A new model for the transport of particles in a thermostatted system

We introduce an elementary microscopic model for the free expansion of a gas from a smaller to a larger reservoir; a ``pump'' takes the particles back to the original reservoir, so as to maintain a stationary situation. The system is dissipative and thermostatted (with an elementary non Gaussian reversible thermostat). We consider here only the case of noninteracting particles. We identify a parameter in the system, playing the role of the field, and investigate numerically the usual transport properties, among them the proportionality of the current to the field for small fields, and the proportionality of the volume contraction rate to the product of field and current, in the same conditions. In spite of the simplicity of the model (and of the difficulty in the thermodynamical interpretation, the model being non interacting) we find apparently normal transport laws. We also make a particularly accurate test of the Gallavotti--Cohen fluctuation formula, which turns out to be always well satisfied (though fluctuations, in some conditions, are rather far from Gaussian). A leading idea of the paper is to look for the minimal requirements that a particle system should satisfy in order to give rise, at least formally, to normal transport.