Propagation of Chaos for a Thermostated Kinetic Model

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

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We consider a system of N point particles moving on a d-dimensional torus Td. Each particle is subject to a uniform field E and random speed conserving collisions vi → vi with {pipe}vi{pipe}{pipe}vi{pipe}. This model is a variant of the Drude-Lorentz 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 mean-field 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 Vlasov-Boltzmann equation, for all finite time t. This is a consequence of "propagation of chaos", which we also prove for this model.

Original languageEnglish (US)
Pages (from-to)265-285
Number of pages21
JournalJournal of Statistical Physics
Issue number1-2
StatePublished - Jan 2014

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


Dive into the research topics of 'Propagation of Chaos for a Thermostated Kinetic Model'. Together they form a unique fingerprint.

Cite this