Extremal principle for the steady-state selection in driven lattice gases with open boundaries

This paper investigates the steady states of one-dimensional driven lattice gases with open boundary conditions. It shows how the extremal principle proposed recently by Popkov and Schutz can be modified to apply to more general cases. Monte Carlo simulations are presented for a one-dimensional totally asymmetric simple exclusion process with nearest neighbor repulsion under parallel update as an example. The simulations enable one to guess the exact phase diagram for this particular lattice gas with deterministic bulk dynamics, by fitting the data to analytic formulas, which appear to be exact in the thermodynamic limit.