Absence of dissipation in trajectory ensembles biased by currents

We consider biased ensembles of trajectories associated with large deviations of currents in equilibrium systems. The biased ensembles are characterised by non-zero currents and lack the time-reversal symmetry of the equilibrium state, but we show that they retain a generalised time-reversal symmetry, involving a spatial transformation that inverts the current. This means that these ensembles lack dissipation. Hence, they differ significantly from non-equilibrium steady states where currents are induced by external forces. One consequence of this result is that maximum entropy assumptions (MaxEnt/MaxCal), widely used for modelling thermal systems away from equilibrium, have quite unexpected implications, including apparent superfluid behaviour in a classical model of shear flow.