Odd Dynamics of Passive Objects in a Chiral Active Bath

When submerged in a chiral active bath, a passive object becomes a spinning ratchet imbued with odd transport properties. We present the most general Langevin dynamics for a rigid body in a chiral active bath, in the adiabatic limit of large object mass. For rotationally symmetric objects, odd diffusion and odd mobility are connected by an Einstein relation, that we show numerically to break down outside the adiabatic limit. As the object symmetry decreases, its dynamics becomes increasingly irreversible: A massive disk exhibits an effective equilibrium dynamics, while a rod admits distinct translational and rotational temperatures, and a wedge is fully irreversible. Conversely, this departure from equilibrium can be read in universal far-field currents and density modulations of the bath, which we measure numerically and derive analytically.