Methodological notes

Irreversibility and the probabilistic treatment of the dynamics of classical particles

L.D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Chernogolovka, Moscow Region, Russian Federation

It is shown that B B Kadomtsev’s idea of small ’external noise’ securing a time-irreversible evolution reduces the justification of statistical physics to a fundamentally new formulation which requires that the dynamics of a multiparticle system be treated by neglecting small acceleration particles. It turns out that this formulation not only leads naturally to irreversible evolution but also suggests a new way of constructing kinetic equations capable of correctly accounting for fluctuations. At the early, small-time, stage of evolution, the original correlations are forgotten and ’post-collisional’ ones form. It is the final portion of the first stage and the formation of the ’post-collisional’ correlations which can be described by a closed form kinetic equation. A relation between Kadomtsev’s external noise idea and Bogolyubov’s derivation of kinetic equations is established, leading to a new physical interpretation of the ’molecular chaos’ hypothesis.

Fulltext is available at IOP
PACS: 03.65.−w, 03.65.Bz, 05.40.−a, 05.45.−a (all)
DOI: 10.1070/PU1999v042n06ABEH000479
Citation: Gordienko S N "Irreversibility and the probabilistic treatment of the dynamics of classical particles" Phys. Usp. 42 573–590 (1999)
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Оригинал: Гордиенко С Н «Необратимость и вероятностное описание динамики классических частиц.» УФН 169 653–672 (1999); DOI: 10.3367/UFNr.0169.199906e.0653

References (15) ↓ Cited by (4) Similar articles (20)

  1. Kadomtsev B B Dinamika i Informatsiya (Dynamics and Information, Moscow: Red. UFN, 1997, 1999)
  2. Krylov N S Raboty po Obosnovaniyu Statisticheskoî Fiziki (Papers on Statistical Physics Foundation, Moscow: Izd. AN USSR, 1950)
  3. Mayorov S A, Tkachev A N, Yakovlenko S I Usp. Fiz. Nauk 164 297 (1994) [Phys. Usp. 37 279 (1994)]
  4. Bogolyubov N N Problemy Dinamicheskoî Teorii v Statisticheskoî Fizike (Problems of Dynamical Theory in Statistical Physics, Moscow: Gostekhizdat, 1946)
  5. Gordienko S N Zh. Eksp. Teor. Fiz. 106 436 (1994) [Sov. Phys. JETP 79 267 (1994)]
  6. Gordienko S N Fizika Plazmy 23 754 (1997)
  7. Bogolyubov N N Izbrannye Trudy Tom 3 (Selected Works) Vol. 3 (Kiev: Naukova Dumka, 1973)
  8. Shelest A V Metod Bogolyubova v Dinamicheskoî Teorii Kineticheskikh Uravneniî (Bogolyubov’s Method in Dynamical Theory of Kinetic Equations, Moscow: Nauka, 1990)
  9. Sandri G Ann. Phys. (N.Y.) 24 332 (1963)
  10. Leontovich M A Zh. Eksp. Teor. Fiz. 5 211 (1935)
  11. Kadomtsev B B Zh. Eksp. Teor. Fiz. 32 943 (1957) [Sov. Phys. JETP 5 675 (1957)]
  12. Kadomtsev B B Zh. Eksp. Teor. Fiz. 33 151 (1957) [Sov. Phys. JETP 6 531 (1958)]
  13. Klimontovich Yu L Turbulentnoe Dvizhenie i Struktura Khaosa (Turbulent Motion and the Structure of Chaos, Moscow: Nauka, 1990) [Translated into English (Dordrecht: Kluwer Acad. Publ., 1991)]
  14. Arnol’d V I Matematicheskie Metody Klassicheskoî Mekhaniki (Mathematical Methods of Classical Mechanics, Moscow: Nauka, 1979) [Translated into English (New York: Springer-Verlag, 1978)]
  15. Kac M Probability and Related Topics in Physical Science

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