Problems in the statistical theory of open systems: Criteria for the relative degree of order in self-organization processes

Soviet Physics - Uspekhi

Volumn 32, Issue 5, 1989, Pages 416-433

  Klimontovich, Yu L ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84956225973     PISSN: 00385670     EISSN: 21695296     Source Type: Journal    
DOI: 10.1070/PU1989v032n05ABEH002717     Document Type: Article

References (85)

1. G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems, Wiley, N. Y., 1977 [Russ, transl. Mir, M., 1979]
2. I. Prigogine, From Being to Becoming, Freeman, San Francisco, 1980 [Russ, transl., Nauka, M., 1985].
3. H. Haken, Introduction to Synergetics, Springer, N.Y., 1977 [Russ, transl., Mir, M., 1980].
4. H. Haken, Advanced Synergetics, Springer, N. Y., 1983 [Russ, transl., Mir, M. 1985]
5. E. Lorenz, J. Atmos. Sei., 20, 130 (1963).
6. Ya. G. Sinai, Nonlinear Waves [in Russian], edited by A. V. Gaponov-Grekhov, Nauka, M., 1979.
7. V. I. Arnold, Usp. Fiz. Nauk 141, 569 (1983) [Sov. Phys.-Usp. 26, 1025 (1983)].
8. Ya. G. Sinai and L. P. Shil’nikova (eds.), Strange Attractors [Russ, transl., Mir, M., 1984].
9. G. M. Zaslavskii, Chaos in Dynamic Systems, Harwood, Chur, 1984 [Russ, original, Nauka, M., 1984]
10. A. S. Monin, Usp. Fiz. Nauk 150, 61 (1986) [Sov. Phys.-Usp. 29, 843 (1986)].
11. A. V. Holden (ed.), Chaos, Princeton Univ. Press, 1986.
12. H. G. Schuster, Deterministic Chaos, VCH Publ., 1987 [Russ, transl., Nauka, M., 1988].
13. J. Eckmann and D. Ruelle, Rev. Mod. Phys. 57, 617 (1985).
14. R. May, Nature, 261, 459 (1976).
15. J. Gleick, Chaos, Heinemann, London, 1988.
16. M. J. Feigenbaum, Los Alamos Science 1, No. 14 (1980) [Russ, transl. Usp. Fiz. Nauk 141, 343 (1983)].
17. V. S. Anishchenko, Stochastic Self-Oscillations in Radiophysical Systems [in Russian], Saratov University Press, Saratov, 1, 1985; 2, 1986.
18. A. P. Shapiro and S. P. Lupov, Recurrence Equations in the Theory of Population Biology [in Russian], Nauka, M., 1983.
19. A. D. Bazykin, Mathematical Biophysics of Interacting Populations [in Russian], Nauka, M., 1985.
20. A. N. Sharkovskii, Ukr. Mat. Zh. 16, 71 (1964).
21. A. N. Sharkovskii, Yu. L. Maistrenko, and E. Yu. Romanenko, Difference Equations and Their Applicaitons [in Russian], Naukova Dumka, Kiev, 1986.
22. Yu. I. Neimark and P. S. Landa, Stochastic and Chaotic Oscillations [in Russian], Nauka, M., 1987.
23. S. Grossmann and S. Thomas, Z. Naturforsch. 32, 1353 (1977).
24. A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion, Springer, N. Y., 1983 [Russ, transl., Mir, M„ 1984].
25. L. S. Polak and A. S. Mikhailov, Self-Organization in Nonequilibrium PhysiocochemicalSystems [in Russian], Nauka, M., 1975.
26. B. M. Smirnov, Usp. Fiz. Nauk 149, 177 (1986) [Sov. Phys.-Usp. 29, 481 (1986)].
27. I. M. Sokolov, Usp. Fiz. Nauk 150, 221 (1986) [Sov. Phys.-Usp. 29, 924 (1986)].
28. A. V. Gaponov-Grekhov and M. I. Rabinovich (eds.), Nonlinear Waves; Structures and Bifurcations, Nauka, M., 1987.
29. Ya. B. Zeldovich, S. A. Molchanov, A. A. Ruzmaikin, and D. D. Sokolov, Usp. Fiz. Nauk 152, 3 (1987) [Sov. Phys.-Usp. 30, 353 (1987)].
