Work probability distribution in systems driven out of equilibrium

TL;DR

This paper derives a differential equation for the work distribution in out-of-equilibrium stochastic systems, explores its path integral representation, and discusses implications for free energy calculations and fluctuation analysis.

Contribution

It introduces a differential equation framework for work distribution evolution and connects it with path integral methods for systems driven out of equilibrium.

Findings

Work distribution can be represented by a path integral dominated by classical paths.

The derived equation describes the evolution of work distribution for both microscopic and collective variables.

The applicability of the Jarzynski equality is analyzed in the context of large work fluctuations.

Abstract

We derive the differential equation describing the time evolution of the work probability distribution function of a stochastic system which is driven out of equilibrium by the manipulation of a parameter. We consider both systems described by their microscopic state or by a collective variable which identifies a quasiequilibrium state. We show that the work probability distribution can be represented by a path integral, which is dominated by ``classical'' paths in the large system size limit. We compare these results with simulated manipulation of mean-field systems. We discuss the range of applicability of the Jarzynski equality for evaluating the system free energy using these out-of-equilibrium manipulations. Large fluctuations in the work and the shape of the work distribution tails are also discussed.