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. •A stationary current from the smaller to the larger density reservoir is investigated.•The Fourier Law in systems with Kac potential and metastable boundaries is studied.•The mean field limit of our model is discussed.