From Hamiltonian Mechanics to Continuous Media. Dissipative Structures. Criteria of Self-Organization

  • Yu. L. Klimontovich
Part of the Springer Series in Synergetics book series (SSSYN, volume 66)


This paper presents some main ideas and the results of modern statistical theory in regard to macroscopic open systems.


Entropy Production Knudsen Number Dynamic Instability Flicker Noise Spatial Diffusion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [K1]
    Klimontovich, Yu.L.: On Nonequilibrium Fluctuations in a Gas. TMF 8 1971, 109Google Scholar
  2. [K2]
    Klimontovich, Yu.L.: Kinetic Theory of Non Ideal Gases and Non Ideal Plasmas. Nauka, Moscow, 1975; Pergamon Press, Oxford, 1982Google Scholar
  3. [K3]
    Klimontovich, Yu.L.: The Kinetic Theory of Electromagnetic Processes. Nauka, Moscow, 1980; Springer, Berlin, Heidelberg, 1983Google Scholar
  4. [K4]
    Klimontovich, Yu.L.: Statistical Physics. Nauka, Moscow, 1982; Harwood Aca-demic Publishers, New York, 1986Google Scholar
  5. [K5]
    Klimontovich, Yu.L.: Turbulent Motion and the Structure of Chaos. Nauka, Moscow, 1990; Kluwer Acad. Pub., Dordrecht, 1991MATHCrossRefGoogle Scholar
  6. [K6]
    Klimontovich, Yu.L.: Statistical Theory of Open Systems. Kluwer Academic Publishers, Dordrecht, 1994Google Scholar
  7. [MY]
    Monin, A.S., Yaglom, A.M.: Statistical Fluid Mechanics. Nauka, Moscow, 1965; MIT, 1971Google Scholar
  8. [LL]
    Landau, L.D., Lifshitz, E.M.: Fluid Mechanics. Nauka, Moscow, 1986; Perga- mon Press, Oxford, 1959Google Scholar
  9. [K7]
    Klimontovich, Yu.L.: Statistical Theory for Non Equilibrium Processes in a Plasma. Nauka, Moscow, 1964; Pergamon Press, Oxford, 1967Google Scholar
  10. [Kr]
    Krylov, N.S.: Works for the Foundation of Statistical Physics. Moscow, Nauka, 1950Google Scholar
  11. [Pr]
    Prigogine, I.: From Being to Becoming. Freeman, San Francisco, 1980; Nauka, Moscow, 1985Google Scholar
  12. [PrS]
    Prigogine, I., Stengers, I.: Order out of Chaos. Heinemann, London, 1984; Progress, Moscow, 1986Google Scholar
  13. [RSC]
    Romanovski, Yu.M., Stepanova, N.V., Chernavsky, D.S.: Mathematical Biology. Nauka, Moscow, 1984Google Scholar
  14. [K8]
    Klimontovich, Yu.L.: Entropy Evolution in Self-Organization Processes. H- Theorem and S-Theorem. Physica A 1421987, 390MathSciNetADSCrossRefGoogle Scholar
  15. [Lor]
    Lorenz, E.: Deterministic Nonperiodic Flow. J. Atm. Sci. 201963, 167Google Scholar
  16. [H1]
    Haken, H.: Synergetics. Springer, Berlin, Heidelberg, 1978; Mir, Moscow, 1980MATHGoogle Scholar
  17. [Ani]
    Anishchenko, V.S.: Complex Oscillations in Complex Systems. Nauka, Moscow, 1990MATHGoogle Scholar
  18. [NeL]
    Neimark, Yu.I., Landa, P.S.: Stochastic and Chaotic Oscillations. Nauka, Moscow, 1987; Kluwer Acad. Publ., Dordrecht, 1992Google Scholar
  19. [LiP]
    Lifshitz, E.M., Pitaevsky, L.P.: Statistical Physics. Nauka, Moscow, 1978Google Scholar
  20. [NiP]
    Nicolis, G., Prigogine, I.: Self Organization in Non Equilibrium Systems. Wiley, New York, 1977; Mir, Moscow, 1979Google Scholar
  21. [H2]
    Haken, H.: Advanced Synergetics. Springer, Berlin, Heidelberg, 1983; Mir, Moscow, 1985Google Scholar
  22. [Mic]
    Michailov, A.S.: Foundations of Synergetics I. Springer, Berlin, Heidelberg, 1990Google Scholar
  23. [MiL]
    Michailov, A.S., Loskutov, A.Yu.: Foundations of Synergetics II. Springer, Berlin, Heidelberg, 1991Google Scholar
