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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2011, Issue 1(22), Pages 124–133
DOI: https://doi.org/10.14498/vsgtu897 (Mi vsgtu897) 		 
This article is cited in 9 scientific papers (total in 9 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
Full-text PDF (553 kB) Citations (9)
(published under the terms of the Creative Commons Attribution 4.0 International License)
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DOI: https://doi.org/10.14498/vsgtu897
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.
Original article submitted 21/XII/2010
revision submitted – 15/III/2011
English version:
P-Adic Numbers, Ultrametric Analysis, and Applications, 2011, Volume 3, Issue 3, Pages 205–211
DOI: https://doi.org/10.1134/S2070046611030046
Bibliographic databases:
Document Type: Article
UDC: 517.958
MSC: 82C05
Language: Russian
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{https://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}
Linking options:
  • https://www.mathnet.ru/eng/vsgtu897
  • https://www.mathnet.ru/eng/vsgtu/v122/p124
    • This publication is cited in the following 9 articles:
    1. Anatolij K. Prykarpatski, “Quantum Current Algebra in Action: Linearization, Integrability of Classical and Factorization of Quantum Nonlinear Dynamical Systems”, Universe, 8:5 (2022), 288  crossref
    2. Ivankiv L.I., Prykarpatsky Ya.A., Samoilenko V.H., Prykarpatski A.K., “Quantum Current Algebra Symmetry and Description of Boltzmann Type Kinetic Equations in Statistical Physics”, Symmetry-Basel, 13:8 (2021), 1452  crossref  isi  scopus
    3. Prykarpatsky Yarema A, Kycia Radoslaw, Prykarpatski Anatolij K, “On the Bogolubov's chain of kinetic equations, the invariant subspaces and the corresponding Dirac type reduction”, Ann Math Phys, 2021, 074  crossref
    4. A. I. Mikhailov, “O granitsakh reduktsii”, Vestnik Moskovskogo universiteta. Seriya 7: Filosofiya, 2017, no. 5, 61–76  elib
    5. A. S. Trushechkin, “Microscopic solutions of kinetic equations and the irreversibility problem”, Proc. Steklov Inst. Math., 285 (2014), 251–274  mathnet  crossref  crossref  isi  elib  elib
    6. A. S. Trushechkin, “Microscopic and soliton-like solutions of the Boltzmann–Enskog and generalized Enskog equations for elastic and inelastic hard spheres”, Kinet. Relat. Models, 7:4 (2014), 755–778  mathnet  crossref  isi  scopus
    7. 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
    8. 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
    9. A. S. Trushechkin, “Derivation of the particle dynamics from kinetic equations”, P-Adic Numbers Ultrametric Anal. Appl., 4:2 (2012), 130–142  mathnet  crossref  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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    		Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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