A Nonlinear Map for the Decay to Equilibrium of Ideal Gases

TL;DR

This paper introduces a nonlinear operator modeling the decay to equilibrium in ideal gases, demonstrating how the velocity distribution evolves towards Maxwellian distribution while conserving momentum and energy, with entropy increasing over time.

Contribution

The paper presents a novel nonlinear map that describes the decay to equilibrium in ideal gases, conserving key physical quantities and illustrating entropy increase.

Findings

The nonlinear map converges to Maxwellian velocity distribution.

The system conserves momentum and energy during evolution.

Entropy increases as the system approaches equilibrium.

Abstract

An operator that governs the discrete time evolution of the velocity distribution of an out-of-equilibrium ideal gas will be presented. This nonlinear map, which conserves the momentum and the energy of the ideal gas, has the Maxwellian Velocity Distribution (MVD) as an asymptotic equilibrium. Moreover, the system displays the increasing of the entropy during the decay to the MVD.