  24. [Mur]
    Murray, G.: Lectures on Nonlinear Differential Equations Models in Biology. Clarendon Press, Oxford, 1977Google Scholar
  25. [VRY]
    Vasiliev, V.A., Romanovsky, Yu.M., Yachno, V.G.: Autuwaves. Nauka, Moscow, 1987Google Scholar
  26. [K9]
    Klimontovich, Yu.L.: Some Problems of the Statistical Description of Hydro- dynamic Motion and Autowaves Processes. Physica A 1791991, 471ADSCrossRefGoogle Scholar
  27. [K10]
    Klimontovich, Yu.L.: On the Necessity and the Possibility of the Unified De-scription of Kinetic and Hydrodynamic Processes. TMF 921992, 312MathSciNetMATHGoogle Scholar
  28. [K11]
    Klimontovich, Yu.L.: The Unified Description of Kinetic and Hydrodynamic Processes in Gases and Plasmas. Phys. Let. A 1701992, 434ADSCrossRefGoogle Scholar
  29. [VK]
    Van Kampen, N.G.: Stochastic Processes in Physics and Chemistry. North- Holland, Amsterdam, 1983Google Scholar
  30. [Ris]
    Risken, H.: The Fokker-Planck Equation. Springer, Berlin, 1984MATHGoogle Scholar
  31. [Gar]
    Gardiner, C.W.: Handbook of Stochastic Methods for Physics, Chemistry, and Natural Sciences. Springer, Berlin, Heidelberg, 1984Google Scholar
  32. [GGK]
    Gantsevich, S.V., Gurevich, V.L., Katilus, R.: Theory of Fluctuations in NonEquilibrium Electron Gas. Rivista del Nuovo Cimento 21979, 1ADSCrossRefGoogle Scholar
  33. [KoS]
    Kogan, Sh.M., Shul’man, A.Ya.: To the Theory of Fluctuations in a Nonequilibrium Gas. ZhETF 561969, 862Google Scholar
  34. [Kei]
    Keizer, J.: Statistical Thermodynamics of Nonequilibrium Processes. Springer,Berlin, Heidelberg, New York, 1987CrossRefGoogle Scholar
  35. [K12]
    Klimontovich, Yu.L.: Natural Flicker Noise. Pis’ma v ZhTF 91983, 406Google Scholar
  36. [K13]
    Klimontovich, Yu.L., Boon, J.P.: Natural Flicker Noise (1/f-noise) in Music. Europhys. Lett. 3 41987, 395ADSCrossRefGoogle Scholar
  37. [K14]
    Klimontovich, Yu.L.: Natural Flicker Noise (1/f-noise) and Superconductivity. Pis’ma v ZhETF 51 11990, 43Google Scholar
  38. [Kog]
    Kogan, Sh.M.: The Low Frequency Current Noise with Spectrum 1/f in Solid State, Usp. Fiz. Nauk, 1451985, 285; Sov. Phys. Usp. 281985, 171Google Scholar
  39. [VoC]
    Voos, R.F., Clarke, J.: “1/f Noise” in Music: Music from 1/f Noise. J. Acoust. Soc. Am. 643 1 1978, 258Google Scholar
  40. [K15]
    Klimontovich, Yu.L.: Entropy Decrease in the Processes of Self-Organization. S-Theorem. Pis’ma v ZhTF 91983, 1089Google Scholar
  41. [K16]
    Klimontovich, Yu.L.: S-Theorem. Z. Phys. B. 661987, 125MathSciNetADSCrossRefGoogle Scholar
  42. [K17]
    Klimontovich, Yu.L.: Problems in the Statistical Theorie of Open Systems: Criteria for Relative Degree of Order of States in Self-Organization Processes. Usp. Fiz., Nauk 158, May 1989, 59; Sov. Phys. Usp. 32 5 May 1989MathSciNetGoogle Scholar
  43. [EbK]
    Ebeling, W., Klimontovich, Yu.L.: Selforganization and Turbulence in Liquids. Teubner, Leipzig 1984Google Scholar
  44. [H3]
    Haken, H.: Synergetic Computers and Cognition. A Top-Down Approach to Neural Nets. Springer-Verlag, Berlin, Heidelberg, 1991MATHGoogle Scholar
  45. [FuH]
    Fuchs, A., Haken H.: In Neural and Synergetic Computers. Ed. H. Haken, Springer-Verlag, Berlin, 1988, 16Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Yu. L. Klimontovich
    • 1
  1. 1.Department of PhysicsMoscow State UniversityMoscowRussia

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