Initial ensemble dependence of Jarzynski equality in the thermodynamic limit

Abstract

We investigate the initial ensemble dependence of the Jarzynski relation for nonequilibrium work performed on a classical system in the thermodynamic limit. It is shown that the Jarzynski equality holds also for a microcanonical ensemble only if the work process is quasi statically slow. If work is performed by a rapid perturbation, the average of exponentiated work expanded on a microcanonical system markedly deviates from the Jarzynski equality. Such deviation in fact quantifies the ratio of the energy distributions of nonequilibrium states in relative to equilibrium distribution. We exemplify these points in a simple model system both for the cases of deterministic and stochastic dynamics.