  A geometrically polar granular rod confined in 2-D geometry, subjected to a
sinusoidal vertical oscillation, undergoes noisy self-propulsion in a direction
determined by its polarity. When surrounded by a medium of crystalline
spherical beads, it displays substantial negative fluctuations in its velocity.
We find that the large deviation function (LDF) for the normalized velocity is
strongly non-Gaussian with a kink at zero velocity, and that the antisymmetric
part of the LDF is linear, resembling the fluctuation relation known for
entropy production, even when the velocity distribution is clearly
non-Gaussian. We extract an analogue of the phase space contraction rate and
find that it compares well with an independent estimate based on the
persistence of forward and reverse velocities.
