Uniform Approximation of a Maxwellian Thermostat by Finite Reservoirs

TL;DR

This paper demonstrates that a large reservoir of particles can be effectively approximated by a Maxwellian thermostat in a particle system, providing a uniform-in-time approximation in specific norms.

Contribution

It introduces a Kac-style collision process model for particle-reservoir interactions and proves the uniform approximation by a Maxwellian thermostat as the reservoir size grows.

Findings

Effective approximation of reservoir by Maxwellian thermostat for large N

Uniform-in-time accuracy in L^2 norm and GTW distance

Validation of the model for particle systems in contact with large reservoirs

Abstract

We study the evolution of a system of M particles in contact with a large reservoir of N>>M particles. The reservoir is initially in equilibrium at temperature T=1/\beta. The evolution of the system and reservoir is described via a suitable Kac-style collision process. We show that for large N, this evolution can be effectively described by replacing the reservoir with a Maxwellian thermostat at temperature T. This description provides an approximation that is uniform in time both in a suitable L^2 norm and in the Gabetta-Toscani-Wennberg (GTW) distance.