  We investigate nonequilibrium effects in the transport of interacting
electrons in quantum conductors, proposing the nonlocal thermoelectric response
as a direct indicator of the presence of interactions, nonthermal states and
the effect of correlations. This is done by assuming a quantum Hall setup where
two channels (connected to reservoirs at different temperatures) co-propagate
for a finite distance, such that a thermoelectrical response is only expected
if the electron-electron interaction mediates heat exchange between the
channels. This way, the nonlocal Seebeck response measures the interaction
strength. Considering zero-range interactions, we solve the charge and energy
currents and noises of a non-equilibrium integrable interacting system,
determining the universal interaction-dependent length scale of energy
equilibration. Further, a setup with two controllable quantum point contacts
allows thermoelectricity to monitor the interacting system thermalisation as
well as the fundamental role of cross-correlations in the heat exchange at
intermediate length scales.
