Periodic boundary condition induced breakdown of the equipartition principle and other kinetic effects of finite sample size in classical hard-sphere molecular dynamics simulation

Randall B Shirts; Scott R Burt; Aaron M Johnson

doi:10.1063/1.2359432

Periodic boundary condition induced breakdown of the equipartition principle and other kinetic effects of finite sample size in classical hard-sphere molecular dynamics simulation

J Chem Phys. 2006 Oct 28;125(16):164102. doi: 10.1063/1.2359432.

Authors

Randall B Shirts¹, Scott R Burt, Aaron M Johnson

Affiliation

¹ Department of Chemistry and Biochemistry, Brigham Young University, Provo, Utah 84602-5700, USA.

PMID: 17092058
DOI: 10.1063/1.2359432

Abstract

We examine consequences of the non-Boltzmann nature of probability distributions for one-particle kinetic energy, momentum, and velocity for finite systems of classical hard spheres with constant total energy and nonidentical masses. By comparing two cases, reflecting walls (NVE or microcanonical ensemble) and periodic boundaries (NVEPG or molecular dynamics ensemble), we describe three consequences of the center-of-mass constraint in periodic boundary conditions: the equipartition theorem no longer holds for unequal masses, the ratio of the average relative velocity to the average velocity is increased by a factor of [N/(N-1)]1/2, and the ratio of average collision energy to average kinetic energy is increased by a factor of N/(N-1). Simulations in one, two, and three dimensions confirm the analytic results for arbitrary dimension.