  We analyse and interpret the effects of breaking detailed balance on the
convergence to equilibrium of conservative interacting particle systems and
their hydrodynamic scaling limits. For finite systems of interacting particles,
we review existing results showing that irreversible processes converge faster
to their steady state than reversible ones. We show how this behaviour appears
in the hydrodynamic limit of such processes, as described by macroscopic
fluctuation theory, and we provide a quantitative expression for the
acceleration of convergence in this setting. We give a geometrical
interpretation of this acceleration, in terms of currents that are
\emph{antisymmetric} under time-reversal and orthogonal to the free energy
gradient, which act to drive the system away from states where (reversible)
gradient-descent dynamics result in slow convergence to equilibrium.
