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Physics of our days


Fluctuation kinetics of reactions

 a,
a All-Russian Scientific Research Institute of Experimental Physics — Federal Nuclear Centre, prosp. Mira 37, Sarov, Nizhny Novgorod region, 607190, Russian Federation

The fluctuation kinetics of reactions corresponds to a description of the reacting systems at a mesoscopic level. In this approach, a description is written in terms of concentration distributions which are continuous but fluctuating. The basic principles and methods of fluctuation kinetics are illustrated by several specific examples. Particular emphasis is placed on cases in which powerful mechanisms intensify microscopic fluctuations associated with the atomistic nature of the individual reaction events to the point that they determine the outcome of events at macroscopic scales. The situation is analogous to macroscopic quantum effects. In the first main section of the paper, the induction period of a branching chemical reaction is calculated under the assumption of a complete mixing of the reactants and also for the case with spatially inhomogeneous fluctuations. The second section of the paper discusses fluctuations in the course of a two-particle recombination reaction. The third section takes up the spontaneous breaking of chiral symmetry in the course of biological evolution and a possible role of fundamental weak interactions. Appendix I gives the solution of the general problem in which the point of a second-order phase transition in a distributed system is traversed at a finite rate. Appendix II describes mathematical methods of the fluctuation kinetics of reactions.

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Fulltext is also available at DOI: 10.1070/PU1987v030n11ABEH002979
PACS: 87.15.Rn, 82.20.−w (all)
DOI: 10.1070/PU1987v030n11ABEH002979
URL: https://ufn.ru/en/articles/1987/11/d/
Citation: Zel’dovich Ya B, Mikhailov A S "Fluctuation kinetics of reactions" Sov. Phys. Usp. 30 977–992 (1987)
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Оригинал: Зельдович Я Б, Михайлов А С «Флуктуационная кинетика реакций» УФН 153 469–496 (1987); DOI: 10.3367/UFNr.0153.198711d.0469

References (63) ↓ Cited by (44) Similar articles (5)

