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C*-Algebras, Approximately Proper Equivalence Relations, and Thermodynamic Formalism

R. Exel·A. Lopes
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Abstract

We introduce a non-commutative generalization of the notion of (approximately proper) equivalence relation and propose the construction of a "quotient space". We then consider certain one-parameter groups of automorphisms of the resulting C*-algebra and prove the existence of KMS states at every temperature. In a model originating from Thermodynamics we prove that these states are unique as well. We also show a relationship between maximizing measures (the analogue of the Aubry-Mather measures for expanding maps) and ground states. In the last section we explore an interesting example of phase transitions.

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R. Exel, A. Lopes. 2002-07-02. C*-Algebras, Approximately Proper Equivalence Relations, and Thermodynamic Formalism. https://arxiv.org/abs/math/0206074

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