Advertisement

Communications in Mathematical Physics

, Volume 31, Issue 4, pp 291–294 | Cite as

A continuity property of the entropy density for spin lattice systems

  • M. Fannes
Article

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.

Keywords

Entropy Neural Network Statistical Physic Complex System Nonlinear Dynamics 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Lanford, O., Robinson, D.W.: J. Math. Phys.9, 1120 (1968).Google Scholar
  2. 2.
    Fannes, M.: The entropy density of quasi free states, Preprint July 1972 KUL Leuven Belgium.Google Scholar
  3. 3.
    Kato, T.: Perturbation theory for linear operators. Theorem III.6.10. Berlin-Heidelberg-New York: Springer 1966.Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • M. Fannes
    • 1
    • 2
  1. 1.Universiteit LeuvenBelgium
  2. 2.Dept. Nat. Celestijnenlaan 200 DInstituut voor theoretische fysicaHeverleeBelgium

Personalised recommendations