Open interacting particle systems and Ising measures

We first survey some open questions concerning stochastic interacting particle systems with open boundaries. Then, an asymmetric exclusion process with open boundaries that generalizes the lattice gas model of Katz, Lebowitz, and Spohn is introduced and invariance of the one-dimensional Ising measure is proved. The stationary current is computed in explicit form and is shown to exhibit current reversal at some density. Based on the extremal-current principle for one-dimensional driven diffusive systems with one conservation law, the phase diagram for boundary-induced phase transitions is conjectured for this case. There are two extremal-current phases, unlike in the open ASEP (one extremal-current phase) or in the conventional KLS model (one or three extremal-current phases).