MPEJ Volume 7, No. 3, 22 pp.
Received: Oct 23, 2001. Revised: Nov 14, 2001. Accepted: Nov 17, 2001.
G. Benettin, L. Rondoni:
A new model for the transport of particles in a thermostatted system
ABSTRACT: 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.