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

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Abstract

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.

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Authors and Affiliations

  1. Steklov Mathematical Institute, RAS, Moscow, Russia

    V. V. Kozlov

  2. Moscow State University, Moscow, Russia

    D. V. Treshchev

Authors
  1. V. V. Kozlov
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  2. D. V. Treshchev
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 1, pp. 120–137, April, 2007.

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Kozlov, V.V., Treshchev, D.V. Fine-grained and coarse-grained entropy in problems of statistical mechanics. Theor Math Phys 151, 539–555 (2007). https://doi.org/10.1007/s11232-007-0040-1

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  • DOI: https://doi.org/10.1007/s11232-007-0040-1

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