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We study a passive probe immersed in a fluid of active particles. Despite thesystem's non-equilibrium nature, the trajectory of the probe does not exhibitnon-equilibrium signatures: its velocity distribution remains Gaussian, thesecond fluctuation dissipation theorem is not fundamentally violated, and themotion does not indicate breaking of time reversal symmetry. To tell that theprobe is out of equilibrium requires examination of its behavior in tandem withthat of the active fluid: the kinetic temperature of the probe does notequilibrate to that of the surrounding active particles. As a strategy todiagnose non-equilibrium from probe trajectories alone, we propose to examinetheir response to a small perturbation which reveals a non-equilibriumsignature through a violation of the first fluctuation dissipation theorem.

Passive particle in an active bath: How can we tell it is out of equilibrium?