A collection of invariant measures is the freezing collection for some potential if and only if it has constant entropy and is the equilibrium collection for some potential.
On the zero-t emperature limit of Gibbs states
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On the Equivalence of Equilibrium and Freezing States in Dynamical Systems
A collection of invariant measures is the freezing collection for some potential if and only if it has constant entropy and is the equilibrium collection for some potential.