Studies in Molecular Dynamics. IV. The Pressure, Collision Rate, and Their Number Dependence for Hard Disks

The pressure for four, 12, and 72 hard disks determined dynamically from the virial theorem or the collision rate is shown to be identical to that determined by the Monte Carlo method. To show this equivalence, it is necessary to take into account that the center-of-mass velocity is kept fixed in the dynamic system. This numerical agreement suggests the validity of the quasiergodic hypothesis even for small systems. The (lnN)/N dependence of the phase-transition pressure on the number of particles N is simply explained in terms of the communal entropy.