(248h) Theory and Monte Carlo Simulation of Ideal Gas with Shell Particles in Canonical, Isothermal-Isobaric, Grand Canonical and Gibbs Ensembles

Theories of small systems play an important role in the fundamental understanding of statistical mechanics, finite size effects and the validation of molecular simulations because no computer can simulate fluids in the thermodynamic limit. Previously, a shell particle in the isothermal-isobaric ensemble resolved ambiguity in the partition function, removed translationally redundant degrees of freedom and demonstrated quantitative differences from traditional simulations. In this work, shell particles are included in the canonical, grand canonical and Gibbs ensembles using ideal gas theory and Metropolis Monte Carlo simulation. We investigated the system size dependence of various ways of conducting ensemble averages. Furthermore, Gibbs ensemble simulations with shell particles removed a known instability that occurs without shell particles when a system reaches zero particles and infinitesimal volume. These expressions serve as a convenient test for Monte Carlo simulations.