  The Kubo fluctuation-dissipation theorem relates the current fluctuations of
a system in an equilibrium state with the linear AC-conductance. This theorem
holds also out of equilibrium provided that the system is in a stationary state
and that the linear conductance is replaced by the (dynamic) conductance with
respect to the non equilibrium state. We provide a simple proof for that
statement and then apply it in two cases. We first show that in an excess noise
measurement at zero temperature, in which the impedance matching is maintained
while driving a mesoscopic sample out of equilibrium, it is the nonsymmetrized
noise power spectrum which is measured, even if the bare measurement, i.e.
without extracting the excess part of the noise, obtains the symmetrized noise.
As a second application we derive a commutation relation for the two components
of fermionic or bosonic currents which holds in every stationary state and
which is a generalization of the one valid only for bosonic currents. As is
usually the case, such a commutation relation can be used e.g. to derive
Heisenberg uncertainty relationships among these current components.
