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We show that in mesoscopic four-terminal thermoelectric devices with twoelectrodes (the source and the drain) and two heat baths, inelastic scatteringprocesses can lead to unconventional thermoelectric transport. The source (orthe drain) can be cooled by passing a thermal current between the two heatbaths, with no net heat exchange between the heat baths and the electrodes.This effect, termed as cooling by heat current, is a mesoscopic heat drageffect. In addition, there is a transverse thermoelectric effect whereelectrical current and power can be generated by a transverse temperature bias(i.e., the temperature bias between the two heat baths). This transversethermoelectric effect, originates from inelastic scattering processes, may haveadvantages for improved figures of merit and power factor due to spatialseparation of charge and heat transport. We study the Onsager current-affinityrelations, the linear-response transport properties, and the transversethermoelectric figure of merit of the four-terminal thermoelectric devices forvarious system parameters. In addition, we investigate the efficiency and powerof the cooling by transverse current effect in both linear and nonlineartransport regimes. We also demonstrate that by exploiting the inelastictransport in the quantum-dot four-terminal systems, a type of Maxwell's demoncan be realized using nonequilibrium heat baths.

physical review. b./physical review. b

Unconventional four-terminal thermoelectric transport due to inelastic  transport: cooling by transverse current, transverse thermoelectric effect  and Maxwell demon