  1. Polak L S Nonequilibrium Chemical Kinetics And Its Applications (in Russian) (Nauka, Moscow, 1979)
  2. Nicolis G and I Prigogine Self-Organization In Non-Equilibrium Systems (Wiley, New York, 1977); Russ. transl., Nicolis G and I Prigogine Self-Organization In Non-Equilibrium Systems (Mir, M.], 1979)
  3. Haken H Introduction To Synergetics (Springer-Verlag, N. Y., 1977); Russ. transl., Haken H Introduction To Synergetics (Mir, M.], 1980)
  4. Polak L S and A S Mikha&ibreve;lov Self-Organization In Nonequilibrium Physicochemical Systems (in Russian) (Nauka, M., 1983)
  5. Ovchinnikov A A, S F Timashev, and A A Bely&ibreve; Kinetics of Diffusion-Controlled Chemical Processes (in Russian) (Khimiya, M., 1986)
  6. Horsthemke W and R Lefever Noise-Induced Transitions (Springer-Verlag, N. Y., 1983); Russ. transl., Horsthemke W and R Lefever Noise-Induced Transitions (Mir, M.], 1987)
  7. Mikha&ibreve;lov A S and I V Uporov Usp. Fiz. Nauk 144 79 (1984); Mikha&ibreve;lov A S and I V Uporov Sov. Phys. Usp. 27 695 (1984)
  8. Zel’dovich Ya B Dokl. Akad. Nauk SSSR 257 1173 (1981); Zel’dovich Ya B Dokl. Phys. Chem. 257 (1981)
  9. Kolmogrov A N, I E Petrovski&ibreve;, and N S Piskunov Vestn. Mosk. Univ. Ser. 1. Matematika, Mekhanika 1 1 (1937)
  10. Fisher R A Ann. Eugenics 7 355 (1937)
  11. Kolmogorov A N Izv. Akad. Nauk SSSR. Ser. Mat. 1 1 (1937)
  12. Mikha&ibreve;lov A S and IV Uporov Zh.Eksp.Teor. Fiz. 84 1481 (1983); Mikha&ibreve;lov A S and IV Uporov Sov. Phys. JETP 57 863 (1983)
  13. Nicolis G, F Baras, and M Malek-Mansour Non-Equilibrium Dynamics In Chemical Systems eds C Vidal and A Pacault (Springer-Verlag, N. Y., 1984) p. 184
  14. Mikhailov A S and A Engel Phys. Lett. A 117 257 (1986)
  15. Zel’dovich Ya B Elektrokhimiya 13 677 (1977); Zel’dovich Ya B Sov. Electrochem. 13 581 (1977)
  16. Ovchinnikov A A and Ya B Zeldovich Chem. Phys. 28 215 (1978)
  17. Burlatski&ibreve; S F and A A Ovchinnikov Pis’ma Zh. Eksp. Teor. Fiz. 43 494 (1986); Burlatski&ibreve; S F and A A Ovchinnikov JETP Lett. 43 638 (1986)
  18. Zel’dovich Ya B Zh. Tekh. Fiz. 19 1199 (1949)
  19. Sokolov I M Pis’ma Zh. Eksp. Teor. Fiz. 44 53 (1986); Sokolov I M JETP Lett. 44 67 (1986)
  20. Shandrin S F, A G Doroshkevich, and Ya B Zel’dovich Usp. Fiz. Nauk 139 83 (1983); Shandrin S F, A G Doroshkevich, and Ya B Zel’dovich Sov. Phys. Usp. 26 46 (1983)
  21. Bludman S Nuovo Cimento 9 433 (1958)
  22. Zel’dovich Ya B Zh. Eksp. Teor. Fiz. 36 964 (1959); Zel’dovich Ya B Sov. Phys. JETP 9 682 (1959)
  23. Khriplovich I B Parity Nonconservation In Atomic Phenomena (in Russian) (Nauka, Moscow, 1981)
  24. Bucksbaum P, E Commins, and L Hunter Appl. Phys. B328 280 (1982)
  25. Bogdanov Yu V, II Sobel’man, V N Sorokin, and II Struk Pis’ma Zh. Eksp. Teor. Fiz. 31 234 (1980); Bogdanov Yu V, II Sobel’man, V N Sorokin, and II Struk JETP Lett. 31 214 (1980)
  26. Hollister M, G Apperson, L Lewis, et al Phys. Rev. Lett. 46 643 (1981)
  27. Barkov L M and M S Zolotarev Zh. Eksp. Teor. Fiz. 79 713 (1980); Barkov L M and M S Zolotarev Sov. Phys. JETP 52 360 (1980)
  28. Borich G N, Yu V Bogdanov, S I Kanorski&ibreve;, I I Sobel’man, et al Zh. Eksp. Teor. Fiz. 87 776 (1984); Borich G N, Yu V Bogdanov, S I Kanorski&ibreve;, I I Sobel’man, et al Sov. Phys. JETP 60 442 (1984)
  29. Mason S F and G E Tranter Proc. R. Soc. London A397 45 (1985)
  30. Zel’dovich B Ya and D B Saakyan Zh. Eksp. Teor. Fiz. 78 2233 (1980); Zel’dovich B Ya and D B Saakyan Sov. Phys. JETP 51 1118 (1980)
  31. Kizel’ V A Physical Causes Of The Dissymmetry Of Living Systems (in Russian) (Nauka, Moscow, 1985)
