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Uniform Approximation of a Maxwellian Thermostat by Finite Reservoirs

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.

preprint2016arXivOpen access
Federico BonettoMichael LossHagop TossounianRanjini Vaidyanathan
math-phmath.MP
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Federico BonettoMichael LossHagop TossounianRanjini Vaidyanathan

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