Some Probabilistic Aspects of the Boltzmann-Equation

  • Mark Kac
Part of the Acta Physica Austriaca book series (FEWBODY, volume 10/1973)


Discussion of the probabilistic nature of the Boltzmann equation centered around the Master Equation approach. Some purely mathematical implications as well as some recent work on adding fluctuating terms to the Boltzmann equation will also be reviewed briefly.


Boltzmann Equation Master Equation Irreversible Thermodynamic Linearize Boltzmann Equation Probabilistic Aspect 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    H.P. McKean, Jr., An Exponential Formula for Solving Boltzmann’s Equation for a Maxwellian Gas, J. of Comb. Theory, 2 (1967) pp. 358–382CrossRefMATHMathSciNetGoogle Scholar
  2. [2]
    H.P. McKean, Jr., Propagation of Chaos for a Class of Non-linear Parabolic Equations, in Lecture Series in Differential Equations, Vol. II, Ed. A.K. Aziz, Van Nostrand Reinhold Co., 1969.Google Scholar
  3. [3]
    L.D. Landau and E.M. Lifshitz, Fluid Mechanics, Perga-mon Press, 1959. See especially Chapter XVII.Google Scholar
  4. [4]
    R.F. Fox, Contributions to the Theory of Non-Equilibrium Thermodynamics, Thesis, Rockefeller University, 1969.Google Scholar
  5. [5]
    R.F. Fox and G.E. Uhlenbeck, Contributions to the Theory of Non-Equilibrium Thermodynamics I and II, Physics of Fluids, 13 (1970) pp.1893–1902 and 2881–2890.CrossRefMATHADSMathSciNetGoogle Scholar
  6. [6]
    M. Kac, Foundations of Kinetic Theory, Proc. Third Berkeley Symp. on Math. Stat. and Prob., Vol. III (1956) pp. 171–197.ADSGoogle Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • Mark Kac
    • 1
  1. 1.The Rockefeller UniversityNew YorkUSA

Personalised recommendations