Foundations of Physics

, Volume 6, Issue 3, pp 249–262 | Cite as

New information-theoretic foundations for quantum statistics

  • William Band
  • James L. Park


When the state of a physical system is not fully determined by available data, it should be possible nevertheless to make a systematic guess concerning the unknown state by applying the principles of information theory. The resulting theoretical blend of informational and mechanical constructs should then constitute a modern structure for statistical physics. Such a program has been attempted by a number of authors, most notably Jaynes, with seeming success. However, we demonstrated in a recent publication that the standard list of so-called “mutually exclusive and exhaustive” quantum states that is commonly employed by these authors is in fact not exhaustive. It follows that the information-theoretic foundations of quantum statistics must be reformulated. The present paper discusses the fundamental problems involved and establishes a format for the correct application of information theory to quantum mechanical situations.


Statistical Physic Information Theory Quantum Statistic Physical System Fundamental Problem 
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  1. 1.
    E. T. Jaynes,Phys. Rev. 108, 171 (1957).Google Scholar
  2. 2.
    A. Katz,Principles of Statistical Mechanics (W. H. Freeman, San Francisco, 1967).Google Scholar
  3. 3.
    A. Hobson,Concepts in Statistical Mechanics (Gordon and Breach, New York, 1971).Google Scholar
  4. 4.
    J. von Neumann,Mathematical Foundations of Quantum Mechanics, transl. by R. T. Beyer (Princeton U. P., Princeton, N.J., 1955), p. 379.Google Scholar
  5. 5.
    J. W. Gibbs,Elementary Principles in Statistical Mechanics (1901), inThe Collected Works, Vol. 2 (Longmans, Green, and Co., New York, 1928).Google Scholar
  6. 6.
    J. L. Park and W. Band,Found. Phys. 6, 157 (1976).Google Scholar
  7. 7.
    E. T. Jaynes, inDelaware Seminar in the Foundations of Physics, ed. by Mario Bunge (Springer-Verlag, New York, 1967), p. 77.Google Scholar
  8. 8.
    J. L. Park and W. Band,Found. Phys. 1, 211 (1971);1, 339 (1971).Google Scholar
  9. 9.
    W. Heisenberg,Physics and Philosophy (Harper and Row, New York, 1958).Google Scholar
  10. 10.
    H. Margenau,The Nature of Physical Reality (McGraw-Hill, New York, 1950).Google Scholar
  11. 11.
    K. R. Popper, inQuantum Theory and Reality, ed. by Mario Bunge (Springer-Verlag, New York, 1967).Google Scholar
  12. 12.
    A. Landé,New Foundations of Quantum Mechanics (Cambridge U. P., Cambridge, 1965);Quantum Mechanics in a New Key (Exposition Press, New York, 1973).Google Scholar
  13. 13.
    H. Margenau and J. L. Park,Found. Phys. 3, 19 (1973).Google Scholar
  14. 14.
    E. T. Jaynes,Found. Phys. 3, 477 (1973).Google Scholar
  15. 15.
    E. T. Jaynes,IEEE Trans. Systems Sci. Cybernetics SSC-4, 227 (1968).Google Scholar
  16. 16.
    S. Watanabe,Knowing and Guessing (Wiley, New York, 1969).Google Scholar
  17. 17.
    A. Hobson,J. Stat. Phys. 1, 383 (1969).Google Scholar

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • William Band
    • 1
  • James L. Park
    • 1
  1. 1.Department of PhysicsWashington State UniversityPullman

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