Non-linear quantum critical dynamics and fluctuation-dissipation ratios far from equilibrium

•Critical Kondo destruction explains the unusual properties of quantum critical heavy fermion compounds.•We review the concept of effective temperatures in models of critical Kondo destruction.•We compare effective temperatures found near non-interacting and fully interacting fixed points.•A comparison with non-interacting quantum impurity models is presented.

Non-thermal correlations of strongly correlated electron systems and the far-from-equilibrium properties of phases of condensed matter have become a topical research area. Here, an overview of the non-linear dynamics found near continuous zero-temperature phase transitions within the context of effective temperatures is presented. In particular, we focus on models of critical Kondo destruction. Such a quantum critical state, where Kondo screening is destroyed in a critical fashion, is realized in a number of rare earth intermetallics. This raises the possibility of experimentally testing for the existence of fluctuation-dissipation relations far from equilibrium in terms of effective temperatures. Finally, we present an analysis of a non-interacting, critical reference system, the pseudogap resonant level model, in terms of effective temperatures and contrast these results with those obtained near interacting quantum critical points.