Fluctuating hydrodynamics of active particles interacting via taxis and quorum sensing: static and dynamics

In this article we derive and test the fluctuating hydrodynamic description of active particles interacting via taxis and quorum sensing, both for mono-disperse systems and for mixtures of co-existing species of active particles. We compute the average steady-state density profile in the presence of spatial motility regulation, as well as the structure factor and intermediate scattering function for interacting systems. By comparing our predictions to microscopic numerical simulations, we show that our fluctuating hydrodynamics correctly predicts the large-scale static and dynamical properties of the system. We also discuss how the theory breaks down when structures emerge at scales smaller or comparable to the persistence length of the particles. When the density field is the unique hydrodynamic mode of the system, we show that active Brownian particles, run-and-tumble particles and active Ornstein-Uhlenbeck particles, interacting via quorum-sensing or chemotactic interactions, display undistinguishable large-scale properties. This form of universality implies an interesting robustness of the predicted physics but also that large-scale observations of patterns are insufficient to assess their microscopic origins. In particular, our results predict that chemotaxis-induced and motility-induced phase separation should share strong qualitative similarities at the macroscopic scale.