Absence of dissipation in trajectory ensembles biased by currents

TL;DR

This paper shows that certain biased trajectory ensembles with non-zero currents in equilibrium systems maintain a generalized time-reversal symmetry and lack dissipation, challenging traditional views on non-equilibrium steady states.

Contribution

It reveals that biased ensembles with currents preserve a generalized symmetry and do not dissipate, contrasting with typical non-equilibrium states, and explores implications for MaxEnt/MaxCal models.

Findings

Biased ensembles retain a generalized time-reversal symmetry.

These ensembles lack dissipation despite having non-zero currents.

MaxEnt/MaxCal models can imply superfluid-like behavior in classical shear flow.

Abstract

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.