Mutual Information as a Two-Point Correlation Function in Stochastic Lattice Models

TL;DR

This paper explores mutual information as a local measure in stochastic lattice models, revealing its scaling behavior aligns with known phenomenological theories in statistical physics.

Contribution

It introduces mutual information as a two-point correlation function in lattice models and demonstrates its scaling properties through a specific growth model.

Findings

Mutual information exhibits scaling properties consistent with phenomenological models.

Local entropy can be meaningfully defined in lattice systems with infinite configurations.

Mutual information acts as a correlation measure in stochastic growth processes.

Abstract

In statistical physics entropy is usually introduced as a global quantity which expresses the amount of information that would be needed to specify the microscopic configuration of a system. However, for lattice models with infinitely many possible configurations per lattice site it is also meaningful to introduce entropy as a local observable that describes the information content of a single lattice site. Likewise, the mutual information can be interpreted as a two-point correlation function. Studying a particular growth model we demonstrate that the mutual information exhibits scaling properties that are consistent with the established phenomenological scaling picture.