  We study a passive probe immersed in a fluid of active particles. Despite the
system's non-equilibrium nature, the trajectory of the probe does not exhibit
non-equilibrium signatures: its velocity distribution remains Gaussian, the
second fluctuation dissipation theorem is not fundamentally violated, and the
motion does not indicate breaking of time reversal symmetry. To tell that the
probe is out of equilibrium requires examination of its behavior in tandem with
that of the active fluid: the kinetic temperature of the probe does not
equilibrate to that of the surrounding active particles. As a strategy to
diagnose non-equilibrium from probe trajectories alone, we propose to examine
their response to a small perturbation which reveals a non-equilibrium
signature through a violation of the first fluctuation dissipation theorem.
