  We study the thermal and non-thermal steady state scaling functions and the
steady-state dynamics of a model of local quantum criticality. The model we
consider, i.e. the pseudogap Kondo model, allows us to study the concept of
effective temperatures near fully interacting as well as weak-coupling fixed
points. In the vicinity of each fixed point we establish the existence of an
effective temperature --different at each fixed point-- such that the
equilibrium fluctuation-dissipation theorem is recovered. Most notably,
steady-state scaling functions in terms of the effective temperatures coincide
with the equilibrium scaling functions. This result extends to higher
correlation functions as is explicitly demonstrated for the Kondo singlet
strength. The non-linear charge transport is also studied and analyzed in terms
of the effective temperature.
