Existence of equilibrium states of systems of hard spheres in the Boltzmann-Enskog limit within the frame work of the grand canonical ensemble

Abstract

We study equilibrium states of systems of hard spheres in the Boltzmann-Enskog limit (d→0, 1/v→∞ (z→∞), and d ³ (1/v)=const (d ³ z=const)). For this purpose, we use the Kirkwood-Salsburg equations. We prove that, in the Boltzmann-Enskog limit, solutions of these equations exist and the limit distribution functions are constant. By using the cluster and compatibility conditions, we prove that all distribution functions are equal to the product of one-particle distribution functions, which can be represented as power series in z=d ³ z with certain coefficients.