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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2011, Issue 1(22), Pages 124–133 (Mi vsgtu897)  

This article is cited in 4 scientific papers (total in 4 papers)

Procedings of the 2nd International Conference "Mathematical Physics and its Applications"
Mathematical Physics

The functional mechanics: Evolution of the moments of distribution function and the Poincaré recurrence theorem

A. I. Mikhailov

Lab. of Bioresource Systems Snalysis, Russian Federal Research Institute of Fisheries and Oceanography, Moscow

Abstract: One of modern approaches to a problem of the coordination of classical mechanics and the statistical physics — the functional mechanics is considered. Deviations from classical trajectories are calculated and evolution of the moments of distribution function is constructed. The relation between the received results and absence of paradox of Poincaré–Zermelo in the functional mechanics is discussed. Destruction of periodicity of movement in the functional mechanics is shown and decrement of attenuation for classical invariants of movement on a trajectory of functional mechanical averages is calculated.

Keywords: classical mechanics, irreversibility problem, Liouville equation

DOI: https://doi.org/10.14498/vsgtu897

Full text: PDF file (553 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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English version:
P-Adic Numbers, Ultrametric Analysis, and Applications, 2011, 3:3, 205–211

Bibliographic databases:

ArXiv: 1305.4057
Document Type: Article
UDC: 517.958
MSC: 82C05
Original article submitted 21/XII/2010
revision submitted – 15/III/2011

Citation: A. I. Mikhailov, “The functional mechanics: Evolution of the moments of distribution function and the Poincaré recurrence theorem”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(22) (2011), 124–133; P-Adic Numbers, Ultrametric Analysis, and Applications, 3:3 (2011), 205–211

Citation in format AMSBIB
\Bibitem{Mik11}
\by A.~I.~Mikhailov
\paper The functional mechanics: Evolution of the moments of distribution function and the Poincar\'e recurrence theorem
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2011
\vol 1(22)
\pages 124--133
\mathnet{http://mi.mathnet.ru/vsgtu897}
\crossref{https://doi.org/10.14498/vsgtu897}
\elib{http://elibrary.ru/item.asp?id=16387168}
\transl
\jour P-Adic Numbers, Ultrametric Analysis, and Applications
\yr 2011
\vol 3
\issue 3
\pages 205--211
\crossref{https://doi.org/10.1134/S2070046611030046}


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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. A. I. Mikhailov, “Infinitnoe dvizhenie v klassicheskoi funktsionalnoi mekhanike”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(30) (2013), 222–232  mathnet  crossref
    2. A. S. Trushechkin, “O strogom opredelenii mikroskopicheskikh reshenii uravneniya Boltsmana–Enskoga”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(30) (2013), 270–278  mathnet  crossref
    3. A. S. Trushechkin, “Microscopic solutions of kinetic equations and the irreversibility problem”, Proc. Steklov Inst. Math., 285 (2014), 251–274  mathnet  crossref  crossref  isi
    4. A. I. Mikhailov, “O granitsakh reduktsii”, Vestnik Moskovskogo universiteta. Seriya 7: Filosofiya, 2017, no. 5, 61–76  elib
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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