Nonlinear hydrodynamics of lattice-gas automata with semi-detailed balance

Equations governing the evolution of the hydrodynamic variables in a lattice-gas automaton, arbitrarily far from equilibrium, are derived from the micro-dynamical description of the automaton, under the condition that the local collision rules satisfy semi-detailed balance. This condition guarantees that a factorized local equilibrium distribution (for each node) of the Fermi-Dirac form is invariant under the collision step but not under propagation. The main result is the set of fully nonlinear hydrodynamic equations for the automaton in the lattice-Boltzmann approximation; these equations have a validity domain extending beyond the region close to equilibrium. Linearization of the hydrodynamic equations derived here leads to Green-Kubo formulae for the transport coefficients.