  The electrical and heat currents flowing through a quantum dot are calculated
in the presence of a time-modulated gate voltage with the help of the
out-of-equilibrium Green function technique. From the first harmonics of the
currents, we extract the electrical and thermoelectrical trans-admittances and
ac-conductances. Next, by a careful comparison of the ac-conductances with the
finite-frequency electrical and mixed electrical-heat noises, we establish the
fluctuation-dissipation relations linking these quantities, which are thus
generalized out-of-equilibrium for a quantum system. It is shown that the
electrical ac-conductance associated to the displacement current is directly
linked to the electrical noise summed over reservoirs, whereas the relation
between the thermoelectrical ac-conductance and the mixed noise contains an
additional term proportional to the energy step that the electrons must
overcome when traveling through the junction. A numerical study reveals however
that a fluctuation-dissipation relation involving a single reservoir applies
for both electrical and thermoelectrical ac-conductances when the frequency
dominates over the other characteristic energies.
