The fast rate limit of driven diffusive systems

We study the stationary nonequilibrium states of the van Beijeren/Schulman model of a driven lattice gas in two dimensions. In this model, jumps are much faster in the direction of the driving force than orthogonal to it. Van Kampen's Ω-expansion provides a suitable description of the model in the high-temperature region and specifies the critical temperature and the spinodal curve. We find the rate dependence of T_c and show that independently of the jump rates the critical exponents of the transition are classical, except for anomalous energy fluctuations. We then study the stationary solution of the deterministic equations (zeroth-order Ω-expansion). They can be obtained as trajectories of a dissipative dynamical system with a three-dimensional phase space. Within a certain temperature range below T_c, these equations have a kink solution whose asymptotic densities we identify with those of phase coexistence. They appear to coincide with the results of the "Maxwell construction." This provides a dynamical justification for the use of this construction in this nonequilibrium model. The relation of the Freidlin-Wentzell theory of small random perturbations of dynamical systems to the steady-state distribution below T_c is discussed.