Dense inhomogeneous fluids: Functional perturbation theory, the generalized Langevin equation, and kinetic theory

We present a functional perturbation theory (FPT) to describe the dynamical behavior of dense, inhomogeneous fluid mixtures, and from this show rigorously that the generalized Langevin equations are a first order form of this FPT. These equations lead to linearized kinetic equations for the singlet dynamical distribution function and for the higher distribution functions. These kinetic equations for inhomogeneous fluid mixtures reduce to those of Sung and Dahler [J. Chem. Phys. 80, 3025 (1984)] in the case of homogeneous fluids. Finally, we prove that the kinetic equations derived can be used to derive a ‘‘smoothed density’’ postulate, in which the local transport coefficients for inhomogeneous fluids are equated to those for a homogeneous fluid of the same smoothed density.