Quantum Statistical Mechanics

  • Walter T. GrandyJr.
Part of the Fundamental Theories of Physics book series (FTPH, volume 19)


The preceding formulation of statistical mechanics is perhaps the simplest application of probability theory to the many-body problem. Although it is consistent with the principles of quantum mechanics, it is not manifestly so. That is, the PME itself is based on the notions of information and measurement, but a general formulation should also incorporate explicitly the quantum-mechanical theory of measurement. The present chapter is directed toward this generalization, beginning with a brief review of some selected formal aspects of quantum mechanics.


Partition Function Pure State Maximum Entropy Unitary Transformation Grand Canonical Ensemble 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Balescu, R.: 1968, ‘Relativistic Statistical Thermodynamics’, Physica 40, 309.ADSzbMATHCrossRefGoogle Scholar
  2. Bohr, N.: 1932, ‘Chemistry and the Quantum Theory of Atomic Constitution’, J. Chem. Soc. London (Pt.I), 349Google Scholar
  3. Bowers, R.L., and R.L. Zimmerman: 1973, ‘Relativistic Quantum Many-Body Theory in Rieman-nian Space-Time’, Phys. Rev. D 7, 296.ADSCrossRefGoogle Scholar
  4. Brooks, D.R., and E.O Wiley: 1986, Evolution as Entropy, Univ.of Chicago Press, Chicago.Google Scholar
  5. Burges, R.: 1973,Pressure Fluctuations in an Ideal Gas;, Phys Letters 44A, 37.ADSGoogle Scholar
  6. Callen, H.B.: 1960, Thermodynamic, Wiley, New York.Google Scholar
  7. Carnot, S.: 1824, Refexions la puissance motrice du feu, Bachelier, Paris [English translation,E. Mendoza: 1960, Reflections on the Motive Power of Fire, Dover, New York.].Google Scholar
  8. Clausius, R. J.E.: 1850, ‘Uber die bewegende Kraft der Wärme, und die gesetze, welche sich daraus für die Wärmelehre Selbst ableiten lassen’, Ann. d. Phys. 89, 368, 500.ADSGoogle Scholar
  9. Clausius, R. J.E.: 1865, ‘Uber verschiedene für die Anwendung bequeme Formen der Hauptgleichun-gen der mechanischen Wärmetheorie’, Ann. d. Phys. 125, 390.Google Scholar
  10. Clausius, R.J.E.: 1879, Die Mechanische Wärmetheorie, Vols.I,II, 2nd ed., Vieweg, Braunschweig [English translation, W.R. Browne: 1879, The Mechanical Theory of Heat, Macmillan, London].Google Scholar
  11. Currie, D.G.: 1962, ‘The Hamiltonian Description of Interaction for Classical Relativistic Particles’,Ph.D thesis, Univ. of Rochester (unpublished).Google Scholar
  12. Currie, D.G., T.F. Jordan, and E.C.G. Sudarshan: 1963, ‘Relativistic Invariance and HamiltonianTheories of Interacting Particles’, Rev.Mod. Phys. 35, 350.MathSciNetADSCrossRefGoogle Scholar
  13. Dashen, R., S.-K. Ma, and H.J. Bernstein: 1969, ‘S-Matrix Formulation of Statistical Mechanics’, Phys. Rev. 187, 345.ADSzbMATHCrossRefGoogle Scholar
  14. Eddington, A.S.: 1928, The Nature of the Physical World, Macmillan, New York, p.74.Google Scholar
  15. Gibbs, J.W.:1876–78, ‘On the Equilibrium of Heterogeneous Systems’,Trans. Conn. Acad. 3, 229.Google Scholar
  16. Gibbs, J.W.: 1961, The Scientiüc Papers, Vol.1, Dover, New York, pp.165–168.Google Scholar
  17. Grandy, W.T., Jr.: 1981, ‘Indistinguishability, Symmetrisation And Maximum Entropy’, Eur. J. Phys. 2, 86. CrossRefGoogle Scholar
  18. Hahn, E.L.: 1950, ‘Spin Echoes’,Phys. Rev. 80, 580.ADSzbMATHCrossRefGoogle Scholar
  19. Havas, P., and R.J. Swenson: 1979, ‘Relativistic Thermodynamics of Fluids. I’, Ann. Phys. (N.Y.) 118, 259.MathSciNetADSCrossRefGoogle Scholar
  20. Heims, S.P., and E.T. Jaynes: 1962, ‘Theory of Gyromagnetic Effects and Some Related Magnetic Phenomena’, Rev.Mod. Phys. 34, 143.MathSciNetADSzbMATHCrossRefGoogle Scholar
  21. Huang, K.: 1963, Statistical Mechanics, Wiley, New York.Google Scholar
  22. Jaynes, E.T.: 1957, ‘Information Theory and Statistical Mechanics’, Phys. Rev. 108, 171.MathSciNetADSCrossRefGoogle Scholar
  23. Jaynes, E.T.: 1965, ‘Gibbs vs. Boltzmann Entropies’, Am. J. Phys. 33, 391.ADSzbMATHCrossRefGoogle Scholar
  24. Jordan, T.F.: 1969, Linear Operators in Quantum Mechanics, Wiley, New York.Google Scholar
  25. Kittel, C.: 1969, Thermal Physics, Wiley, New York.Google Scholar
