Thermodynamic formalism for Haar systems in noncommutative integration: transverse functions and entropy of transverse measures
| Autor: | Jairo K. Mengue, Artur O. Lopes |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
A priori probability
Pure mathematics General Mathematics FOS: Physical sciences Haar Dynamical Systems (math.DS) 37D35 Entropy (classical thermodynamics) Transfer operator Mathematics::Category Theory FOS: Mathematics Equivalence relation Mathematics - Dynamical Systems Condensed Matter - Statistical Mechanics Mathematical Physics Mathematics Statistical Mechanics (cond-mat.stat-mech) business.industry Applied Mathematics Probability (math.PR) Mathematical Physics (math-ph) Modular design Noncommutative geometry Transverse plane business Mathematics - Probability |
| Zdroj: | Ergodic Theory and Dynamical Systems. 41:1835-1863 |
| ISSN: | 1469-4417 0143-3857 |
| DOI: | 10.1017/etds.2020.24 |
| Popis: | We consider here a certain class of groupoids obtained via an equivalence relation (the so-called subgroupoids of pair groupoids). We generalize to Haar systems in these groupoids some results related to entropy and pressure which are well known in thermodynamic formalism. We introduce a transfer operator, where the equivalence relation (which defines the groupoid) plays the role of the dynamics and the corresponding transverse function plays the role of the a priori probability. We also introduce the concept of invariant transverse probability and of entropy for an invariant transverse probability, as well as of pressure for transverse functions. Moreover, we explore the relation between quasi-invariant probabilities and transverse measures. Some of the general results presented here are not for continuous modular functions but for the more general class of measurable modular functions. |
| Databáze: | OpenAIRE |
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