Abstract
The theory of transport phenomena in a gas is considered from a statistical mechanical viewpoint. The formalism is based on the Liouville equation for the time evolution of an ensemble of systems and the Bogoliubov-Born-Green-Kirkwood-Yvon equations which are integrals of the Liouville equation. The BBGKY hierarchy is truncated by a factorization principle which is a generalization of the molecular chaos assumption. For purely repulsive potentials, the set of equations obtained by truncating at f(3) is shown to give rise to the three-body interaction term obtained by Hollinger and Curtiss and by a different argument by Bogoliubov. The two coupled equations obtained by truncating the BBGKY hierarchy at f(3) are considered in detail. An approximation to these equations leads to a Boltzmann equation which is a soft potential generalization of the Enskog dense gas equation for rigid spheres. This Boltzmann equation includes both collisional transfer and three body collision effects.
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