Propagation of Chaos for a Thermostated Kinetic Model
Abstract
We consider a system of N point particles moving on a ddimensional torus {T}^{d}. Each particle is subject to a uniform field E and random speed conserving collisions {v}_{i}to{v}_{i}' with {v}_{i}={v}_{i}'. This model is a variant of the DrudeLorentz model of electrical conduction (Ashcroft and Mermin in Solid state physics. Brooks Cole, Pacific Grove, 1983). 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 meanfield type of interaction between the particles. Here we prove that, starting from a product measure, in the limit N→∞, the one particle velocity distribution f(q,v,t) satisfies a self consistent VlasovBoltzmann equation, for all finite time t. This is a consequence of "propagation of chaos", which we also prove for this model.
 Publication:

Journal of Statistical Physics
 Pub Date:
 January 2014
 DOI:
 10.1007/s1095501308612
 arXiv:
 arXiv:1305.7282
 Bibcode:
 2014JSP...154..265B
 Keywords:

 Mathematical Physics;
 60K35;
 82B40
 EPrint:
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