Time-reversal symmetry breaking and emergence in driven-dissipative Ising models

TL;DR

This paper demonstrates that driven-dissipative Ising models break fluctuation-dissipation relations and time-reversal symmetry at criticality, challenging the notion of effective thermal behavior in such non-equilibrium systems.

Contribution

It reveals that both FDR and TRS are broken at critical points in driven-dissipative Ising models, with modified relations still holding, and TRS remains broken even with weak dissipation.

Findings

FDR and TRS are broken at criticality in these models

Modified FDR and TRS relations still hold with significant consequences

TRS remains broken even in the weakly-dissipative limit at criticality

Abstract

Fluctuation-dissipation relations (FDRs) and time-reversal symmetry (TRS), two pillars of statistical mechanics, are both broken in generic driven-dissipative systems. These systems rather lead to non-equilibrium steady states far from thermal equilibrium. Driven-dissipative Ising-type models, however, are widely believed to exhibit effective thermal critical behavior near their phase transitions. Contrary to this picture, we show that both the FDR and TRS are broken even macroscopically at, or near, criticality. This is shown by inspecting different observables, both even and odd operators under time-reversal transformation, that overlap with the order parameter. Remarkably, however, a modified form of the FDR as well as TRS still holds, but with drastic consequences for the correlation and response functions as well as the Onsager reciprocity relations. Finally, we find that, at criticality, TRS remains broken even in the weakly-dissipative limit.