On the speed of approach to equilibrium for a collisionless gas

TL;DR

This paper analyzes how quickly a collisionless gas approaches thermal equilibrium within a vessel, providing lower bounds on decay rates and examining the impact of low-speed particles on thermalization.

Contribution

It establishes lower bounds for decay rates of the gas's approach to equilibrium and explores the effects of low-speed particles, especially in symmetric cases.

Findings

Lower bounds for decay rates under uniform $L^p$ bounds

Decay estimates in spherically symmetric cases

Influence of low-speed particles on thermalization

Abstract

We investigate the speed of approach to Maxwellian equilibrium for a collisionless gas enclosed in a vessel whose wall are kept at a uniform, constant temperature, assuming diffuse reflection of gas molecules on the vessel wall. We establish lower bounds for potential decay rates assuming uniform $L^p$ bounds on the initial distribution function. We also obtain a decay estimate in the spherically symmetric case. We discuss with particular care the influence of low-speed particles on thermalization by the wall.