Hydrodynamics and time correlation functions for cellular automata

Hydrodynamic excitations in lattice gas cellular automata are described in terms of equilibrium time correlation functions for the local conserved variables. For large space and time scales the linearized hydrodynamic equations are obtained to Navier-Stokes order. Exact expressions for the associated susceptibilities and transport coefficients are identified in terms of correlation functions. The general form of the time correlation functions for conserved densities in the hydrodynamic limit is given and illustrated by some examples suitable for comparison with computer simulation. The transport coefficients are related to time correlation functions for the conserved fluxes in a way analogous to the Green-Kubo expressions for continuous fluids. The general results are applied for a one-component fluid and several types of binary diffusion. Also discussed are the effects of unphysical slow modes such as staggered particle or momentum densities.