Abstract
The entropy density of spin lattice systems is known to be a weak upper semi-continuous functional on the set of the lattice invariant states. (It is even weak discontinuous.) However we prove here that it is continuous with respect to the norm topology on those states.
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References
Lanford, O., Robinson, D.W.: J. Math. Phys.9, 1120 (1968).
Fannes, M.: The entropy density of quasi free states, Preprint July 1972 KUL Leuven Belgium.
Kato, T.: Perturbation theory for linear operators. Theorem III.6.10. Berlin-Heidelberg-New York: Springer 1966.
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Aspirant van het Belgisch N.F.W.O.
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Fannes, M. A continuity property of the entropy density for spin lattice systems. Commun.Math. Phys. 31, 291–294 (1973). https://doi.org/10.1007/BF01646490
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DOI: https://doi.org/10.1007/BF01646490