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

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics, University of Manchester, Sackville Street, Manchester, M60 1QD, U.K.

    I. D. Morris

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  1. I. D. Morris
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Morris, I.D. Entropy for Zero-Temperature Limits of Gibbs-Equilibrium States for Countable-Alphabet Subshifts of Finite Type. J Stat Phys 126, 315–324 (2007). https://doi.org/10.1007/s10955-006-9215-7

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  • DOI: https://doi.org/10.1007/s10955-006-9215-7

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