Shared Information in Stationary States at Criticality

TL;DR

This paper introduces estimators for shared information in stationary states of stochastic models, analyzing their behavior at criticality and across phase transitions using analytical, numerical, and Monte Carlo methods.

Contribution

It proposes new information-theoretic estimators for shared information and studies their finite-size scaling behavior at critical points in one-dimensional systems.

Findings

Estimators remain finite for finite correlation length.

Estimators diverge as correlation length diverges.

Finite-size scaling functions vary across different phase transitions.

Abstract

We consider bipartitions of one-dimensional extended systems whose probability distribution functions describe stationary states of stochastic models. We define estimators of the shared information between the two subsystems. If the correlation length is finite, the estimators stay finite for large system sizes. If the correlation length diverges, so do the estimators. The definition of the estimators is inspired by information theory. We look at several models and compare the behavior of the estimators in the finite-size scaling limit. Analytical and numerical methods as well as Monte Carlo simulations are used. We show how the finite-size scaling functions change for various phase transitions, including the case where one has conformal invariance.