Work distribution and path integrals in general mean-field systems

TL;DR

This paper derives the evolution equation for work and collective variables in mean-field systems out of equilibrium, demonstrating the Jarzynski equality at the path integral level and in the thermodynamic limit.

Contribution

It introduces a path integral approach to analyze work distribution in mean-field systems driven out of equilibrium, extending the understanding of fluctuation relations.

Findings

Derivation of the joint probability evolution equation for collective variables and work.

Validation of the Jarzynski equality at the path integral level.

Demonstration of the equality's validity in the thermodynamic limit.

Abstract

We consider a mean-field system described by a general collective variable $M$, driven out of equilibrium by the manipulation of a parameter $\mu$. Given a general dynamics compatible with its equilibrium distribution, we derive the evolution equation for the joint probability distribution function of $M$ and the work $W$ done on the system. We solve this equation by path integrals. We show how the Jarzynski equality holds identically at the path integral level and for the classical paths which dominate the expression in the thermodynamic limit. We discuss some implications of our results.