When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation

TL;DR

This paper demonstrates that active Brownian particles and run-and-tumble particles are equivalent under certain conditions, and both can undergo motility-induced phase separation driven solely by their motility parameters, highlighting a universal aspect of active matter.

Contribution

The study establishes conditions under which ABPs and RTPs are mathematically equivalent and explores the implications for phase separation in active systems.

Findings

ABPs and RTPs are equivalent when motility depends only on density.

Both systems can phase separate without attractive forces.

Equivalence breaks down when motility depends on orientation.

Abstract

Active Brownian particles (ABPs, such as self-phoretic colloids) swim at fixed speed $v$ along a body-axis ${\bf u}$ that rotates by slow angular diffusion. Run-and-tumble particles (RTPs, such as motile bacteria) swim with constant $\u$ until a random tumble event suddenly decorrelates the orientation. We show that when the motility parameters depend on density $\rho$ but not on ${\bf u}$, the coarse-grained fluctuating hydrodynamics of interacting ABPs and RTPs can be mapped onto each other and are thus strictly equivalent. In both cases, a steeply enough decreasing $v(\rho)$ causes phase separation in dimensions $d=2,3$, even when no attractive forces act between the particles. This points to a generic role for motility-induced phase separation in active matter. However, we show that the ABP/RTP equivalence does not automatically extend to the more general case of $\u$-dependent motilities.