Theoretical and Mathematical Physics

, Volume 134, Issue 3, pp 339–350 | Cite as

Weak Convergence of Solutions of the Liouville Equation for Nonlinear Hamiltonian Systems

  • V. V. Kozlov
  • D. V. Treshchev


We suggest sufficient conditions for the existence of weak limits of solutions of the Liouville equation as time increases indefinitely. The presence of the weak limit of the probability distribution density leads to a new interpretation of the second law of thermodynamics for entropy increase.

Hamiltonian system Liouville equation weak convergence entropy 


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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • V. V. Kozlov
    • 1
  • D. V. Treshchev
    • 1
  1. 1.Moscow State UniversityMoscowRussia

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