The free energy of expansion and contraction: Treatment of arbitrary systems using the Jarzynski equality

Abstract

Thermodynamic integration, free energy perturbation, and slow change techniques have long been utilised in the calculation of free energy differences between two states of a system that has under- gone some transformation. With the introduction of the Jarzynski equality and the Crooks relation, new approaches are possible. This paper investigates an important phenomenon - systems under- going a change in volume/density - and derives both the Jarzynski equality and Crooks relation of such systems using a statistical mechanical approach. These results apply to systems with arbitrary particle interactions and densities. The application of this approach to the expansion/compression of particles confined within a vessel with a piston and within a periodic system is considered.