In this paper, for the first time a theory is formulated that predicts
velocity and spatial correlations between occupation numbers that occur in
lattice gas automata 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 zeroth
approximation the standard nonlinear Boltzmann equation is obtained; the next
approximation yields the ring kinetic equation, similar to that for hard sphere
systems, describing the time evolution of pair correlations. As a quantitative
test we calculate equal time correlation functions in equilibrium for two
models that violate semi-detailed balance. One is a model of interacting random
walkers on a line, the other one is a two-dimensional fluid type model on a
triangular lattice. The numerical predictions agree very well with computer
simulations.Comment: 31 pages LaTeX, 12 uuencoded tar-compressed Encapsulated PostScript
figures (`psfig' macro), hardcopies available on request, 78kb + 52k