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arXiv · 1708.02272

Positive entropy equilibrium states

Vaughn Climenhaga·Van Cyr
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Abstract

For transitive shifts of finite type, and more generally for shifts with specification, it is well-known that every equilibrium state for a Holder continuous potential has positive entropy as long as the shift has positive topological entropy. We give a non-uniform specification condition under which this property continues to hold, and demonstrate that it does not necessarily hold for other non-uniform versions of specification that have been introduced elsewhere.

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Vaughn Climenhaga, Van Cyr. 2017-08-07. Positive entropy equilibrium states. https://arxiv.org/abs/1708.02272

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