Propagation of Chaos for a Thermostated Kinetic Model
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.
Keywords
Cite
@article{arxiv.1305.7282,
title = {Propagation of Chaos for a Thermostated Kinetic Model},
author = {F. Bonetto and E. A. Carlen and R. Esposito and J. L. Lebowitz and R. Marra},
journal= {arXiv preprint arXiv:1305.7282},
year = {2015}
}
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