On a Thermostated Kac Model with Rescaling

Roberto Cortez, Hagop Tossounian

Research output: Contribution to journalArticlepeer-review


We introduce a global thermostat on Kac’s 1D model for the velocities of particles in a space-homogeneous gas subjected to binary collisions, also interacting with a (local) Maxwellian thermostat. The global thermostat rescales the velocities of all the particles, thus restoring the total energy of the system, which leads to an additional drift term in the corresponding nonlinear kinetic equation. We prove ergodicity for this equation and show that its equilibrium distribution has a density that, depending on the parameters of the model, can exhibit heavy tails, and whose behaviour at the origin can range from being analytic, to being Ck, and even to blowing-up. Finally, we prove propagation of chaos for the associated N-particle system, with a uniform-in-time rate of order N-η in the squared 2-Wasserstein metric, for an explicit η∈ (0 , 1 / 3].

Original languageEnglish
JournalAnnales Henri Poincare
Early online date21 Mar 2021
Publication statusE-pub ahead of print - 21 Mar 2021

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics


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