  We develop a theory of tunneling spectroscopy of interacting electrons in a
non-equilibrium quantum wire coupled to reservoirs. The problem is modelled as
an out-of-equilibrium Luttinger liquid with spatially dependent interaction.
The interaction leads to the renormalization of the tunneling density of
states, as well as to the redistribution of electrons over energies. Energy
relaxation is controlled by plasmon scattering at the boundaries between
regions with different interaction strength, and affects the distribution
function of electrons in the wire as well as that of electrons emitted from the
interacting regions into non-interacting electrodes.
