Periodic boundary conditions and the correct molecular-dynamics ensemble

The use of periodic boundary conditions in molecular-dynamics simulations leads to the microcanonical ensemble of Ray and Zhang J.R. Ray, H. Zhang, Phys. Rev. E 59 (1999) 4781] in which the total linear momentum and the generator of infinitesimal Galilean boosts are conserved quantities in addition to the total energy E, the volume V, and the number of particles N of the system. We find that the invariance of should be of importance in the analysis of ensemble averages of quantities that only depend on the spatial coordinate . As an application we study the density profile of an isolated system of hard disks with periodic boundary conditions in the absence of external forces. We find that the periodic boundary conditions give rise to an anomalous inhomogeneity in the density profile of the system. This inhomogeneity is only relevant for systems with a very small number of disks and is related to the conservation of the center of mass coordinates.