Theoretical and Mathematical Physics

, Volume 151, Issue 1, pp 539–555 | Cite as

Fine-grained and coarse-grained entropy in problems of statistical mechanics

  • V. V. Kozlov
  • D. V. Treshchev


We consider dynamical systems with a phase space Γ that preserve a measure μ. A partition of Γ into parts of finite μ-measure generates the coarse-grained entropy, a functional that is defined on the space of probability measures on Γ and generalizes the usual (ordinary or fine-grained) Gibbs entropy. We study the approximation properties of the coarse-grained entropy under refinement of the partition and also the properties of the coarse-grained entropy as a function of time.


invariant measure Gibbs entropy coarse-grained entropy 


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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • V. V. Kozlov
    • 1
  • D. V. Treshchev
    • 2
  1. 1.Steklov Mathematical InstituteRASMoscowRussia
  2. 2.Moscow State UniversityMoscowRussia

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