How to derive a predictive active field theory: a step-by-step tutorial

TL;DR

This paper provides a detailed tutorial on deriving predictive field theories for active matter systems using the interaction-expansion method, facilitating systematic coarse-graining from microscopic models.

Contribution

It introduces and explains the interaction-expansion method for deriving active field theories, including a derivation of active model B+ from microscopic interactions.

Findings

Systematic derivation of active model B+ from microscopic models.

Clarification of the interaction-expansion method for coarse-graining.

Discussion of extensions and future applications of the method.

Abstract

The study of active soft matter has developed into one of the most rapidly growing areas of physics. Field theories, which can be developed either via phenomenological considerations or by coarse-graining of a microscopic model, are a very useful tool for understanding active systems. Here, we provide a detailed review of a particular coarse-graining procedure, the interaction-expansion method (IEM). The IEM allows for the systematic microscopic derivation of predictive field theories for systems of interacting active particles. We explain in detail how it can be used for a microscopic derivation of active model B+, which is a widely used scalar active matter model. Extensions and possible future applications are also discussed.