  We investigate the steady-state entropy production rate (EPR) in the
Hydrodynamic Vicsek Model (HVM) and Diffusive Flocking Model (DFM). Both models
display a transition from an isotropic gas to a polar liquid (flocking) phase,
in addition to traveling polar clusters and microphase-separation in the
miscibility gap. The phase diagram of the DFM, which may be considered an
extension of the HVM, contains additional structure at low densities where we
find a novel crystal phase in which a stationary hexagonal lattice of
high-density ridges surround low density valleys. From an assessment of the
scaling of the EPR at low noise, we uncover that the dynamics in this limit may
be organised into three main classes based on the dominant contribution. Truly
nonequilibrium dynamics is characterised by a divergent EPR in this limit, and
sustains global time-reversal symmetry (TRS) violating currents at zero noise.
On the other hand, marginally nonequilibrium and effectively equilibrium
dynamics have a finite EPR in this limit, and TRS is broken only at the level
of fluctuations. For the latter of these two cases, detailed balance is
restored in the small noise limit and we recover effective Boltzmann statistics
to lowest nontrivial order. We further demonstrate that the scaling of the EPR
may change depending on the dynamical variables that are tracked when it is
computed, and the protocol chosen for time-reversal. Results acquired from
numerical simulations of the dynamics confirm both the asymptotic scaling
relations we derive and our quantitative predictions.
