Letters in Mathematical Physics

, Volume 6, Issue 4, pp 289–291 | Cite as

On a question of Bratteli and Robinson

  • A. C. D. Van Enter
Article

Abstract

We give a partial answer to a question raised by Bratteli and Robinson, by showing that the mean entropy equals the mean conditional entropy for a large class of translation invariant states. In the general case we show that equality holds if and only if the mean conditional entropy is upper semicontinuous in the w*-topology.

Keywords

Entropy Statistical Physic Group Theory Large Class Invariant State 

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References

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    BratteliO. and RobinsonD.W., Operator Algebras and Quantum Statistical Mechanics II, Springer-Verlag, New York, Heidelberg, Berlin, 1981.Google Scholar
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    LanfordO.E. and RobinsonD.W., Comm. Math. Phys. 9, 327–338 (1968); Lanford, O.E., in A. Lenard (ed.), Statistical Mechanics and Mathematical Problems, Springer-Verlag, Berlin, Heidelberg, New York, 1973.Google Scholar
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    LiebE.H. and RuskaiM.B., J. Math. Phys. 14, 1938–1941 (1973).CrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company 1982

Authors and Affiliations

  • A. C. D. Van Enter
    • 1
  1. 1.Sonderforschungsbereich 123Universität HeidelbergHeidelberg 1W. Germany

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