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arXiv · 1305.7282

Propagation of Chaos for a Thermostated Kinetic Model

F. Bonetto·E. A. Carlen·R. Esposito·J. L. Lebowitz·R. Marra
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Abstract

We consider a system of N point particles moving on a d-dimensional torus. Each particle is subject to a uniform field E and random speed conserving collisions. This model is a variant of the Drude-Lorentz model of electrical conduction. In order to avoid heating by the external field, the particles also interact with a Gaussian thermostat which keeps the total kinetic energy of the system constant. The thermostat induces a mean-field type of interaction between the particles. Here we prove that, starting from a product measure, in the large N limit, the one particle velocity distribution satisfies a self consistent Vlasov-Boltzmann equation.. This is a consequence of "propagation of chaos", which we also prove for this model.

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F. Bonetto, E. A. Carlen, R. Esposito, J. L. Lebowitz, R. Marra. 2013-06-03. Propagation of Chaos for a Thermostated Kinetic Model. https://doi.org/10.1007/s10955-013-0861-2

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