Time-dependent density functional theory and the kinetics of lattice gas systems in contact with a wall

We develop an improved mean-field theory which allows us to describe the diffusive dynamics near phase transformations in condensed systems. Starting from a master equation for a stochastic lattice gas we obtain evolution equations on the single-particle level, whose stationary solutions in principle are consistent with the exact equilibrium statistics. Our method, which generalizes an approach proposed earlier, is based on a combination of a local equilibrium assumption and the lattice version of classical density functional theory. In the continuum limit, which is worked out for attractive interactions, generalized Cahn–Hilliard-type equations are recovered. Microscopic kinetic coefficients can be identified, which in general depend on the instantaneous local correlations in the nonequilibrium state. Moreover we study semi-infinite systems interacting with a planar wall and derive the appropriate boundary conditions to be imposed on the continuum equations. Applications to problems of the kinetics of ph...