Journal of Statistical Physics

, Volume 126, Issue 2, pp 315–324 | Cite as

Entropy for Zero-Temperature Limits of Gibbs-Equilibrium States for Countable-Alphabet Subshifts of Finite Type

  • I. D. Morris
Article

Abstract

Let Σ A be a finitely primitive subshift of finite type over a countable alphabet. For suitable potentials f : Σ A we can associate an invariant Gibbs equilibrium state μ tf to the potential tf for each t ≥ 1. In this note, we show that the entropy h tf ) converges in the limit t→ ∞ to the maximum entropy of those invariant measures which maximize ∫ f dμ. We further show that every weak-* accumulation point of the family of measures μ tf has entropy equal to this value. This answers a pair of questions posed by O. Jenkinson, R. D. Mauldin and M. Urbański.

Keywords

Gibbs state equilibrium state ground state maximizing measure countable alphabet subshift of finite type entropy 

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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • I. D. Morris
    • 1
  1. 1.School of MathematicsUniversity of ManchesterManchesterU.K.

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