MONTE-CARLO EVALUATION OF ENSEMBLE AVERAGES INVOLVING PARTICLE NUMBER VARIATIONS IN DENSE FLUID SYSTEMS

A general formalism is presented for the calculation of thermodynamic properties via statistical ensembles augmented with nonphysical states. These augmented ensembles can be readily incorporated into Monte Carlo molecular simulation methods. Of particular interest is evaluation of thermodynamic properties by Monte Carlo applications which involve particle number variations. The augmented states can be constructed to facilitate Markov transitions between states with varying number of particles. This in turn can greatly increase the convergence rates of property averages, especially for high density systems. This benefit is analogous to chemical catalysis, which by introducing low activation energy reaction pathways increases reaction rate (i.e., convergence rate) without affecting the overall equilibrium. The utility of augmented ensembles is demonstrated through novel Monte Carlo implementations which are efficient regardless of system density of grand ensemble simulation and test particle activity evaluation. Applications to pure hard-sphere and 12-6 Lennard-Jones fluid systems are specifically considered.