Multiscale perturbative approach to active matter with motility regulation

Abstract

We present a coarse-graining method applicable to dry scalar active matter with motility regulation. Our approach, based on a multiscale perturbative expansion of the backward Kolmogorov equation, does not rely on any specific microscopic dynamics for the particles' orientations. Its generality allows us to address different forms of motility regulation, from space-dependent self-propulsion speed to taxis, and to extend the analysis to a class of non-Markovian orientational dynamics. Furthermore, we identify general conditions on the microscopic dynamics that ensure the existence of an effective large-scale equilibrium regime. When the latter are violated, our theoretical framework is able to quantitatively capture the emergence of large-scale particle currents. We directly apply our coarse-grained theory to several models of self-propelled agents, ranging from single particles to active polymers, and test our analytical predictions with numerical simulations. Finally, we show that our theory naturally extends to active matter with density-mediated interactions, such as quorum sensing, with potential applications to self-organizing soft materials.