# Linear response theory and Green-Kubo relations for active matter

## TL;DR

This paper develops a theoretical framework for understanding how active matter systems, specifically Active Brownian Particles, respond to external forces, revealing deviations from equilibrium relations due to activity and interactions.

## Contribution

It extends fluctuation-dissipation theorem and Green-Kubo relations to active matter, providing analytical expressions and simulation validation for transport properties.

## Key findings

- Derived Green-Kubo formulas for active particle diffusivity and mobility.
- Quantified deviations from Stokes-Einstein relation in active systems.
- Validated theoretical predictions with unperturbed simulation data.

## Abstract

We address the question of how interacting active systems in a non-equilibrium steady-state respond to an external perturbation. We establish an extended fluctuation-dissipation theorem for Active Brownian Particles (ABP) which highlights the role played by the local violation of detailed balance due to activity. By making use of a Markovian approximation we derive closed Green-Kubo expressions for the diffusivity and mobility of ABP and quantify the deviations from the Stokes-Einstein relation. We compute the linear response function to an external force using unperturbed simulations of ABP and compare the results with the analytical predictions of the transport coefficients. Our results show the importance of the interplay between activity and interactions in the departure from equilibrium linear response.