Statistical Mechanics and Kinetic Theory of Lattice Gas Cellular Automata

Abstract

These lecture notes present an introduction to the theory of lattice gas automata using the methods of non-equilibrium statistical mechanics and kinetic theory. The micro-dynamic, Boltzmann and Liouville equation are studied. The importance of the semi-detailed balance condition is that it guarantees universal equilibrium states, which are described by the Gibbs’ distributions of statistical mechanics. The lack of Galilei in-variance introduces the non-Galilean factor, for which an exact third order fluctuation formula is derived. The Navier Stokes equation is obtained by applying a Chapman-Enskog type method to the Liouville equation, which results into a Green Kubo formula for the viscosity. Also included is an explicit evaluation of this formula in the Boltzmann approximation.