30. M. Eigen, Self-organization of Matter and the Evolution of Biological Macromolecules, Naturwissenschaften 58, 465 (1971) [Russ, transl., Mir, M„ 1973)].
31. M. V. Volkenshtein, Usp. Fiz. Nauk 143, 429 (1984) [Sov. Phys.-Usp. 27, 515 (1984)].
32. W. Ebeling and R. Feistei, Physik der Selbst-Organization und Evolu-tion, Akademie-Verlag, BerHn, 1982.
33. J. W. Gibbs, Thermodynamics; Statistical Physics in: The Collected Works of J. Willard Gibbs, Yale Univ. Press, New Haven, 1948 [Russ, transl., (Ed) D. N. Zubarev, Nauka, M., 1982].
34. Yu. L. Klimontovich, Statistical Physics, Harwood, N. Y., 1986 [Russ. original, Nauka, M., 1982]
35. M. A. Leontovich, Introduction to Thermodynamics; Statistical Physics, [in Russian], Nauka, M., 1983.
36. R. L. Stratonovich, Nonequilibrium Nonlinear Thermodynamics [in Russian], Nauka, M., 1985.
37. C. W. Gardiner, Handbook of Stochastic Methods for Physicists, Chemists, and the Natural Sciences, Springer, Berlin, 1983 [Russ, transl., Mir, M„ 1986]
38. Yu. L. Klimontovich, Physica, A 142, 390 (1987).
39. Yu. L. Klimontovich, Pis’maZh. Tekh. Fiz. 9, 1412 (1983) [Sov.Tech. Phys. Lett. 9, 606 (1983)].
40. Yu. L. Klimontovich, Pis’maZh. Tekh. Fiz. , 10, 80 (1984) [10, 33 (1984)].
41. W. Ebeling and Yu. L. Klimontovich, Self-Organization and Turbulence in Liquids, Teubner, Leipzig, 1984.
42. Yu. L. Klimontovich, Z. Phys. B66, 125 (1987).
43. Yu. L. Klimontovich, PismaZh. Tekh. Fiz. 14, 631 (1988) [Sov.Tech. Phys. Lett. 14, 281 (1988)].
44. N. S. Krylov, Papers on the Foundations of Statistical Physics [in Russian], Nauka, M., 1950.
45. Yu. L. Klimontovich, Teor. Mat. Fiz. 9, 109 (1971) [Theor. Math. Phys. (USSR) 9, 1013 (1971)].
46. Yu. L. Klimontovich, Usp. Fiz. Nauk 110, 537 (1973) [Sov. Phys. Usp. 16, 512 (1974)].
47. Yu. L. Klimontovich, Kinetic Theory of Nonideal Gases and Nonideal Plasmas, Pergamon Press, Oxford, 1982 [Russ, original, Nauka, M., 1975]
48. O. A. Grechanyi, Statistical Theory of Irreversible Processes in Systems Far from Thermodynamic Equilibrium [in Russian], Naukova Dumka, Kiev, 1988.
49. Yu. L. Klimontovich, Physica A142, 374 (1987).
50. Yu. M. Romanovskii, N. V. Stepanova, and D. S. Chernavskii, Mathematical Biophysics [in Russian], Nauka, M., 1984.
51. R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics, Wiley, N. Y„ 1975 [Russ, transl., Mir, M., 1978].
52. H. Haken, Z. Phys. B61, 329 (1985); Z. Phys., B62, 255 (1985).
53. H. Haken, Information and Self-Organization, Springer, N. Y., 1988.
54. M. I. Rabinovich and D. I. Trubetskov, Introduction to the Theory of Oscillations [in Russian], Nauka, M., 1984.
55. V.V. S. Anishchenko and V. V. Astakhov, Radiotekh. Elektron. 28, 1109 (1983) [Radio. Eng. Electron. Phys. (USSR) 28(6), 59 (1983)].
56. V.V. S. Anishchenko and Yu. L. Klimontovich, PissmaZh. Tekh. Fiz. 10, 816 (1984) [Sov. Tech. Phys. Lett. 10, 342 (1984)].
57. Yu. L. Klimontovich and M. Bonits, PissmaZh. Tekh. Fiz., 12, 1353 (1986) [12, 559 (1986)]; Z. Phys. B70, 241 (1986).
