Erasure entropies and Gibbs measures

TL;DR

This paper explores the relationship between erasure entropies and Gibbs measures, providing formulas for erasure entropy in Gibbs measures and exact solutions for certain 2D Ising models, advancing understanding in statistical mechanics.

Contribution

It establishes a detailed connection between erasure entropies and Gibbs measures, including explicit formulas and exact solutions for specific models.

Findings

Derived a formula for erasure entropy of Gibbs measures.

Provided an exact solution for erasure entropy in 2D Ising models.

Clarified the relation between erasure entropies and statistical mechanics concepts.

Abstract

Recently Verdu and Weissman introduced erasure entropies, which are meant to measure the information carried by one or more symbols given all of the remaining symbols in the realization of the random process or field. A natural relation to Gibbs measures has also been observed. In his short note we study this relation further, review a few earlier contributions from statistical mechanics, and provide the formula for the erasure entropy of a Gibbs measure in terms of the corresponding potentia. For some 2-dimensonal Ising models, for which Verdu and Weissman suggested a numerical procedure, we show how to obtain an exact formula for the erasure entropy. l