  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.
