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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 151, Number 1, Pages 120–137
DOI: https://doi.org/10.4213/tmf6015 (Mi tmf6015) 		 
This article is cited in 22 scientific papers (total in 22 papers)

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

V. V. Kozlova, D. V. Treschevba

a Steklov Mathematical Institute, Russian Academy of Sciences
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (475 kB) Citations (22)
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DOI: https://doi.org/10.4213/tmf6015
Abstract: We consider dynamical systems with a phase space $\Gamma$ that preserve a measure $\mu$. A partition of $\Gamma$ into parts of finite $\mu$-measure generates the coarse-grained entropy, a functional that is defined on the space of probability measures on $\Gamma$ 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.
Keywords: invariant measure, Gibbs entropy, coarse-grained entropy.
Received: 24.07.2006
English version:
Theoretical and Mathematical Physics, 2007, Volume 151, Issue 1, Pages 539–555
DOI: https://doi.org/10.1007/s11232-007-0040-1
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. V. Kozlov, D. V. Treschev, “Fine-grained and coarse-grained entropy in problems of statistical mechanics”, TMF, 151:1 (2007), 120–137; Theoret. and Math. Phys., 151:1 (2007), 539–555
Citation in format AMSBIB
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    • This publication is cited in the following 22 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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