On the calculation of the single-particle momentum and energy distributions for a hard-core fluid in the microcanonical molecular dynamics ensemble

The microcanonical molecular dynamics ensemble describes a system with a fixed number of particles in a given volume and with constant total energy and total linear momentum. The primary phase integrals of this ensemble for a hard-core fluid are derived by using geometrical arguments. The single-particle momentum distribution function is derived by means of a Khinchin decomposition in the momentum-space of the system under study. The momentum moduli distribution and the energy distribution are also derived. These distributions are compared with the corresponding to the microcanonical and canonical ensembles. We show that for systems with few particles, the differences are significant. This fact could be important in the analysis of the results obtained from molecular dynamics of systems with periodic boundary conditions and a small number of particles.