A Variational Principle for the Specific Entropy for Symbolic Systems with Uncountable Alphabets

TL;DR

This paper establishes a variational principle for specific entropy in symbolic systems with uncountable alphabets and proves the uniqueness of equilibrium states for Walters potentials.

Contribution

It introduces a variational principle for specific entropy in symbolic dynamics with uncountable alphabets and demonstrates the uniqueness of equilibrium states for Walters potentials.

Findings

Established a variational principle for specific entropy in uncountable alphabet systems.

Proved the uniqueness of equilibrium states for Walters potentials.

Extended classical results to more general symbolic systems.

Abstract

In this paper we derived a variational principle for the specific entropy on the context of symbolic dynamics of compact metric space alphabets and use this result to obtain the uniqueness of the equilibrium states associated to a Walters potential.