Gaussian for slow, finite driving.

Exact solutions show possible failure of perturbative expansions.

Non-analytic behavior appears in higher-order moments.

Abstract

Diffusive motion in an externally driven potential is considered. It is shown that the distribution of work required to drive the system from an initial equilibrium state to another is Gaussian for slow but finite driving. Our result is obtained by projection method techniques exploiting a small parameter defined as the switching rate between the two states of the system. The exact solution for a simple model system shows that such an expansion may fail in higher orders, since the mean and the variance following from the exact distribution show non-analytic behavior.