C*- Algebras and Thermodynamic Formalism
Dynamical Systems
2021-10-14 v3 Operator Algebras
Abstract
We present a detailed exposition (for a Dynamical System audience) of the content of the paper: R. Exel and A. Lopes, Algebras, approximately proper equivalence relations and Thermodynamic Formalism, {\it Erg. Theo. and Dyn. Syst.}, Vol 24, pp 1051-1082 (2004). We show only the uniqueness of the \beta-KMS (in a certain C*-Algebra obtained from the operators acting in of a Gibbs invariant probability ) and its relation with the eigen-probability for the dual of a certain Ruele operator. We consider an example for a case of Hofbauer type where there exist a Phase transition for the Gibbs state. There is no Phase transition for the KMS state.
Keywords
Cite
@article{arxiv.0705.4060,
title = {C*- Algebras and Thermodynamic Formalism},
author = {Ruy Exel and Artur O. Lopes},
journal= {arXiv preprint arXiv:0705.4060},
year = {2021}
}