Calculation of the chemical potential in the Gibbs ensemble

Abstract

An expression for the chemical potential in the Gibbs ensemble is derived. For finite system sizes this expression for the chemical potential differs system-atically from Widom's test particle insertion method for the N, V, T ensemble. In order to compare these two methods for calculating the chemical potential, Monte Carlo simulations in the Gibbs ensemble for a Lennard-Jones system have been performed. These calculations suggest that for a small number of particles the Widom expression gives a chemical potential for the liquid phase which is systematically higher than the chemical potential of the gas phase. However, when the expression for the chemical potential which is derived here is used, it turns out that the chemical potentials of the coexisting phases are equal at all studied conditions.