The Concept of Probability in Statistical Mechanics

  • D. A. Lavis

Abstract

Thermodynamics was first formulated to describe the thermal properties of matter and, although its scope has now been enlarged, its relationship with the other main theories of physics, general and special relativity, classical and quantum mechanics and elementary particle theory, is still rather uneasy. As Sklar remarks [1, p. 4], it “is surprising that there is any place at all in this picture for a discipline such as thermodynamics” . It could be argued that it was this perception, leading to the conclusion that there is indeed no room for thermodynamics, which was the driving force behind the development of statistical mechanics. Of course, if this point has any weight, it must be seen in the historic context of the late nineteenth century, when attitudes to atomic models were rather ambivalent [1, 2]. Writing in the introduction to his Lectures on Gas Theory about the decline of support for atomism in continental Europe, Boltzmann [3, p. 24] remarks (presumably, sadly) that “it has been concluded that the assumption that heat is motion of the smallest particles of matter will eventually be proved false and discarded”. The energeticist case is presented starkly by Mach:1

Keywords

Entropy Europe Coherence Harman 

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References

  1. [1]
    L. Sklar, “Physics and Chance”, Cambridge U.P., 1993.CrossRefGoogle Scholar
  2. [2]
    Y.M. Guttmann, The Concept of Probability in Statistical Physics, Cam- bridge U. P., 1999.MATHCrossRefGoogle Scholar
  3. [3]
    L. Boltzmann, “Lectures on Gas Theory”, English translation by S. G. Brush 1964,California U. P., 1896.Google Scholar
  4. [4]
    P.M. Harman, “The Natural Philosophy of James Clerk Maxwell”, Cambridge U. P., 1998.MATHGoogle Scholar
  5. [5]
    S.G. Brush, “Kinetic Theory”, Vol. 1, Pergamon, 1965.MATHGoogle Scholar
  6. [6]
    S.G. Brush, “Kinetic Theory”, Vol. 2, Pergamon, 1966.Google Scholar
  7. [7]
    C. Cercignani, “Ludwig Boltzmann: The Man Who TVusted Atoms”, Oxford U. P., 1998.Google Scholar
  8. [8]
    J. Loschmidt, Wiener Beri. 73, 139, 1876Google Scholar
  9. [9]
    J. Loschmidt, Wiener Beri.75, 67, 1877.Google Scholar
  10. [10]
    E. Ott, “Chaos in Dynamical Systems”, (C.U.P.).Google Scholar
  11. [11]
    R.C. Tolman, “The Principles of Statistical Mechanics”, Oxford U. P., 1938.Google Scholar
  12. [12]
    A. Hobson, “Concepts in Statistical Mechanics”, Gordon and Breach, 1971.Google Scholar
  13. [12]
    D.A. Lavis, Brit. J. Phil. Sci. 28, 255–279, 1977.MathSciNetCrossRefGoogle Scholar
  14. [13]
    D.A. Gillies, “An Objective Theory of Probability”, Methuen, 1973.Google Scholar
  15. [14]
    R. Von Mises, “Probability, Statistics and Truth”, George, Allen and Unwin, 1957.MATHGoogle Scholar
  16. [15]
    K.R. Popper, Brit., J. Phil. Sci. 10, 1959, 25–42.ADSCrossRefGoogle Scholar
  17. [16]
    K.R. Popper, “The Logic of Scientific Discovery”, Hutchinson, 1959.MATHGoogle Scholar
  18. [17]
    W.T. Grandy and P.W. Milonni (Editors), “Physics and Probability: Essays in Honour of E. T. Jaynes”, Cambridge U. P., 1993.Google Scholar
  19. [18]
    E.T. Jaynes, “Papers on Probability, Statistics and Statistical Physics”, Edited by R. D. Rosenkratz, Reidel, 1983.MATHGoogle Scholar
  20. J.M. Keynes, “A Treatise on Probability”, Macmillan.Google Scholar
  21. [20]
    G.D. Birkhoff, Proc. Nat. Ac. Sci. 17, 1931, 656–660.ADSCrossRefGoogle Scholar
  22. [21]
    A.I. Khinchin, “The Mathematical Foundations of Statistical Mechanics”, Dover, 1949.Google Scholar
  23. [22]
    R. Kubo, “Statistical Mechanics”, North-Holland, 1965.MATHGoogle Scholar
  24. [23]
    R.M. Lewis, Arch. Rat. Mech. Anal.5, 1960, 355.MATHCrossRefGoogle Scholar
  25. [24]
    H. Grad, Comm. Pure and App. Maths. 5, 1952, 455–494.MathSciNetMATHCrossRefGoogle Scholar
  26. [25]
    I. Prigogine, “Non-Equilibrium Statistical Mechanics”, Interscience-Wiley.Google Scholar
  27. [26]
    R. Balescu, “Equilibrium and Non-Equilibrium Statistical Mechanics”, Wiley, 1975.Google Scholar
  28. [27]
    J.P. Dougherty, Stud. Hist. Phil. Sci. 24, 1993, 843–866.MathSciNetMATHCrossRefGoogle Scholar
  29. [28]
    J.P. Dougherty, Phil. Trans. Roy. Soc. A, 346, 1994, 259–305.MathSciNetADSMATHCrossRefGoogle Scholar
  30. [29]
    A.I. Khinchin, “Analytical Foundations of Physical Statistics”, Dover, 1961.Google Scholar
  31. [30]
    C.E. Shannon, and W. Weaver, “The Mathematical Theory of Communica- tion”, Illinois U. P., 1964.Google Scholar
  32. [31]
    J. Friedman and A.J. Shimony Stat. Phys. 3, 1971, 381.ADSCrossRefGoogle Scholar
  33. [32]
    D.A. Lavis and P.J. Milligan, Brit. J. Phil. Sci. 36, 1985, 193–210.Google Scholar
  34. [33]
    J.L. Lebowitz, Physics Today, September, 1993. 32–38.Google Scholar
  35. [34]
    J. Bricmont, Physicalia Mag. 17, 1995, 159–208.Google Scholar
  36. [35]
    P.Ehrenfest, and T., “The Conceptual Foundations of the Statistical Approach in Mechanics”, 1912; English translation Cornell U. P., 1959.Google Scholar
  37. [36]
    H. Barnum, C.M. Caves, C. Fuchs and R. Schack, Physics Today, November 1994, 11–13.Google Scholar
  38. [37]
    D.J. Driebe, Physics Today, November 1994, 13–15.Google Scholar
  39. [38]
    I. Progogine, Les Lois du Chaos, Flammarion, 1994.Google Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • D. A. Lavis
    • 1
  1. 1.Department of Mathematics King’s CollegeUK

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