Projection operators in classical kinetic theory

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Abstract
Zwanzig's projected kinetic equation is rederived by a perturbation method. A choice of projection is proposed which, in conjunction with appropriate initial-value conditions, yields kinetic equations for the two time distribution functions of phase subsets for a system in equilibrium. These equations are generalizations of the Fokker-Planck equations in which the dissipative terms are non-Markoffian. It is shown that exact equations for the van Hove self and distinct correlation functions are particular cases of these equations.