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We investigate nonequilibrium effects in the transport of interactingelectrons in quantum conductors, proposing the nonlocal thermoelectric responseas a direct indicator of the presence of interactions, nonthermal states andthe effect of correlations. This is done by assuming a quantum Hall setup wheretwo channels (connected to reservoirs at different temperatures) co-propagatefor a finite distance, such that a thermoelectrical response is only expectedif the electron-electron interaction mediates heat exchange between thechannels. This way, the nonlocal Seebeck response measures the interactionstrength. Considering zero-range interactions, we solve the charge and energycurrents and noises of a non-equilibrium integrable interacting system,determining the universal interaction-dependent length scale of energyequilibration. Further, a setup with two controllable quantum point contactsallows thermoelectricity to monitor the interacting system thermalisation aswell as the fundamental role of cross-correlations in the heat exchange atintermediate length scales.

Nonlocal thermoelectric detection of interaction and correlations in edge states