  Active baths are characterized by a non-Gaussian velocity distribution and a
quadratic dependence with active velocity $v_0$ of the kinetic temperature and
diffusion coefficient. While these results hold in over-damped 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 equilibrium-like behavior.
