Description of far-from-equilibrium processes by mean-field lattice gas models

Mean-field kinetic equations are a valuable tool to study the atomic dynamics and spin dynamics of simple lattice gas and Ising models. They can be derived from the microscopic master equation of the system and contain analytical expressions for kinetic coefficients and thermodynamic quantities which are usually introduced phenomenologically. We review several methods to obtain such equations, and discuss applications to the dynamics of order–disorder transitions, spinodal decomposition, and dendritic growth in the isothermal or chemical model. In the case of dendritic growth we show that the mean-field kinetic equations are equivalent to standard continuum equations for this problem and derive expressions for macroscopic quantities, e.g. the surface tension and kinetic coefficients, as functions of the microscopic order parameters. In spinodal decomposition, we focus our attention on the vacancy mechanism, which is a more faithful picture of diffusion in solids than the more widely examined exchange mech...