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TMF, 2010, Volume 164, Number 3, Pages 354–362 (Mi tmf6544)  

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

Bogoliubov equations and functional mechanics

I. V. Volovich

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The functional classical mechanics based on the probability approach, where a particle is described not by a trajectory in the phase space but by a probability distribution, was recently proposed for solving the irreversibility problem, i.e., the problem of matching the time reversibility of microscopic dynamics equations and the irreversibility of macrosystem dynamics. In the framework of functional mechanics, we derive Bogoliubov–Boltzmann-type equations for finitely many particles. We show that a closed equation for a one-particle distribution function can be rigorously derived in functional mechanics without any additional assumptions required in the Bogoliubov method. We consider the possibility of using diffusion processes and the Fokker–Planck–Kolmogorov equation to describe isolated particles.

Keywords: Boltzmann equation, Bogoliubov equation, kinetic theory

DOI: https://doi.org/10.4213/tmf6544

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English version:
Theoretical and Mathematical Physics, 2010, 164:3, 1128–1135

Bibliographic databases:

Citation: I. V. Volovich, “Bogoliubov equations and functional mechanics”, TMF, 164:3 (2010), 354–362; Theoret. and Math. Phys., 164:3 (2010), 1128–1135

Citation in format AMSBIB
\by I.~V.~Volovich
\paper Bogoliubov equations and functional mechanics
\jour TMF
\yr 2010
\vol 164
\issue 3
\pages 354--362
\jour Theoret. and Math. Phys.
\yr 2010
\vol 164
\issue 3
\pages 1128--1135

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  • http://mi.mathnet.ru/eng/tmf/v164/i3/p354

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    This publication is cited in the following articles:
    1. A. S. Trushechkin, “Uravnenie Boltsmana i $H$-teorema v funktsionalnoi formulirovke klassicheskoi mekhaniki”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(22) (2011), 158–164  mathnet  crossref
    2. E. V. Piskovskii, “O klassicheskom i funktsionalnom podkhodakh k mekhanike”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(22) (2011), 134–139  mathnet  crossref
    3. 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
    4. I. Ya. Aref'eva, I. V. Volovich, E. V. Piskovskiy, “Rolling in the Higgs model and elliptic functions”, Theoret. and Math. Phys., 172:1 (2012), 1001–1016  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    5. I. Ya. Aref'eva, I. V. Volovich, “Asymptotic expansion of solutions in a rolling problem”, Proc. Steklov Inst. Math., 277 (2012), 1–15  mathnet  crossref  mathscinet  isi  elib  elib
    6. I. Ya. Aref'eva, I. V. Volovich, “Holographic thermalization”, Theoret. and Math. Phys., 174:2 (2013), 186–196  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    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, “Microscopic solutions of kinetic equations and the irreversibility problem”, Proc. Steklov Inst. Math., 285 (2014), 251–274  mathnet  crossref  crossref  isi  elib  elib
    10. Trushechkin A., “Microscopic and Soliton-Like Solutions of the Boltzmann Enskog and Generalized Enskog Equations For Elastic and Inelastic Hard Spheres”, Kinet. Relat. Mod., 7:4 (2014), 755–778  crossref  mathscinet  zmath  isi  scopus
    11. Dragovich B. Khrennikov A.Yu. Kozyrev S.V. Volovich I.V. Zelenov E.I., “P-Adic Mathematical Physics: the First 30 Years”, P-Adic Numbers Ultrametric Anal. Appl., 9:2 (2017), 87–121  crossref  mathscinet  zmath  isi  scopus
    12. V. V. Zharinov, “Binary relations, Bäcklund transformations, and wave packet propagation”, Theoret. and Math. Phys., 205:1 (2020), 1245–1263  mathnet  crossref  crossref  mathscinet  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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