Latent heat and the Fourier law
  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. 
Matteo Colangeli, Anna De Masi, Errico Presutti
cond-mat.stat-mech