Quantum criticality far from equilibrium appears thermal

In their work, Ribeiro, Zamani, and Kirchner report on the study of a model system of unconventional quantum criticality both in thermal equilibrium and for current-carrying states beyond the linear-response regime. Quantum criticality refers to the behavior near continuous phase transitions at zero temperature. At zero temperature, vacuum fluctuations and thus quantum coherence become an integral part of the critical, i.e. scale invariant, fluctuation spectrum. Interestingly, it is found that all considered observables, including the dynamic order parameter susceptibility and the conductance, reproduce their equilibrium behavior when expressed in terms of an effective temperature. This effective temperature turns out to be the same for all the observables studied by the authors. Ribeiro and coworkers define the effective temperature through an extension of the fluctuation-dissipation theorem for the static part of the order parameter susceptibility. This leads to an effective temperature as the validity of the fluctuation-dissipation theorem is generally confined to the linear-response regime. The class of continuous quantum phase transitions that lack a classical counterpart, i.e. an entropy-driven phase transition occurring at a non-zero temperature, is commonly referred to as unconventional quantum criticality. How these findings will help classifying unconventional quantum criticality is subject of ongoing research.

Steady-State Dynamics and Effective Temperature for a Model
of Quantum Criticality in an Open System
P. Ribeiro, F. Zamani, & S.Kirchner
PRL 115, 220602 (2015)