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A new approach for the justification of ensembles in quantum statistical mechanics — II

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Abstract

The results of the first paper in this series are generalized to include spin, permutation symmetry, and time dependence. In particular, the question of time invariance of localness in the Heisenberg picture is discussed and it is conjectured that an operator that is initially local will remain local over time. In order to treat macroscopic systems, it is shown that the ensemble decomposition of the previous paper can be used to “coarsegrain” configuration space. Finally, a physical interpretation of the ensemble decomposition in terms of “redundant macroscopic information” is used to give a derivation of the generalized microcanonical average.

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References

  1. J. E. Keizer,J. Stat. Phys. 2:213 (1970).

    Google Scholar 

  2. A. Messiah,Quantum Mechanics, Vol. II (John Wiley and Sons, New York, 1958), Chapter 14.

    Google Scholar 

  3. I. E. Segal and R. A. Kunze,Integrals and Operators (McGraw-Hill Book Co., New York, 1968), Chapter VII.

    Google Scholar 

  4. A. Messiah,Quantum Mechanics, Vol. II (John Wiley and Sons, New York, 1958), Chapter 13.

    Google Scholar 

  5. A. Messiah,Quantum Mechanics, Vol. I (John Wiley and Sons, New York, 1958), p. 328.

    Google Scholar 

  6. R. Hermann,Linear Algebra and Quantum Mechanics, unpublished notes, 1967.

  7. P. Roman,Advanced Quantum Mechanics (Addison-Wesley Publishing Co., Reading, Massachusetts, 1965), p. 45.

    Google Scholar 

  8. G. W. Mackey,Mathematical Foundations of Quantum Mechanics, (W. A. Benjamin, New York, 1963), p. 81.

    Google Scholar 

  9. A. Messiah,Quantum Mechanics, Vol. I (John Wiley and Sons, New York, 1958), p. 75.

    Google Scholar 

  10. G. Emch, inLectures in Theoretical Physics, Boulder, 1965, Vol. 8a, (University of Colorado Press, Boulder, Colorado (1966).

    Google Scholar 

  11. I. E. Farquhar,Ergodic Theory in Statistical Mechanics (Interscience Publishers, London, 1964), p. 149.

    Google Scholar 

  12. T. L. Hill,Introduction to Statistical Thermodynamics (Addison-Wesley Publishing Co., Reading, Massachusetts, 1960), p. 28.

    Google Scholar 

  13. R. M. Lewis,Arch. Ratl. Mech. Anal. 5:355 (1960).

    Google Scholar 

  14. I. E. Farquhar,Ergodic Theory in Statistical Mechanics (Interscience Publishers, London, 1964)

    Google Scholar 

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Author notes

  1. Joel E. Keizer

    Present address: Battelle Memorial Institute, Columbus, Ohio

Authors and Affiliations

  1. Division of Natural Science, University of California, Santa Cruz

    Joel E. Keizer

Authors
  1. Joel E. Keizer
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Additional information

This work was supported in part by research grants from the National Science Foundation and the U.S. Public Health Service. Some of the material in this paper is contained in a doctoral dissertation submitted by the author to the University of Oregon (1969).

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Keizer, J.E. A new approach for the justification of ensembles in quantum statistical mechanics — II. J Stat Phys 2, 233–249 (1970). https://doi.org/10.1007/BF01030744

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