On the Kinetic Theory of Dense Gases

Abstract

A statistical mechanical theory of a dense gas that is not in equilibrium is presented, which is completely analogous to the well known theory of a dense gas in equilibrium. In particular, an expansion of the pair distribution function in powers of the density for a gas not in equilibrium is given, corresponding with that in equilibrium to all orders in the density, that can be represented by the same diagrams. The expansion can be reduced to that derived by Bogolubov, Uhlenbeck, and Choh from a solution of the B‐B‐G‐K‐Y hierarchy. The conditions for the validity of the expansion are, for an infinite system at not too high density, and after the lapse of some time after t = 0: (1) a statistical assumption at t = 0; (2) some conditions on the interaction potential; (3) coarse‐grained distribution functions. A simple generalization of the Boltzmann equation to general order in the density is included. Also, the connection with a Master equation for a spatially homogeneous system is discussed.