GENERALIZED BOLTZMANN-EQUATION FOR LATTICE-GAS AUTOMATA

In this paper a theory is formulated that predicts velocity and spatia l correlations between occupation numbers that occur in lattice gas au tomata violating semi-detailed balance. Starting from a coupled BBGKY hierarchy for the n-particle distribution functions, cluster expansion techniques are used to derive approximate kinetic equations. In zerot h approximation the standard nonlinear Boltzmann equation is obtained; the next approximation yields the ring kinetic equation, similar to t hat for hard-sphere systems, describing the time evolution of pair cor relations. The ring equation is solved to determine the (nonvanishing) pair correlation functions in equilibrium for two models that violate semi-detailed balance. One is a model of interacting random walkers o n a line, the other one is a two-dimensional fluid-type model on a tri angular lattice. The numerical predictions agree very well with comput er simulations.