The kinetic theory for lattice-gas cellular automata is extended beyond Boltzmann's mean-field approximation by including correlated ring-type collisions. This theory provides explicit expressions for time-correlation functions for all times in terms of a ring collision integral. We also obtain some exact results for time-correlation functions for short times. In particular, deviations from the Boltzmann equation result observed in computer simulations of the velocity-autocorrelation function of three-dimensional systems after two time steps are explained. For long times the results obtained reduce to those found using phenomenological mode-coupling theory.
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Kirkpatrick et al. (1991) studied this question.
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