An ergodic measure is an equilibrium state for some continuous potential if and only if entropy is upper semicontinuous at it, for amenable group actions on compact metrizable spaces with finite topological entropy.
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Which Phases Are Thermodynamically Realizable? A Local Entropy Criterion
An ergodic measure is an equilibrium state for some continuous potential if and only if entropy is upper semicontinuous at it, for amenable group actions on compact metrizable spaces with finite topological entropy.