When an active bath behaves as an equilibrium one

Active scalar baths consisting of active Brownian particles are characterized by a non-Gaussian velocity distribution, a kinetic temperature, and a diffusion coefficient that scale with the square of the active velocity $v_0$. While these results hold in overdamped active systems, inertial effects lead to normal velocity distributions, with kinetic temperature and diffusion coefficient increasing as $\sim v_0^{\alpha }$ with $1<\alpha <2$. Remarkably, the late-time diffusivity and mobility decrease with mass. Moreover, we show that the equilibrium Einstein relation is asymptotically recovered with inertia. In summary, the inertial mass restores an equilibriumlike behavior.