  We consider strongly correlated quantum circuits where a dc drive is added on
top of an initial out-of-equilibrium (OE) stationary state. Within a
perturbative approach, we derive unifying OE fluctuation relations for high
frequency current noise, shown to be completely determined by zero-frequency
noise and dc current. We apply them to the fractional quantum Hall effect at
arbitrary incompressible filling factors, driven by OE sources, without
knowledge of the underlying model. We show that such OE relations provide
robust methods for an unambiguous determination of the fractional charge or of
key interaction parameters entering in the exploration of anyonic statistics
within an anyon collider.
