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Uniform Approximation of a Maxwellian Thermostat by Finite Reservoirs

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Abstract

We study a system of M particles in contact with a large but finite reservoir of \({N \gg M}\) particles within the framework of the Kac master equation modeling random collisions. The reservoir is initially in equilibrium at temperature \({T=\beta^{-1}}\). We show that for large N, this evolution can be approximated by an effective equation in which the reservoir is described by a Maxwellian thermostat at temperature T. This approximation is proven for a suitable \({L^2}\) norm as well as for the Gabetta–Toscani–Wennberg (GTW) distance and is uniform in time.

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, USA

    F. Bonetto, M. Loss, H. Tossounian & R. Vaidyanathan

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  1. F. Bonetto
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  2. M. Loss
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  3. H. Tossounian
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  4. R. Vaidyanathan
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Correspondence to F. Bonetto.

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Communicated by C. Mouhot

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Bonetto, F., Loss, M., Tossounian, H. et al. Uniform Approximation of a Maxwellian Thermostat by Finite Reservoirs. Commun. Math. Phys. 351, 311–339 (2017). https://doi.org/10.1007/s00220-016-2803-8

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  • DOI: https://doi.org/10.1007/s00220-016-2803-8

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