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Reviews of topical problems


Thermodynamic fluctuations within the Gibbs and Einstein approaches

,
Peoples' Friendship University of Russia, ul. Miklukho-Maklaya, 6, Moscow, 117198, Russian Federation

A comparative analysis of the descriptions of fluctuations in statistical mechanics (the Gibbs approach) and in statistical thermodynamics (the Einstein approach) is given. On this basis solutions are obtained for the Gibbs and Einstein problems that arise in pressure fluctuation calculations for a spatially limited equilibrium (or slightly nonequilibrium) macroscopic system. A modern formulation of the Gibbs approach which allows one to calculate equilibrium pressure fluctuations without making any additional assumptions is presented; to this end the generalized Bogolyubov-Zubarev and Hellmann-Feynman theorems are proved for the classical and quantum descriptions of a macrosystem. A statistical version of the Einstein approach is developed which shows a fundamental difference in pressure fluctuation results obtained within the context of two approaches. Both the ’genetic’ relation between the Gibbs and Einstein approaches and the conceptual distinction between their physical grounds are demonstrated. To illustrate the results, which are valid for any thermodynamic system, an ideal nondegenerate gas of microparticles is considered, both classically and quantum mechanically. Based on the results obtained, the correspondence between the micro- and macroscopic descriptions is considered and the prospects of statistical thermodynamics are discussed.

Fulltext pdf (660 KB)
Fulltext is also available at DOI: 10.1070/PU2000v043n12ABEH000828
PACS: 05.20.Gg, 05.30.Ch, 05.40.−a, 05.70.Ce (all)
DOI: 10.1070/PU2000v043n12ABEH000828
URL: https://ufn.ru/en/articles/2000/12/a/
000167166600001
Citation: Rudoi Yu G, Sukhanov A D "Thermodynamic fluctuations within the Gibbs and Einstein approaches" Phys. Usp. 43 1169–1199 (2000)
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Оригинал: Рудой Ю Г, Суханов А Д «Термодинамические флуктуации в подходах Гиббса и Эйнштейна» УФН 170 1265–1296 (2000); DOI: 10.3367/UFNr.0170.200012a.1265

References (55) ↓ Cited by (25) Similar articles (20)

