Studies in Molecular Dynamics. II. Behavior of a Small Number of Elastic Spheres

The equation of state and the collision rate for systems ranging in size from four to 500 particles are described. The dependence of the results on the number of particles is qualitatively discussed and in this way insight is gained as to what is required of more accurate analytical theories. By comparing the results to various analytical theories now available their region of validity is established. The number of particles necessary at various densities to obtain a quantitative description of the equilibrium properties is delineated. Whether a first-order phase transition exists for hard spheres remains open until larger systems are investigated.