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Active Brownian particles (ABPs) and Run-and-Tumble particles (RTPs) bothself-propel at fixed speed $v$ along a body-axis ${\bf u}$ that reorientseither through slow angular diffusion (ABPs) or sudden complete randomisation(RTPs). We compare the physics of these two model systems both at microscopicand macroscopic scales. Using exact results for their steady-state distributionin the presence of external potentials, we show that they both admit the sameeffective equilibrium regime perturbatively that breaks down for strongerexternal potentials, in a model-dependent way. In the presence of collisionalrepulsions such particles slow down at high density: their propulsive effort isunchanged, but their average speed along ${\bf u}$ becomes $v(\rho) < v$. Afruitful avenue is then to construct a mean-field description in whichparticles are ghost-like and have no collisions, but swim at a variable speed$v$ that is an explicit function or functional of the density $\rho$. We givenumerical evidence that the recently shown equivalence of the fluctuatinghydrodynamics of ABPs and RTPs in this case, which we detail here, extends tomicroscopic models of ABPs and RTPs interacting with repulsive forces.

Active Brownian Particles and Run-and-Tumble Particles: a Comparative Study