Propagation of Chaos for the Thermostatted Kac Master Equation

Eric Carlen, Dawan Mustafa, Bernt Wennberg

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

The Kac model is a simplified model of an N-particle system in which the collisions of a real particle system are modeled by random jumps of pairs of particle velocities. Kac proved propagation of chaos for this model, and hence provided a rigorous validation of the corresponding Boltzmann equation. Starting with the same model we consider an N-particle system in which the particles are accelerated between the jumps by a constant uniform force field which conserves the total energy of the system. We show propagation of chaos for this model.

Original languageEnglish (US)
Pages (from-to)1341-1378
Number of pages38
JournalJournal of Statistical Physics
Volume158
Issue number6
DOIs
StatePublished - Jan 1 2015

    Fingerprint

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Kinetic equation with a thermostat
  • Master equation
  • Propagation of chaos

Cite this