Entropy for Zero-Temperature Limits of Gibbs-Equilibrium States for Countable-Alphabet Subshifts of Finite Type
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Let Σ A be a finitely primitive subshift of finite type over a countable alphabet. For suitable potentials f : Σ A → ℝ 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(μ 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.
KeywordsGibbs state equilibrium state ground state maximizing measure countable alphabet subshift of finite type entropy
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