Statistical–mechanical description of diffusion in interacting lattice gases

A Mori-type equation for the lattice concentration of an interacting lattice gas is constructed on the basis of the master equation in the framework of the nonequilibrium statistical ensemble method due to Zubarev. The general expression for the diffusion coefficient, which takes into account particle jumps of arbitrary length, spatial dispersion and memory effects is derived. In contrast to systems with reversible dynamics the relevant or quasiequilibrium distribution significantly contributes to the diffusion coefficient. This contribution is represented by two cofactors, namely the kinetic diffusion coefficient and the correlation function of concentration fluctuations. For lattice gases with thermally activated hopping dynamics in hydrodynamic (zero frequency and long wave) limit the former is reduced to Zhdanovʹs form that reflects an important role of equilibrium characteristics, i.e. the chemical potential and the two-site vacancy distribution function. The self-consistent diagram approximation is used to evaluate these characteristics for a two-dimensional lattice gas with nearest-neighbor attractive interaction on a square lattice. Results for the diffusion coefficient coincide within a few per cent with Monte-Carlo simulation data.