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We study the photo-assisted noise generated by time-dependent or randomsources and transmission amplitudes. We show that it obeys a perturbativenon-equilibrium fluctuation relation that fully extends the lateral-bandtransmission picture in terms of many-body correlated states. This relationholds in non-equilibrium strongly correlated systems such as the integer orfractional quantum Hall regime as well as in quantum circuits formed by anormal or Josephson junctions strongly coupled to an electromagneticenvironment, with a possible temperature bias. We then show that thephoto-assisted noise is universally super-poissonian, giving an alternative toa theorem by L. Levitov {\it et al} which states that an ac voltage increasesthe noise. Restricted to a linear dc current, we show that the latter does notapply to a non-linear superconducting junction. Then we characterize minimalexcitations in non-linear conductors by ensuring a poissonian photo-assistednoise, and show that these can carry a non-trivial charge value in thefractional quantum Hall regime. We also propose methods for shot noisespectroscopy and for a robust determination of the fractional charge which ismore advantageous than those we have proposed previously and implementedexperimentally.

AC driven strongly correlated quantum circuits and Hall edge states: Unified photo-assisted noise and revisited minimal excitations