  1. Laughlin R B Rev. Mod. Phys. 71 863 (1999) [Usp. Fiz. Nauk 170 292 (2000)]; Störmer H L Rev. Mod. Phys. 71 875 (1999) [Usp. Fiz. Nauk 170 304 (2000)]
  2. Gibbs J W Elementary Principles in Statistical Mechanics (New York: C. Scribner’s Sons, 1902) [Translated into Russian (Moscow: Nauka, 1982)]
  3. Einstein A Ann. Phys. Leipzig 33 1275 (1910) [Translated into Russian in Izbrannye Sochineniya Vol. 3 (Moscow: Nauka, 1966) p. 216]
  4. Kittel C Phys. Today 41 (5) 93 (1988)
  5. Mandelbrot B Phys. Today 42 (1) 71 (1989)
  6. Planck M Einführung in die Theoretisch Physik Vol. 5 Einführung in die Theorie der Wärme (Leipzig: Verlag von S. Hirzel, 1930) [Translated into Russian (Moscow-Leningrad: ONTI, 1935) Ch. 5] [Translated into English as Introduction to Theoretical Physics Vol. 5 Theory of Heat (New York: Macmillan, 1949)]
  7. Landau L D, Lifshitz E M Statisticheskaya Fizika Part I (Statistical Physics) 3rd ed. (Moscow: Nauka, 1976) [Translated into English (Oxford: Pergamon Press, 1980)]
  8. Münster A Physica 26 1117 (1960); Nuovo Cimento Suppl. 13 (1960); Statistical Thermodynamics Vol. 1, 2nd ed. (Berlin: Springer-Verlag, 1969)
  9. Bogolyubov N N "Kvazisrednie v zadachakh statisticheskoî mekhaniki" ("Quasi-means in problems of statistical mechanics"), Preprint OIYaID-781 (Dubna: OIYaI, 1961); Izbrannye Trudy (Selected Works) Vol. 3 (Kiev: Naukova Dumka, 1971) [Translated into English (New York: Gordon and Breach, 1990-1991)]
  10. Bogolyubov N N Problemy Dinamicheskoî Teorii v Statisticheskoî Fizike (Dynamical Theory Problems in Statistical Physics, Moscow-Leningrad: Gostekhizdat, 1946); Izbrannye Trudy (Selected Works) Vol. 2 (Kiev: Naukova Dumka, 1970) [Translated into English (New York: Gordon and Breach, 1990-1991)]
  11. Zubarev D N Neravnovesnaya Statisticheskaya Termodinamika (Nonequilibrium Statistical Thermodynamics, Moscow: Nauka, 1971) [Translated into English (New York: Consultants Bureau, 1974)]
  12. Hellmann H G A Kvantovaya Khimiya (Quantum Chemistry, Moscow-Leningrad: GITTL, 1937); a revised and compact edition in German Einführung in die Quantenchemie (Leipzig, Wien: F. Deuticke, 1937)
  13. Feynman R P Phys. Rev. 56 340 (1939); Feynman R P Statistical Mechanics (Reading, Mass.: W. A. Benjamin, 1972) [Translated into Russian (Moscow: Mir, 1975)]
  14. Leontovich M A Statisticheskaya Fizika (Statistical Physics) 2nd ed. (Moscow: Nauka, 1983)
  15. Levich V G Kurs Teoreticheskoî Fiziki (Course in Theoretical Physics) Vol. 1, 2nd ed. (Moscow: Nauka, 1969) [Translated into English: Theoretical Physics Vol. 1, 2 (Amsterdam: North-Holland, 1970)]
  16. Kubo R Statistical Mechanics (Amsterdam: North-Holland, 1965) [Translated into Russian (Moscow: Mir, 1967)]
  17. Ansel’m A I Osnovy Statisticheskoî Fiziki i Termodinamiki (Foundations of Statistical Physics and Thermodynamics, Moscow: Nauka, 1973)
  18. Heer C V Statistical Mechanics, Kinetic Theory, and Stochastic Processes (New York: Academic Press, 1972) [Translated into Russian (Moscow: Mir, 1976)]
  19. Rumer Yu B, Ryvkin M Sh Termodinamika, Statisticheskaya Fizika i Kinetika (Thermodynamics, Statistical Physics and Kinetics) 2nd ed. (Moscow: Nauka, 1977) [Translated into English (Moscow: Mir, 1980)]
  20. Kuni F M Statisticheskaya Fizika i Termodinamika (Statistical Physics and Thermodynamics, Moscow: Nauka, 1981)
  21. Kvasnikov I A Termodinamika i Statisticheskaya Fizika. Teoriya Ravnovesnykh Sistem (Thermodynamics and Statistical Physics. Theory of Equilibrium Systems, Moscow: Izd. MGU, 1991); Teoriya Neravnovesnykh Sistem (Theory of Nonequilibrium Systems, Moscow: Izd. MGU, 1987)
  22. Kondrat’ev A S, Romanov V P Zadachi po Statisticheskoî Fizike (Problems in Statistical Physics, Moscow: Nauka, 1992)
