Dynamics in a Gulton staircase is considered based on a model in which many
particles, coupled through an average velocity, are in contact with a Gaus
sian thermostat. Computer simulation gives information on entropy productio
n, the stationary mass current, and distribution functions of both particle
positions and momenta. A Langevin thermostat is also considered for the sa
ke of comparison with a mechanical thermostat. [S1063-651X(99)09105-9].