58. I. Prigogine and I. Stengers, Order out of Chaos, Heinemann, London, 1984 [Russ, transl., Progress, M. (1986)].
59. Yu. L. Klimontovich, Pisma Zh. Tekh. Fiz. 11, 1232 (1985) [Sov. Tech. Phys. Lett. 11, 509 (1985)]; Pisma Zh. Tekh. Fiz. , 13, 175 (1987) [13, 72 (1987)].
60. Yu. L. Klimontovich and V. I. Chetverikov, Pisma Zh. Tekh. Fiz., 13, 977 (1987) [13, 407 (1987)].
61. A. N. Kolmogorov, I. G. Petrovskii, and N. S. Piskunov, Byul. MGU Al, 1 (1937).
62. V. A. Vasil’ev, Yu. M. Romanovskii, and V. G. Yakhno, Aulowaue Processes [in Russian], Nauka, M., 1987. fl'V. I. Krinskiiand A. S. Mikhailov, Autowaves [inRussian], Znanie, M., 1984.
63. M. B. S. Kerner and V. V. Osipov, Mikroelektronika, 10, 407 (1981) [Sov. Microelectron. 10 (1981)].
64. Ya. B. Zeldovich, Chemical Physics and Hydrodynamics [in Russian], Nauka, M., 1984.
65. D. A. Frank-Kamenitskii, Diffusion and Heat Transfer in Chemical Kinetics [in Russian], Nauka, M. (1967).
66. A. M. Turing, Proc. R. Soc. London B237, 37 (1952).
67. A. V. Gaponov-Grekhov and M. I. Rabinovich, Izv. Vyssh. Uchebn. Zaved., Radiofiz. 30, 131 (1987) [Radiophys. Quantum Electron. 30(2), 93 (1987)].
68. Yu. L. Klimontovich, in Self-Organization by Non-linear Processes, W. Ebeling and H. Ulbricht (eds.), Springer, N.Y., 1986.
69. W. Frost and T. H. Moulden, Handbook of Turbulence, Plenum, 1977 [Russ, transl., Mir, M., 1980].
70. Yu. L. Klimontovich and H. Engel-Herbert, Zh. Tekh. Fiz. 54, 440 (1984) [Sov. Phys. Tekh. Phys. 29, 263 (1984)].
71. Prigogine, P Introduction to Thermodynamics of Irreversible Processes, Wiley, N.Y., 1962 [Russ, transl. of 1955 ed., IL, M., I960]
72. W. Ebeling and H. Engel-Herbert, Ann. Phys. (Leipzig) 43, 187 (1986).
73. W. Ebelingand H. Engel-Herbert Physica A149, 182 (1988).
74. W. Ebeling, A. Engel, and B. Esser, J. Stat. Phys. 37, 369 (1984).
75. A. A. Samarskii, V. A. Galaktionov, S. P. Kurdyumov, and A. P. Mikhailov, Stressed Regimes in Problems for Quasilinear Parabolic Equations [Nauka, M., 1987]
76. B. B. Kadomtsev, in Proc. Int. Conf. On Plasma Physics [in Russian], Naukova Dumka, Kiev, 1988.
77. N. Lebedev Phys. Inst. Acad. Sei. USSR 171 (1986)].
78. S. A. Akhmanov, M. A. Vorontsov, D. V. Pruidze, and V. I. Shmal gau-zen, Preprint No. 53 [in Russian], Moscow State University, M., 1986.
79. L. Sh. Ukova, Yu. A. Kravtsov, D. S. Mergelyan, and V. S. Etkin, Izv. Vyssh. Uchebn. Zaved., Radiofiz., 28, 929 (1985) [Radiophys. Quantum Electron. 28 (1985)].
80. M. T. Gaponova-Grekhova (ed.), Autowave Processes in Systems with Diffusion, [in Russian], Institute of Applied Physics, Academy of Sciences of the USSR, Gor’kii, 1981.
81. F. V. Bunkin, N. A. Kirichenko, and B. S. Lukyanchuk, Izv. Akad. Nauk SSSR Ser. Fiz. 49, 1054 (1985) [Bull. Acad. Sei.: USSR, Phys. Ser. 49(6), 13 (1985)].
82. H. J. Farmer, E. Ott, and J. Yorke, Physica D7, 153 (1983).
83. P. Grossberger, J. Stat. Phys. 26, 173 (1981).
84. H. P. V. Elyutin, Usp. Fiz. Nauk 155, 397 (1988) [Sov. Phys.-Usp. 31, 597 (1988)].
85. A. Ya. Lerner (ed)Principles of Self-Organization [Russ, transl., Mir, M„ (1966).