  32. Zel’dovich Ya B Zh. Fiz. Khim 11 685 (1938)
  33. Zel’dovich Ya B Zh. Eksp. Teor. Fiz. 67 2357 (1974); Zel’dovich Ya B Sov. Phys. JETP 40 1170 (1974)
  34. Gol’danski&ibreve; V I, V A Avetisov, and V V Kuz’min Dokl. Akad. Nauk SSSR 290 734 (1986); Gol’danski&ibreve; V I, V A Avetisov, and V V Kuz’min Dokl. Biophys. 290 408 (1986)
  35. Morozov L L Origins Life 9 187 (1979)
  36. Keszthelyi L, J Gzege, G Fajszi, J Pesfai, and V I Goldanskii Origins Of Optical Activity In Nature ed D C Waler (Elsevier, N. Y., 1979) p. 229
  37. Morozov L L, V V Kuzmin, and V I Goldanskii Origins Life 13 119 (1983)
  38. Morozov L L and V I Goldanskii Self-Organization ed V I Krinsky (Springer-Verlag, N. Y., 1984) p. 224
  39. Morozov L L and V I Gol’danski&ibreve; Vestin. Akad. Nauk SSSR No. 6, 54 (1984)
  40. Avetisov V A, S A Anikin, V I Gol’dandki&ibreve;, and V V Kuz’min Dokl. Akad. Nauk SSSR 282 184 (1985); Avetisov V A, S A Anikin, V I Gol’dandki&ibreve;, and V V Kuz’min Dokl. Biophys. 282 115 (1985)
  41. Avetisov V A, S A Anikin, V I Gol’danski&ibreve;, and V V Kuz’min Dokl. Akad. Nauk SSSR 283 1485 (1985); Avetisov V A, S A Anikin, V I Gol’danski&ibreve;, and V V Kuz’min Dokl. Biophys. 283 170 (1985)
  42. Gol’danski&ibreve; V I, V V Kuz’min, and L L Morozov Science And Mankind (In Russian) (Znanie, 1986) p. 139
  43. Nicolis G and I Prigogine Proc. Nat. Acad. Sci. USA 78 659 (1981)
  44. Kondepudi D and I Prigogine Physica (Utrecht) A107 1 (1981)
  45. Kondepudi D and G W Nelson Phys. Rev. Lett. 50 1023 (1983)
  46. Moss F, D Kondepudi, and P V F McClintock Phys. Lett. A112 293 (1985)
  47. Kondepudi D and M J Gao Phys. Rev. A35 340 (1987)
  48. Folsome C E Life Origin: And Evolution (W. H. Freeman, San Francisco, 1979); Russ. transl., Folsome C E Life Origin: And Evolution (Mir, M.], 1982)
  49. Oparin A I Genesis And Development Of Life (Academie Press, N. Y., 1986)
  50. Eigen M and P Schuster The Hypercycle:A Principle Of Natural Self-Organization (Springer-Verlag, N. Y., 1979); Russ. transl., Eigen M and P Schuster The Hypercycle:A Principle Of Natural Self-Organization (Mir, M.], 1982)
  51. Dyson F Origins Of Life (Cambridge Univ. Press, Cambridge, 1985)
  52. Zel’dovich Ya B and A S Mikha&ibreve;lov Khim. Fiz. 5 587 (1986); Zel’dovich Ya B and A S Mikha&ibreve;lov Sov. J. Chem. Phys. 5 (1986)
  53. Ma S-K Modern Theory Of Critical Phenomena (Benjamin, Reading, Mass., 1976); Russ. transl., Ma S-K Modern Theory Of Critical Phenomena (Mir, M.], 1980)
  54. Landau L D and E M Lifshitz Statistical Physics (Pergamon Press, Oxford, 1980); Russ. original, Landau L D and E M Lifshitz Statistical Physics (Nauka, M.], 1976)
  55. Zel’dovich Ya B and A A Ovchinnikov Zh. Eksp. Teor. Fiz. 74 1588 (1978); Zel’dovich Ya B and A A Ovchinnikov Sov. Phys. JETP 47 829 (1978)
  56. Doi M J. Phys. A9 1465 (1976)
  57. Mikhailov A S Phys. Lett. A85 214, 427 (1981)
  58. Mikhailov A A, and V V Yashin J. Stat. Phys. 38 347 (1985)
  59. Gutin A M, A S Mikha&ibreve;lov, and V V Yashin Zh. Eksp. Teor. Fiz. 92 941 (1987); Gutin A M, A S Mikha&ibreve;lov, and V V Yashin Sov. Phys. JETP 65 533 (1987)
  60. Stratonovich R L Selected Questions In The Theory Of Fluctuations In Radio Engineering (in Russian) (Sov. Radio, Moscow, 1961)
  61. Zang A J and T R Cech Science 231 470 (1986)
  62. Farmer J D, S A Kauffman, and N H Packard Physica (Utrecht) D22 50 (1986)
  63. Van den Broeck C and P Mandel Phys. Lett. Ser. A122 36 (1987)
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