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On a question of Bratteli and Robinson

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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.

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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.

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    IsraelR.B., Convexity in the Theory of Lattice Gases, Princeton University Press, Princeton, N.J., 1979.

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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.

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    LiebE.H. and RuskaiM.B., J. Math. Phys. 14, 1938–1941 (1973).

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Van Enter, A.C.D. On a question of Bratteli and Robinson. Lett Math Phys 6, 289–291 (1982). https://doi.org/10.1007/BF00400324

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Keywords

  • Entropy
  • Statistical Physic
  • Group Theory
  • Large Class
  • Invariant State