Kinetic relaxation models for energy transport

Kazuo Aoki*, Peter Markowich, Shigeru Takata

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Kinetic equations with relaxation collision kernels are considered under the basic assumption of two collision invariants, namely mass and energy. The collision kernels are of BGK-type with a general local Gibbs state, which may be quite different from the Gaussian. By the use of the diffusive length/time scales, energy transport systems consisting of two parabolic equations with the position density and the energy density as unknowns are derived on a formal level. The H theorem for the kinetic model is presented, and the entropy for the energy transport systems, which is inherited from the kinetic model, is derived. The energy transport systems for specific examples of the global Gibbs state, such as a power law with negative exponent, a cut-off power law with positive exponent, the Maxwellian, Bose-Einstein, and Fermi-Dirac distributions, arepresented.

Original languageEnglish (US)
Pages (from-to)287-312
Number of pages26
JournalJournal of Statistical Physics
Issue number2
StatePublished - Apr 2007
Externally publishedYes


  • Diffusive limit
  • Energy transport
  • Entropy
  • Gibbs state
  • Kinetic equation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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