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for a classical many-particle system. This equation is then used to develop an exact kinetic equation for the time-correlation function (6g(x, p, 0)bg(x', p', t ) ) [which is the generalization of the Van Hove time-dependent pair correlation function G(r, t)]. In the lowest order of approximation, this kinetic description reduces to the Vlasov-like equation which has been used to study neutron scattering from liquids. A less restrictive approximation is obtained by utilizing weak-coupling perturbation theory to yield a generalized Fokker-Planck equation for the time-correlation function. Other possible approximation schemes are also discussed.

Derivation of Kinetic Equations from the Generalized Langevin Equation