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