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

Active Brownian particles (ABPs, such as self-phoretic colloids) swim at fixed speed v along a body-axis 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 ρ but not on 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(ρ) 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