Predictive local field theory for interacting active Brownian spheres in two spatial dimensions

TL;DR

This paper develops a comprehensive local field theory for active Brownian particles in two dimensions, accurately predicting phase separation and providing explicit coefficients, bridging phenomenological models and detailed particle dynamics.

Contribution

It introduces a rigorous coarse-grained local field theory that includes infinite-order derivatives, unifies existing models, and offers explicit analytical expressions for key parameters.

Findings

Predicts motility-induced phase separation onset.

Provides analytical spinodal expression matching simulations.

Yields an accurate critical point consistent with literature.

Abstract

We present a predictive local field theory for the nonequilibrium dynamics of interacting active Brownian particles with a spherical shape in two spatial dimensions. The theory is derived by a rigorous coarse-graining starting from the Langevin equations that describe the trajectories of the individual particles. For maximal accuracy and generality of the theory, it includes configurational order parameters and derivatives up to infinite order. In addition, we discuss possible approximations of the theory and present reduced models that are easier to apply. We show that our theory contains popular models such as Active Model B + as special cases and that it provides explicit expressions for the coefficients occurring in these and other, often phenomenological, models. As a further outcome, the theory yields an analytical expression for the density-dependent mean swimming speed of the particles. To demonstrate an application of the new theory, we analyze a simple reduced model of the lowest nontrivial order in derivatives, which is able to predict the onset of motility-induced phase separation of the particles. By a linear stability analysis, an analytical expression for the spinodal corresponding to motility-induced phase separation is obtained. This expression is evaluated for the case of particles interacting repulsively by a Weeks-Chandler-Anderson potential. The analytical predictions for the spinodal associated with these particles are found to be in very good agreement with the results of Brownian dynamics simulations that are based on the same Langevin equations as our theory. Furthermore, the critical point predicted by our analytical results agrees excellently with recent computational results from the literature.