  26. Kittel, C.: 1973, ‘On the Nonexistence of Temperature Fluctuations in Small Systems’, Am. J. Phys 41, 1211.ADSCrossRefGoogle Scholar
  27. Klein, O.: 1931, ‘Zur quantenmechanischen Begründung des zweiten Hauptsatzes derGoogle Scholar
  28. Wärmelehre’, Z. Phys. 72, 767.Google Scholar
  29. Kroemer, H.: 1980, ‘How Incorrect is the Classical Partition Function for the Ideal Gas?’, Am. J.7 Phys. 48, 962.Google Scholar
  30. Landau, L.: 1927, ‘Das Dämpfungsproblem in der Wellenmechanik’, Z. Phys. 45, 430.ADSCrossRefGoogle Scholar
  31. Landsberg, P.T.: 1966, ‘Does a Moving Body Appear Cool?’, Nature 212, 571.ADSCrossRefGoogle Scholar
  32. Landsberg, P.T.: 1967, ‘Does a Moving Body Appear Cool?’, Nature 214, 903.ADSCrossRefGoogle Scholar
  33. Lewis, M.B., and A. J.F. Siegert: 1956, ‘Extension of the Condensation Theory of Yang and Lee tothe Pressure Ensemble’, Phys. Rev. 101, 1227.ADSzbMATHCrossRefGoogle Scholar
  34. Lieb, E.H.: 1976, ‘The Stability of Matter’, Rev.Mod. Phys. 48, 553.MathSciNetADSCrossRefGoogle Scholar
  35. Marx, G., E. Gajzagö, and P. Gnädig: 1982, ‘The Universe of Rubik’s Cube’, Eur. J. Phys. 3, 39.CrossRefGoogle Scholar
  36. Maxwell, J.C.: 1878, ‘On Boltzmann’s Theorem on the Average Distribution of Energy in a Systemof Material Points’,Trans. Camb. Phil. Soc. 12, 547.Google Scholar
  37. Morley, P.D., and M.B. Kislinger: 1979, ‘Relativistic Many-Body Theory, Quantum Chromody-namics, and Neutron Stars/Supernovae’, Phys. Reports 51, 63.MathSciNetADSCrossRefGoogle Scholar
  38. Park, J.L., and W. Band: 1976, ‘Mutually Exclusive and Exhaustive Quantum States’,Found. Phys. 6, 157.MathSciNetADSCrossRefGoogle Scholar
  39. Planck, M.: 1949, ScientificAutobiography and Other Papers, F. Gaynor (transi.), PhilosophicalLibrary, New York, pp. 17–18.Google Scholar
  40. Ramsey, N.F.: 1956, ‘Thermodynamics and Statistical Mechanics at Negative Temperatures’, Phys. Rev. 103, 20.ADSzbMATHCrossRefGoogle Scholar
  41. Ruelle, D,: 1969, Statistical Mechanics, Benjamin, New York.zbMATHGoogle Scholar
  42. Scalapino, D.J.: 1961, ‘Irreversible Statistical Mechanics’, Ph.D thesis, Stanford Univ. (unpublished).Google Scholar
  43. Smith, C.W.: 1977, ‘William Thomson and the Creation of Thermodynamics: 1846–1855’, Arch. Hist. Exact Sei. 16, 231.CrossRefGoogle Scholar
  44. ter Haar, D., and H. Wergeland: 1971, ‘Thermodynamics and Statistical Mechanics in the SpecialTheory of Relativity’, Phys. Repts. 1, 31.ADSCrossRefGoogle Scholar
  45. Thomson, W.: 1882, Mathematical and Physical Papers, Vol.1, pp. 174–332.Google Scholar
  46. Titus, W.J.: 1979, ‘Information Theory Density Matrix for a Simple Quantum System’, Am. J. Phys. 47, 357.MathSciNetADSCrossRefGoogle Scholar
  47. Van Hove, L.: 1949, ‘Quelques Propriétés Générales de L‘integrale de Configuration d’un Systèmede Particules Avec Interaction’, Physic a 15, 951.ADSzbMATHCrossRefGoogle Scholar
  48. Van Hove, L.: 1950, ‘Quelques Propriétés Générales de L’integrale de Configuration pour lesGoogle Scholar
  49. Systèmes de Particules à une Dimension’, Physica 16, 137.Google Scholar
  50. von Neumann, J.: 1927a, ‘Wahrscheinlichkeitstheoretischer Aufbau der Quantenmechanik’, Gott. Nach., 273.Google Scholar
  51. von Neumann, J.: 1927b, ‘Thermodynamik quantenmechanischer Gesamtheiten’, Gott. Nach.Google Scholar
  52. von Neumann, J.: 1943, Mathematische Grundlagen der Quantenmechanik, Dover,New York.Google Scholar
  53. Wehrl, A.: 1978, ‘General Properties of Entropy’, Rev. Mod. Phys. 50, 221.MathSciNetADSCrossRefGoogle Scholar
  54. Wilcox, R.M.: 1967, ‘Exponential Operators and Parameter Differentiation in Quantum Physics’, J. Math. Phys. 8, 962.MathSciNetADSzbMATHCrossRefGoogle Scholar
  55. Yang, C.N., and T.D. Lee: 1952, ‘Statistical Theory of Equations of State and Phase Transit ions. I.Theory of Condensation’,Phys. Rev. 87, 404.MathSciNetADSzbMATHCrossRefGoogle Scholar
  56. Yeh, H.-C.: 1984, ‘Remark on the Second Law of Thermodynamics’, Am. J. Phys. 52, 720.ADSCrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1987

Authors and Affiliations

  • Walter T. GrandyJr.
    • 1
  1. 1.Department of Physics and AstronomyUniversity of WyomingUSA

Personalised recommendations