  23. Sommerfeld A Vorlesungen über Theoretische Physik Bd. 5 Thermodynamik und Statistik (Diederich: Wiesbaden, 1952) [Translated into Russian (Moscow: IL, 1955)] [Translated into English as Lectures on Theoretical Physics Vol. 5 Thermodynamics and Statistical Mechanics (New York: Academic Press, 1956)]
  24. Mayer J E, Goeppert-Mayer M Statistical Mechanics 2nd ed. (New York: Wiley, 1977) [Translated into Russian: (Moscow: Mir, 1980)]
  25. Hill T L Statistical Mechanics (New York: McGraw-Hill Book Co., 1956) [Translated into Russian (Moscow: IL, 1960)]
  26. Huang K Statistical Mechanics (New York: John Wiley & Sons, 1963) [Translated into Russian (Moscow: Mir, 1966)]
  27. Isihara A Statistical Physics (New York: Academic Press, 1971) [Translated into Russian (Moscow: Mir, 1973)]
  28. Kittel Ch Thermal Physics (New York: John Wiley and Sons, 1969) [Translated into Russian (Moscow: Nauka, 1977)]
  29. Reif F Statistical Physics (Berkeley Physics Course, Vol. 5, New York: McGraw-Hill Book Co., 1965) 2nd ed. [Translated into Russian: (Moscow: Nauka, 1977)]
  30. Klimontovich Yu L Statisticheskaya Fizika (Statistical Physics, Moscow: Nauka, 1982) [Translated into English (Chur, Switzerland: Harwood Acad. Publ., 1986)]
  31. Terletskiî Ya P Statisticheskaya Fizika (Statistical Physics) 3rd ed. (Moscow: Vysshaya Shkola, 1994) [Translated into English (Amsterdam: North-Holland, 1971)]
  32. Fowler R H Statistical Mechanics 2nd ed. (Cambridge: Cambridge Univ. Press, 1936)
  33. Wergeland H Det. Kgl. Norske Vidensk. Forh. 28 (21) 106 (1955)
  34. Klein M J Physica 26 1073 (1960)
  35. Lindhard J, in The Lesson of Quantum Theory (Eds J de Boer, E Dal, O Ulfbeck, Amsterdam: North-Holland, 1986)
  36. Greene R F, Callen H B Phys. Rev. 83 1231 (1951)
  37. Jaynes E T Phys. Rev. 106 620 (1957); 108 171 (1957)
  38. Venttsel’ E S Teoriya Veroyatnosteî (Probability Theory) 5th ed. (Moscow: Vysshaya Shkola, 1998)
  39. Vladimirov V S Obobshchennye Funktsii v Matematicheskoî Fizike (Generalized Functions in Mathematical Physics, Moscow: Nauka, 1976)
  40. Faddeev L D, Yakubovskiî O A Lektsii po Kvantovoî Mekhanike dlya Studentov-Matematikov (Lectures on Quantum Mechanics for Students in Mathematics, Leningrad: Izd. LGU, 1980)
  41. Maslov V P Funktsional’nyî Analiz 28 28 (1994); Teor. Mat. Fiz. 101 433 (1994) [Theor. Math. Phys. 101 1466 (1994)]
  42. Szilard L Z. Phys. 32 753 (1925)
  43. Mandelbrot B C. R. Acad. Sci. 243 1835 (1956); J. Math. Phys. 5 164 (1964)
  44. Tisza L, Quay P M Ann. Phys.-New York 25 48 (1963)
  45. Schlögl F Ann. Phys.-Leipzig 45 155 (1963); Phys. Rep. 62 267 (1980); J. Phys. Chem. Solids 49 679 (1988)
  46. Lavenda B H Int. J. Theor. Phys. 26 1069 (1987); 27 451 (1988); Lavenda B H Statistical Physics: Probabilistic Approach (New York: Wiley, 1991) [Translated into Russian (Moscow: Mir, 1999)]
  47. Uffink J, van Lith J Found. Phys. 28 323 (1998)
  48. Kadomtsev B B Dinamika i Informatsiya (Dynamics and Information, Moscow: Red. Zh. "Usp. Fiz. Nauk", 1997)
  49. Klyshko D N Usp. Fiz. Nauk 168 975 (1998) [Phys. Usp. 41 885 (1998)]
  50. Mensky M B Usp. Fiz. Nauk 168 1017 (1998) [Phys. Usp. 41 923 (1998)]; Menskiî M B 170 631 (2000) [Phys. Usp. 43 585 (2000)]
  51. Beckenstein J Phys. Rev. D 7 2333 (1973); 9 3292 (1974)
  52. Isaev P S, Mamchur E A Usp. Fiz. Nauk 170 1025 (2000) [Phys. Usp. 43 953 (2000)] [Review of the book: Conceptual Foundations of Quantum Field Theory (Ed. Tian Yu Cao, Cambridge: Cambridge Univ. Press, 1999)]
  53. Mandelbrot B Ann. Math. Stat. 33 1021 (1962)
  54. Lorentz H A Les Theories Statistiques en Thermodinamique (Leipzig-Berlin: B.G. Teubner, 1916) [Translated into Russian (Leningrad-Moscow: ONTI, 1935)]
  55. Fock V A "Preface", in Krylov N S Raboty po Obosnovaniyu Statisticheskoî Fiziki (Works on Validation of Statistical Physics, Moscow-Leningrad: Izd. AN SSSR, 1950); see also Krylov N S Works on the Foundations of Statistical Physics (Princeton, N.J.: Princeton Univ. Press, 1979)
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