  Collections of self-propelled particles that move persistently by
continuously consuming free energy are a paradigmatic example of active matter.
In these systems, unlike Brownian "hot colloids", the breakdown of detailed
balance yields a continuous production of entropy at steady state, even for an
ideal active gas. We quantify the irreversibility for a non-interacting active
particle in two dimensions by treating both conjugated and time-reversed
dynamics. By starting with underdamped dynamics, we identify a hidden rate of
entropy production required to maintain persistence and prevent the rapidly
relaxing momenta from thermalizing, even in the limit of very large friction.
Additionally, comparing two popular models of self-propulsion with identical
dissipation on average, we find that the fluctuations and large deviations in
work done are markedly different, providing thermodynamic insight into the
varying extents to which macroscopically similar active matter systems may
depart from equilibrium.
