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


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.


Entropy Statistical Physic Group Theory Large Class Invariant State 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    BratteliO. and RobinsonD.W., Operator Algebras and Quantum Statistical Mechanics II, Springer-Verlag, New York, Heidelberg, Berlin, 1981.Google Scholar
  2. 2.
    IsraelR.B., Convexity in the Theory of Lattice Gases, Princeton University Press, Princeton, N.J., 1979.Google Scholar
  3. 3.
    ArakiH. and SewellG.L., Comm. Math. Phys. 52, 103–109 (1977); Sewell, G.L., Physics Reports 57, 309–342 (1980).Google Scholar
  4. 4.
    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
  5. 5.
    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

Personalised recommendations