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A New Model for Ideal Gases. Decay to the Maxwellian Distribution

In this work, a new model in kinetic gas theory for deriving the Maxwellian Velocity Distribution (MVD) is proposed. We construct an operator that governs the discrete time evolution of the velocity distribution. This operator, which conserves the momentum and the energy of the ideal gas, has the MVD as a fixed point. Moreover, for any initial out-of-equilibrium velocity distribution, it is shown that the gas decays to the equilibrium distribution, that is, to the MVD.