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The velocity autocorrelation function (VACF) of lattice-gas cellular-automata fluids has been calculated by mode-coupling (MC) theory for finite systems, including sound modes, and compared with computer simulations on small (N10^3) and large (N10^6) two- and three-dimensional (3D) systems for reduced densities f ranging from 0. 05 to 0. 8. For times t up to 6t₀ (mean free times) the simulated VACF agrees with Boltzmann relaxation. In 2D the agreement with MC theory is excellent for t>9t₀ and has been tested over intervals of several acoustic traversal times. In 3D the agreement is still good, but sets in after much larger times (150t₀ at f=0. 1 and 60t₀ at f=0. 8). However, there are disagreements in the smallest systems at the lowest densities, where the observed VACF at largest times is about 6% (f=0. 1) and 9% (f=0. 05) larger than the theoretical values.
Naitoh et al. (Thu,) studied this question.