Microscopic Time Reversibility and the Boltzmann Equation

  • Herbert Spohn
Part of the Lecture Notes in Physics book series (LNP, volume 574)


O.E. Lanford proves that in the Boltzmann-Grad limit the dynamics of hard spheres is governed by the Boltzmann equation (with a technical restriction on the time span). This result allows us to explain, with more precision according to usual standards, the emergence of an irreversible macroscopic equation out of the reversible microscopic dynamics.


Boltzmann Equation Black Body Radiation British Broadcasting Corporation Initial Distribution Function Irreversible Evolution 
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.
    O.E. Lanford, Time Evolution of Large Classical Systems. Lecture Notes in Physics Vol. 38, pp. 1–111, ed. J. Moser, (Springer, Berlin, 1975)Google Scholar
  2. 2.
    H. Spohn, Large Scale Dynamics of Interacting Particles, (Springer, Heidelberg 1991)zbMATHGoogle Scholar
  3. 3.
    C. Cercignani, R. Illner, and M. Pulvirenti, The Mathematical Theory of Dilute Gases, (Springer, New York 1994)zbMATHGoogle Scholar
  4. 4.
    R. Penrose, Shadows of the Mind, (Oxford University Press 1994)Google Scholar
  5. 5.
    R. P. Feynman The Character of Physical Law, (British Broadcasting Corporation, London 1965)Google Scholar
  6. 6.
    R. Penrose, The Emperor’s New Mind (Oxford University Press, 1989)Google Scholar
  7. 7.
    C. Cercignani, Ludwig Boltzmann, The Man Who Trusted Atoms, (Oxford University Press 1998)Google Scholar
  8. 8.
    J. L. Lebowitz, Macroscopic laws, microscopic dynamics, time’s arrow and Boltzmann’s entropy. In: Physica A 194, 1 (1993)ADSMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Herbert Spohn
    • 1
  1. 1.Zentrum Mathematik and Physik DepartmentTU MünchenMünchen

Personalised recommendations