Classical statistical mechanics in the grand canonical ensemble.

Abstract

The methodology developed by Lustig for calculating thermodynamic properties in the microcanonical and canonical ensembles [J.Chem. Phys. 100, 3048 (1994)JCPSA60021-960610.1063/1.466446; Mol. Phys. 110, 3041 (2012)MOPHAM0026-897610.1080/00268976.2012.695032] is applied to derive rigorous expressions for thermodynamic properties of fluids in the grand canonical ensemble. All properties are expressed by phase-space functions, which are related to derivatives of the grand canonical potential with respect to the three independent variables of the ensemble: temperature, volume, and chemical potential. The phase-space functions contain ensemble averages of combinations of the number of particles, potential energy, and derivatives of the potential energy with respect to volume. In addition, expressions for the phase-space functions for temperature-dependent potentials are provided, which are required to account for quantum corrections semiclassically in classical simulations. Using the Lennard-Jones model fluid as a test case, the derived expressions are validated by Monte Carlo simulations. In contrast to expressions for the thermal expansion coefficient, the isothermal compressibility, and the thermal pressure coefficient from the literature, our expressions yield more reliable results for these properties, which agree well with a recent accurate equation of state for the Lennard-Jones model fluid. Moreover, they become equivalent to the corresponding expressions in the canonical ensemble in the thermodynamic limit.