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TMF, 2007, Volume 151, Number 1, Pages 120–137 (Mi tmf6015)  

This article is cited in 12 scientific papers (total in 12 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

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

DOI: https://doi.org/10.4213/tmf6015

Full text: PDF file (475 kB)
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English version:
Theoretical and Mathematical Physics, 2007, 151:1, 539–555

Bibliographic databases:

Received: 24.07.2006

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

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Kozlov, “The generalized Vlasov kinetic equation”, Russian Math. Surveys, 63:4 (2008), 691–726  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Piftankin G., Treschev D., “Gibbs entropy and dynamics”, Chaos, 18:2 (2008), 023116, 11 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. V. I. Bogachev, A. A. Lipchyus, “Approximation of nonlinear integral functionals”, Dokl. Math., 80:2 (2009), 749–754  mathnet  crossref  mathscinet  mathscinet  zmath  isi  elib  elib  scopus
    4. A. S. Trushechkin, “Irreversibility and the role of an instrument in the functional formulation of classical mechanics”, Theoret. and Math. Phys., 164:3 (2010), 1198–1201  mathnet  crossref  crossref  adsnasa  isi
    5. Piftankin G., Treschev D., “Coarse-grained Entropy in Dynamical Systems”, Regular & Chaotic Dynamics, 15:4–5 (2010), 575–597  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. V. V. Kozlov, “Statisticheskaya neobratimost v obratimoi krugovoi modeli Katsa”, Nelineinaya dinam., 7:1 (2011), 101–117  mathnet  elib
    7. Kozlov V.V., “Statistical Irreversibility of the Kac Reversible Circular Model”, Regular & Chaotic Dynamics, 16:5 (2011), 536–549  crossref  mathscinet  zmath  adsnasa  isi  scopus
    8. I. V. Volovich, A. S. Trushechkin, “Asymptotic properties of quantum dynamics in bounded domains at various time scales”, Izv. Math., 76:1 (2012), 39–78  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    9. Yano K., “Entropy of Random Chaotic Interval Map With Noise Which Causes Coarse-Graining”, J. Math. Anal. Appl., 414:1 (2014), 250–258  crossref  mathscinet  zmath  isi
    10. V. I. Bogachev, “Non-uniform Kozlov–Treschev averagings in the ergodic theorem”, Russian Math. Surveys, 75:3 (2020), 393–425  mathnet  crossref  crossref  mathscinet  isi  elib
    11. V. I. Bogachev, “Approximations of Nonlinear Integral Functionals of Entropy Type”, Proc. Steklov Inst. Math., 310 (2020), 1–11  mathnet  crossref  crossref  mathscinet  isi  elib
    12. Safranek D., Aguirre A., Deutsch J.M., “Classical Dynamical Coarse-Grained Entropy and Comparison With the Quantum Version”, Phys. Rev. E, 102:3 (2020), 032106  crossref  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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