  The second law of thermodynamics posits that in closed macroscopic systems
the rate of entropy production must be positive. However, small systems can
exhibit negative entropy production over short timescales, seemingly in
contradiction with this law. The fluctuation theorem quantitatively connects
these two limits, predicting that entropy producing trajectories become
exponentially dominant as the system size and measurement time are increased.
Here we explore the predictions of the fluctuation theorem for a fluid of
point-vortices, where the long-range interactions and existence of negative
absolute temperature states provide an intriguing test bed for the theorem. Our
results suggest that while the theorem broadly holds even at negative absolute
temperatures, the long-range interactions inherent to the vortex matter lead to
anomalously large entropy production over short time intervals. The predictions
of the fluctuation theorem are only fully recovered when sufficient noise is
introduced to the dynamics to overwhelm the vortex-vortex interactions.
