On the generalization of the boltzmann equation to general order in the density

Abstract

An expansion of the pair distribution function as a functional of the first distribution function in powers of the density is derived for a system not in equilibrium. This is achieved, using cluster expansions that are analogous to the Ursell-Uhlenbeck-Kahn- and the Husimi-expansions known from equilibrium statistical mechanics. On the basis of this procedure it is shown, that the density expansions of the non-equilibrium- and the equilibrium pair distribution function can be characterized by the same diagrams, where in the non-equilibrium case the first distribution function takes the role of the density in the equilibrium case. The general term in a systematic generalization of the Boltzmann equation to higher densities follows immediately from the expansion.