The variational principle of topological pressure for actions of sofic groupoids

TL;DR

This paper proves a fundamental relationship between topological pressure and measure-theoretic entropy for actions of sofic groupoids, extending classical thermodynamic formalism to a broader algebraic setting.

Contribution

It introduces the variational principle of topological pressure specifically for actions of sofic groupoids, a novel extension in the field.

Findings

Established the variational principle for sofic groupoid actions

Extended thermodynamic formalism to algebraic structures

Provided a new framework for analyzing topological pressure

Abstract

This article establishes the variational principle of topological pressure for actions of sofic groupoids.