Unifying hydrodynamic theory for motility-regulated active matter: from single particles to interacting polymers

TL;DR

This paper develops a hydrodynamic theory for active matter with spatially-regulated motility, revealing a new phase separation called anti-MIPS where dense regions are more active, applicable from particles to polymers.

Contribution

It introduces a unified hydrodynamic framework for motility-regulated active systems, including a novel anti-MIPS phase for active polymers with internal structure.

Findings

Derived a hydrodynamic model capturing orientation autocorrelation effects.

Identified anti-MIPS, a phase where dense regions have higher activity.

Demonstrated the theory's applicability from single particles to complex polymers.

Abstract

Understanding how microscopic motility shapes emergent collective behaviors is a challenging task in active matter, especially when self-propulsion is regulated by external cues or via quorum-sensing interactions. To address this problem, we derive a closed hydrodynamics for scalar active matter with spatially-regulated motility, under general hypotheses for the microscopic dynamics of the particles' orientations. We show that, at large scales, the contribution of the latter is entirely captured by the autocorrelation tensor of the orientations. This allows us to establish a macroscopic equivalence within a broad class of motility-regulated active systems, from single particles to active polymers. Our formalism allows us to reveal a new form of motility-induced phase separation for quorum-sensing active polymers, which we term anti-MIPS, where dense phases exhibit enhanced activity relative to dilute regions. Our theory shows that anti-MIPS generically arises for motility-regulated agents with internal structure, uncovering the existence of several distinct transition pathways.