We present computer simulations run with a stochastic cellular automaton
which describes d=1 particle systems connected to reservoirs which keep two
different densities at the endpoints. We fix the parameters so that there is a
phase transition (of the van der Waals type) and observe that if the densities
at the boundaries are metastable then, after a transient, the system reaches an
apparently stationary regime where the current flows from the reservoir with
smaller density to the one with larger density
