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We consider biased ensembles of trajectories associated with large deviationsof currents in equilibrium systems. The biased ensembles are characterised bynon-zero currents and lack the time-reversal symmetry of the equilibrium state,but we show that they retain a generalised time-reversal symmetry, involving aspatial transformation that inverts the current. This means that theseensembles lack dissipation. Hence, they differ significantly fromnon-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 fromequilibrium, have quite unexpected implications, including apparent superfluidbehaviour in a classical model of shear flow.

Absence of dissipation in trajectory ensembles biased by currents