Abstract
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.
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References
Balescu, R.: 1968, ‘Relativistic Statistical Thermodynamics’, Physica 40, 309.
Bohr, N.: 1932, ‘Chemistry and the Quantum Theory of Atomic Constitution’, J. Chem. Soc. London (Pt.I), 349
Bowers, R.L., and R.L. Zimmerman: 1973, ‘Relativistic Quantum Many-Body Theory in Rieman-nian Space-Time’, Phys. Rev. D 7, 296.
Brooks, D.R., and E.O Wiley: 1986, Evolution as Entropy, Univ.of Chicago Press, Chicago.
Burges, R.: 1973,Pressure Fluctuations in an Ideal Gas;, Phys Letters 44A, 37.
Callen, H.B.: 1960, Thermodynamic, Wiley, New York.
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.].
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.
Clausius, R. J.E.: 1865, ‘Uber verschiedene für die Anwendung bequeme Formen der Hauptgleichun-gen der mechanischen Wärmetheorie’, Ann. d. Phys. 125, 390.
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].
Currie, D.G.: 1962, ‘The Hamiltonian Description of Interaction for Classical Relativistic Particles’,Ph.D thesis, Univ. of Rochester (unpublished).
Currie, D.G., T.F. Jordan, and E.C.G. Sudarshan: 1963, ‘Relativistic Invariance and HamiltonianTheories of Interacting Particles’, Rev.Mod. Phys. 35, 350.
Dashen, R., S.-K. Ma, and H.J. Bernstein: 1969, ‘S-Matrix Formulation of Statistical Mechanics’, Phys. Rev. 187, 345.
Eddington, A.S.: 1928, The Nature of the Physical World, Macmillan, New York, p.74.
Gibbs, J.W.:1876–78, ‘On the Equilibrium of Heterogeneous Systems’,Trans. Conn. Acad. 3, 229.
Gibbs, J.W.: 1961, The Scientiüc Papers, Vol.1, Dover, New York, pp.165–168.
Grandy, W.T., Jr.: 1981, ‘Indistinguishability, Symmetrisation And Maximum Entropy’, Eur. J. Phys. 2, 86.
Hahn, E.L.: 1950, ‘Spin Echoes’,Phys. Rev. 80, 580.
Havas, P., and R.J. Swenson: 1979, ‘Relativistic Thermodynamics of Fluids. I’, Ann. Phys. (N.Y.) 118, 259.
Heims, S.P., and E.T. Jaynes: 1962, ‘Theory of Gyromagnetic Effects and Some Related Magnetic Phenomena’, Rev.Mod. Phys. 34, 143.
Huang, K.: 1963, Statistical Mechanics, Wiley, New York.
Jaynes, E.T.: 1957, ‘Information Theory and Statistical Mechanics’, Phys. Rev. 108, 171.
Jaynes, E.T.: 1965, ‘Gibbs vs. Boltzmann Entropies’, Am. J. Phys. 33, 391.
Jordan, T.F.: 1969, Linear Operators in Quantum Mechanics, Wiley, New York.
Kittel, C.: 1969, Thermal Physics, Wiley, New York.
Kittel, C.: 1973, ‘On the Nonexistence of Temperature Fluctuations in Small Systems’, Am. J. Phys 41, 1211.
Klein, O.: 1931, ‘Zur quantenmechanischen Begründung des zweiten Hauptsatzes der
Wärmelehre’, Z. Phys. 72, 767.
Kroemer, H.: 1980, ‘How Incorrect is the Classical Partition Function for the Ideal Gas?’, Am. J.7 Phys. 48, 962.
Landau, L.: 1927, ‘Das Dämpfungsproblem in der Wellenmechanik’, Z. Phys. 45, 430.
Landsberg, P.T.: 1966, ‘Does a Moving Body Appear Cool?’, Nature 212, 571.
Landsberg, P.T.: 1967, ‘Does a Moving Body Appear Cool?’, Nature 214, 903.
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.
Lieb, E.H.: 1976, ‘The Stability of Matter’, Rev.Mod. Phys. 48, 553.
Marx, G., E. Gajzagö, and P. Gnädig: 1982, ‘The Universe of Rubik’s Cube’, Eur. J. Phys. 3, 39.
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.
Morley, P.D., and M.B. Kislinger: 1979, ‘Relativistic Many-Body Theory, Quantum Chromody-namics, and Neutron Stars/Supernovae’, Phys. Reports 51, 63.
Park, J.L., and W. Band: 1976, ‘Mutually Exclusive and Exhaustive Quantum States’,Found. Phys. 6, 157.
Planck, M.: 1949, ScientificAutobiography and Other Papers, F. Gaynor (transi.), PhilosophicalLibrary, New York, pp. 17–18.
Ramsey, N.F.: 1956, ‘Thermodynamics and Statistical Mechanics at Negative Temperatures’, Phys. Rev. 103, 20.
Ruelle, D,: 1969, Statistical Mechanics, Benjamin, New York.
Scalapino, D.J.: 1961, ‘Irreversible Statistical Mechanics’, Ph.D thesis, Stanford Univ. (unpublished).
Smith, C.W.: 1977, ‘William Thomson and the Creation of Thermodynamics: 1846–1855’, Arch. Hist. Exact Sei. 16, 231.
ter Haar, D., and H. Wergeland: 1971, ‘Thermodynamics and Statistical Mechanics in the SpecialTheory of Relativity’, Phys. Repts. 1, 31.
Thomson, W.: 1882, Mathematical and Physical Papers, Vol.1, pp. 174–332.
Titus, W.J.: 1979, ‘Information Theory Density Matrix for a Simple Quantum System’, Am. J. Phys. 47, 357.
Van Hove, L.: 1949, ‘Quelques Propriétés Générales de L‘integrale de Configuration d’un Systèmede Particules Avec Interaction’, Physic a 15, 951.
Van Hove, L.: 1950, ‘Quelques Propriétés Générales de L’integrale de Configuration pour les
Systèmes de Particules à une Dimension’, Physica 16, 137.
von Neumann, J.: 1927a, ‘Wahrscheinlichkeitstheoretischer Aufbau der Quantenmechanik’, Gott. Nach., 273.
von Neumann, J.: 1927b, ‘Thermodynamik quantenmechanischer Gesamtheiten’, Gott. Nach.
von Neumann, J.: 1943, Mathematische Grundlagen der Quantenmechanik, Dover,New York.
Wehrl, A.: 1978, ‘General Properties of Entropy’, Rev. Mod. Phys. 50, 221.
Wilcox, R.M.: 1967, ‘Exponential Operators and Parameter Differentiation in Quantum Physics’, J. Math. Phys. 8, 962.
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.
Yeh, H.-C.: 1984, ‘Remark on the Second Law of Thermodynamics’, Am. J. Phys. 52, 720.
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© 1987 D. Reidel Publishing Company, Dordrecht, Holland
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Grandy, W.T. (1987). Quantum Statistical Mechanics. In: Foundations of Statistical Mechanics. Fundamental Theories of Physics, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3867-0_4
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DOI: https://doi.org/10.1007/978-94-009-3867-0_4
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