classical hard spheres, equipartition principle, molecular dynamics, kinetic effects
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.
Original Publication Citation
Shirts, Randall B., Scott R. Burt, and Aaron M. Johnson."Periodic boundary condition induced breakdown of the equipartition principle and other kinetic effects of finite sample size in classical hard-sphere molecular dynamics simulation." The Journal of
BYU ScholarsArchive Citation
Shirts, Randall B.; Burt, Scott R.; and Johnson, Aaron M., "Periodic boundary condition induced breakdown of the equipartition principle and other kinetic effects of finite sample size in classical hard-sphere molecular dynamics simulation" (2006). Faculty Publications. 286.
Physical and Mathematical Sciences
Chemistry and Biochemistry
© 2006 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in The Journal of Chemical Physics and may be found at http://link.aip.org/link/?JCPSA6/125/164102/2
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