Uniform Approximation of a Maxwellian Thermostat by Finite Reservoirs

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/\beta. The evolution of the system and reservoir is described via a suitable Kac-style collision process. We show that for large N...

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Veröffentlicht in:arXiv.org 2016-10
Hauptverfasser: Bonetto, Federico, Loss, Michael, Tossounian, Hagop, Vaidyanathan, Ranjini
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Approximation
Evolution
Mathematical analysis
Mathematics - Mathematical Physics
Physics - Mathematical Physics
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Loss, Michael
Tossounian, Hagop
Vaidyanathan, Ranjini
description 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.
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subjects Approximation
Evolution
Mathematical analysis
Mathematics - Mathematical Physics
Physics - Mathematical Physics
title Uniform Approximation of a Maxwellian Thermostat by Finite Reservoirs
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