Uniform Approximation of a Maxwellian Thermostat by Finite 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/β. 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.

arXiv commentLaTex 23 pages, some of the proofs have been simplified and the introduction rewritten

References in corpus (3)

• The Kac Model Coupled to a Thermostat
• Partially Thermostated Kac Model
• Non-Equilibrium Steady States in Kac's Model Coupled to a Thermostat

Cited by in corpus (8)

• Uniform propagation of chaos for the thermostated Kac model
• Entropy decay for the Kac evolution
• Non-Equilibrium Steady States in Kac's Model Coupled to a Thermostat
• The BGK equation as the limit of an $N$ particle system
• On a thermostated Kac model with rescaling
• Decay of Information for the Kac Evolution
• Equilibration in the Kac Model using the GTW Metric $d_2$
• Grand Canonical Evolution for the Kac Model