Russian Physics Journal

, Volume 50, Issue 8, pp 839–844 | Cite as

Spontaneous violation of symmetry of the classical Liouville equation

  • V. V. Lasukov


An exact solution to the classical Liouville equation is derived. It is found that it can have a partial solution with a broken symmetry with respect to time. Thus, in the general case, it does not follow from the invariance of the fundamental Liouville law concerning time reversal that the past and future play similar roles.


Phase Trajectory Liouville Equation Spontaneous Violation Probabilistic Determinism Lagrangian Factor 
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.
    N. N. Bogolyubov and D. V. Shirkov, Quantum Fields [in Russian], Nauka, Moscow, 1980.MATHGoogle Scholar
  2. 2.
    D. N. Zubarev, V. G. Morozov, and G. Renke, Statistical Mechanics of Nonequilibrium Processes, Vol. 1 [in Russian], Fizmatlit, Moscow, 2002.Google Scholar
  3. 3.
    I. Prigogine, Nonequilibrium Statistical Mechanics, Interscience, New York, 1962.Google Scholar
  4. 4.
    D. Kondepudi and I. Prigogine, Modern Thermodynamics, John Wiley and Sons, Chichester, 1998.MATHGoogle Scholar
  5. 5.
    V. V. Lasukov, Russ. Phys. J., No. 3, 224 (2005).Google Scholar
  6. 6.
    A. A. Sokolov, I. M. Ternov, V. Ch. Zhukovskii, and A. B. Borisov, Gauge Fields [in Russian], Mosc. Gos. Univ., Moscow, 1986.Google Scholar
  7. 7.
    A. D. Linde, Elementary Particle Physics and Inflationary Cosmology [in Russian], Nauka, Moscow, 1990.Google Scholar
  8. 8.
    A. A. Logunov, A Theory of Gravitational Field [in Russian], Nauka, Moscow, 2001.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Tomsk Polytechnical UniversityRussia

Personalised recommendations