# Brownian systems with spatially inhomogeneous activity

## TL;DR

This paper extends the Green-Kubo method to analyze inhomogeneous activity in Brownian systems, accurately predicting spatial variations in orientation and density, validated by simulations.

## Contribution

It introduces a generalized Green-Kubo approach for inhomogeneous active particles and combines it with a Gaussian approximation and density functional theory.

## Key findings

- Accurate analytical expression for average orientation.
- Good agreement between theory and Brownian dynamics simulations.
- Effective prediction of spatial density distribution.

## Abstract

We generalize the Green-Kubo approach, previously applied to bulk systems of spherically symmetric active particles [J. Chem. Phys. 145, 161101 (2016)], to include spatially inhomogeneous activity. The method is applied to predict the spatial dependence of the average orientation per particle and the density. The average orientation is given by an integral over the self-part of the van Hove function and a simple Gaussian approximation to this quantity yields an accurate analytical expression. Taking this analytical result as input to a dynamic density functional theory approximates the spatial dependence of the density in good agreement with simulation data. All theoretical predictions are validated using Brownian dynamics simulations.