Work distribution and path integrals in general mean-field systems

Dipartimento di Scienze Fisiche and Unità INFM Università “Federico II” - Complesso Monte S. Angelo, I-80126 Napoli, Italy

Corresponding author: imparato@na.infn.it

Received: 3 February 2005
Accepted: 20 April 2005

Abstract

We consider a mean-field system described by a general collective variable M, driven out of equilibrium by the manipulation of a parameter μ. 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 that the Jarzynski equality holds identically for these dynamics, both 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.