Functional Integral Representation of Nonequilibrium Statistical Mechanics

Abstract

A functional integral representation of the Green's function of the Liouville equation is presented, and it is shown how the weak-coupling expansion and the binary-collision expansion are generated from the functional integral. Furthermore, when the interaction between particles is represented as a sum of short- and long-ranged components, it is possible to generate a new ``mixed'' expansion. It is shown how this mixed expansion may be used to derive a kinetic equation descriptive of the liquid phase. Under the conditions that successive correlated binary encounters may be neglected and that the effects of the weak interaction on the dynamics of the quasibinary encounter are neglected, the Rice—Allnatt equation is recovered. A discussion of the implications of the derivation is given along with a brief description of those diagrams of the Prigogine theory which are summed in the Rice—Allnatt approximation.