Statistical physics through the lens of real-space mutual information

TL;DR

This paper introduces a machine learning-based algorithm that uses real-space mutual information to identify relevant degrees of freedom in complex physical systems, enhancing the development of effective theories beyond traditional renormalization methods.

Contribution

It presents a novel, interpretable machine learning approach for coarse-graining in statistical physics, connecting information theory with field theory operator identification.

Findings

Successfully applied to an interacting model with emergent degrees of freedom

Overcomes computational challenges in information-theoretic variational principles

Advances automated, interpretable theory building in complex systems

Abstract

Identifying the relevant coarse-grained degrees of freedom in a complex physical system is a key stage in developing powerful effective theories in and out of equilibrium. The celebrated renormalization group provides a framework for this task, but its practical execution in unfamiliar systems is fraught with ad hoc choices, whereas machine learning approaches, though promising, often lack formal interpretability. Recently, the optimal coarse-graining in a statistical system was shown to exist, based on a universal, but computationally difficult information-theoretic variational principle. This limited its applicability to but the simplest systems; moreover, the relation to standard formalism of field theory was unclear. Here we present an algorithm employing state-of-art results in machine-learning-based estimation of information-theoretic quantities, overcoming these challenges. We use this advance to develop a new paradigm in identifying the most relevant field theory operators describing properties of the system, going beyond the existing approaches to real-space renormalization. We evidence its power on an interacting model, where the emergent degrees of freedom are qualitatively different from the microscopic building blocks of the theory. Our results push the boundary of formally interpretable applications of machine learning, conceptually paving the way towards automated theory building.