The topological version of free entropy

TL;DR

This paper introduces topological free entropy and free capacity within $C^*$-algebras, exploring their fundamental properties, related problems, and links to potential theory and random matrix theory.

Contribution

It develops the concepts of topological free entropy and free capacity in the $C^*$-algebra setting, expanding the theoretical framework.

Findings

Establishment of basic properties of topological free entropy

Discussion of core problems in the area

Connections made to potential theory and random matrix theory

Abstract

Notions of topological free entropy and of free capacity are introduced in the $C^*$-algebra context. Basic properties, basic problems and connections to potential theory and random matrix theory are discussed.