# Active Field Theories

## TL;DR

This paper introduces statistical field theories for active matter, focusing on top-down approaches that modify passive systems to account for activity, aiming to understand nonequilibrium behaviors and entropy production.

## Contribution

It presents a framework for constructing active field theories by adding minimal terms to passive models, bridging the gap in understanding their nonequilibrium properties.

## Key findings

- Active field theories can be derived by top-down modifications of passive models.
- These theories exhibit nonzero steady-state entropy production.
- The approach provides insights into the nonequilibrium physics of active matter.

## Abstract

Lecture Notes for Les Houches 2018 Summer School on Active Matter and Nonequilibrium Statistical Physics. These notes give an introduction to statistical field theories of active matter. After showing an example of how such theories can be created bottom-up by explicit coarse graining of active particle models, the main approach taken here is top-down: minimal terms are added to well-studied stochastic field theories of passive systems that break time-reversibility and thereby cause nonzero steady-state entropy production. These theories are, so far, rather poorly understood compared to their passive counterparts.