  We present some computer simulations run on a stochastic CA (cellular
automaton). The CA simulates a gas of particles which are in a channel, the
interval $[1,L]$ in $\mathbb Z$, but also in "reservoirs" $\mathcal R_1$ and
$\mathcal R_2$. The evolution in the channel simulates a lattice gas with
Kawasaki dynamics with attractive Kac interactions, the temperature is chosen
smaller than the mean field critical one. There are also exchanges of particles
between the channel and the reservoirs and among reservoirs. When the rate of
exchanges among reservoirs is in a suitable interval the CA reaches an
apparently stationary state with a non zero current, for different choices of
the initial condition the current changes sign. We have a quite satisfactory
theory of the phenomenon but we miss a full mathematical proof.
