Coarse-graining and fluctuations: Two birds with one stone

TL;DR

This paper explores how large-deviation principles can be used to develop a general approach to coarse-graining in complex systems, linking fluctuations and simplified models.

Contribution

It introduces a novel method that leverages large-deviation principles for systematic coarse-graining of systems with known large-deviation behavior.

Findings

Establishes the connection between large-deviation principles and coarse-graining.

Proposes a variational approach for coarse-graining based on large-deviation functionals.

Provides a framework applicable to systems with well-defined large-deviation principles.

Abstract

We show how the mathematical structure of large-deviation principles matches well with the concept of coarse-graining. For those systems with a large-deviation principle, this may lead to a general approach to coarse-graining through the variational form of the large-deviation functional.