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

TL;DR

This paper introduces a new kinetic model for ideal gases that uses an operator to show how gases evolve towards the Maxwellian Velocity Distribution, conserving momentum and energy.

Contribution

The paper proposes a novel operator-based model that demonstrates decay to the Maxwellian distribution while conserving key physical quantities.

Findings

The operator conserves momentum and energy.

Any initial distribution decays to the Maxwellian distribution.

The Maxwellian distribution is a fixed point of the operator.

Abstract

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.