THERMODYNAMICS OF LATTICE-GAS MODELS WITH DISCRETE VELOCITIES

Abstract

We study the thermodynamical behavior of a model of a lattice gas with discrete velocities in Bose-Einstein, Fermi-Dirac and Boltzmann statistics. The parameters of the model are the space dimension and the number of allowed velocities. Since this last number is finite, the energy spectrum is bounded above implying that the entropy is not an always increasing function of the energy and the temperature may therefore be negative. We show that as the number of velocities increases, the model approaches the behavior of an ideal classical gas in a restricted interval of temperature.