Lattice Lorentz gas

In cellular automaton fluids, where binary collision laws admit reflections, the Stosszahl ansatz and the Boltzmann equation are no longer valid at low densities. This is proven for a class of Lorentz gas models, defined on cubic lattices, for which the diffusion coefficient is calculated from a self-consistent ring kinetic equation or effective medium theory. The calculated results are in excellent agreement with results from molecular dynamics simulations over the whole density interval.