A generalized mean field theory of coarse-graining

TL;DR

This paper introduces a comprehensive mean field theory for creating equilibrium coarse-grained models, unifying inverse and reduction methods, and deriving existing techniques as special cases.

Contribution

It presents a general framework for coarse graining that encompasses existing methods and provides a basis for inverse and reduction approaches in complex systems modeling.

Findings

Unified mean field theory for coarse graining

Derivation of inverse methods from the theory

Application to reduction of equilibrium data

Abstract

A general mean field theory is presented for the construction of equilibrium coarse grained models. Inverse methods that reconstruct microscopic models from low resolution experimental data can be derived as particular implementations of this theory. The theory also applies to the opposite problem of reduction, where relevant information is extracted from available equilibrium ensemble data. These problems are central to the construction of coarse grained representations of complex systems, and commonly used coarse graining methods are derived as particular cases of the general theory.