Advertisement

Foundations of Physics

, Volume 12, Issue 1, pp 59–84 | Cite as

The formalism of equilibrium quantum statistical mechanics revisited

  • Olaf Melsheimer
Article

Abstract

It is shown that the traditional formalism of equilibrium quantum statistical mechanics may fully be incorporated into a general macro-observable approach to quantum statistical mechanics recently proposed by the same author. (1,2) In particular, the partition functions which in the traditional approach are assumed to connect nonnormalized density operators with thermodynamic functions are reinterpreted as functions connecting so-called quantum mechanical effect operators with state parameters. It is argued that these functions although only part of a much richer internal structure of the macro-observable are sufficient to cope with all problems one usually encounters in equilibrium quantum statistical mechanics. p]Denn eigentlich unternehmen wir umsonst, das Wesen eines Dinges auszudrücken. Wirkungen werden wir gewahr, und eine vollständige Geschichte dieser Wirkungen umfaßte wohl allenfalls das Wesen jenes Dinges.

Johann W. v. Goethe Farbenlehre

Keywords

Partition Function Internal Structure State Parameter Statistical Mechanic Traditional Approach 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    O. Melsheimer,Found. Phys. 9, 193 (1979).Google Scholar
  2. 2.
    O. Melsheimer,Found. Phys. 10, 375 (1980).Google Scholar
  3. 3.
    G. Ludwig, The connection between the objective description of macro-systems and quantum mechanics of “many particles,” inOld and New Questions in Physics, Cosmology, Philosophy, and Theoretical Biology: Essays in Honor of Wolfgang Yourgrau, Alwyn van der Merwe, ed. (Plenum Press, New York, 1982), to be published; G. Ludwig,Einführung in die Grundlagen der Theoretischen Physik, Vol. 4 (Bertelsmann Universitätsverlag, 1979).Google Scholar
  4. 4.
    D. Ruelle,Statistical Mechanics (W. A. Benjamin, New York, 1969).Google Scholar
  5. 5.
    F. Reif,Fundamentals of Statistical Mechanics and Thermal Physics (McGraw-Hill, New York, 1965).Google Scholar
  6. 6.
    G. Ludwig,Axiomatische Basis der Quantenmechanik (Springer Verlag, Berlin), to be published.Google Scholar
  7. 7.
    G. Ludwig,Foundations of Quantum Mechanics (Springer-Verlag, Berlin), to be published.Google Scholar
  8. 8.
    E. B. Davies,Quantum Theory of Open Systems (Academic Press, London, 1976).Google Scholar
  9. 9.
    G. Ludwig,Makroskopische Systeme und Quantenmechanik, Notes in Mathematical Physics, No. 5 (University of Marburg, 1972).Google Scholar
  10. 10.
    J. Kluvanek and G. Knowles,Vector Measures and Control Systems (North-Holland, Amsterdam, 1976).Google Scholar
  11. 11.
    J. Horvath,Topological Vector Spaces and Distributions, Vol. 1 (Addison-Wesley, Reading, Massachusetts, 1966).Google Scholar
  12. 12.
    H. Neumann,Int. J. Theor. Phys. 9, 225 (1973).Google Scholar
  13. 13.
    E. M. Alfsen,Compact Convex Sets and Boundary Integrals (Springer Verlag, Berlin, 1971).Google Scholar
  14. 14.
    G. Jamesson,Ordered Linear Spaces, Lecture Notes in Mathematics 14 (Springer Verlag, Berlin, 1970).Google Scholar
  15. 15.
    R. Haag and D. Kastler,J. Math. Phys. 5, 848 (1963).Google Scholar

Copyright information

© Plenum Publishing Corporation 1982

Authors and Affiliations

  • Olaf Melsheimer
    • 1
  1. 1.Arbeitsgruppe “Grundlagen der Physik”Fachbereich Physik der Philipps-Universität MarburgMarburgWest Germany

Personalised recommendations