Multiparticle correlation expansion of relative entropy in lattice systems

TL;DR

This paper develops a method to express the relative entropy between lattice systems as a series based on multiparticle correlations, enabling detailed analysis of structural information contributions.

Contribution

It introduces a general procedure for constructing the multiparticle correlation expansion of relative entropy in lattice systems, including explicit formulas for all terms.

Findings

Coefficients of the multiparticle correlation expansion of excess entropy can be computed using the new formula.

The series expresses the statistical distance as a sum over clusters of increasing size.

The method links correlation functions directly to relative entropy contributions.

Abstract

This paper deals with the construction of the multiparticle correlation expansion of relative entropy for lattice systems. Thanks to this analysis we are able to express the statistical distance between two systems as a series built over clusters of increasing dimension. Each addend is written in terms of correlation functions and expresses the contribution to the relative entropy due to structural information inside the selected cluster. We present a general procedure for the explicit construction of all the terms of the series. As a first application of this result, we show that the coefficients of the multiparticle correlation expansion of the excess entropy can be computed from our formula, as a particular case.