A fluctuation formula for the non-galilean factor in lattice gas automata

Abstract

A lattice gas automaton lacks Galilei invariance, and equilibria of systems moving with a finite speed \u -->\ are not simply related by a Galilei transformation to the equilibrium distribution in the rest frame. In the hydrodynamic description of low speed equilibria in lattice gas automata a factor G(rho) appears in the nonlinear convective term, del --> . G(rho)rho-u --> u -->, of the Navier-Stokes equation, that differs from unity due to lack of Galilei invariance. For this non-Galilean factor an expression in terms of fluctuating quantities is derived, in a grand ensemble where the total momentum is fluctuating around a zero average. The formula is valid as long as there exists a unique equilibrium state. Consequently, the results can also be used for a direct simulation of G(rho) in lattice gas models where the explicit form of the equilibrium distribution is not known, such as in models that violated semi-detailed balance.