Erasure Entropies and Gibbs Measures
2010, v.16, Issue 1, 3-14
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 a random process or field. A natural relation to Gibbs measures has also been observed. In this 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 potential. For some 2-dimensional Ising models, for which Verdu and Weissman suggested a numerical procedure, we show how to obtain an exact formula for the erasure entropy.
Keywords: erasure entropy,Gibbs measures,solvable Ising models,conditional entropy