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We examine the efficiency of an effective two-terminal thermoelectric deviceunder broken time-reversal symmetry. The setup is derived from a three-terminalthermoelectric device comprising a thermal terminal and two electroniccontacts, under a magnetic field. We find that breaking time-reversal symmetryin the presence of the inelastic electron-phonon processes can significantlyenhance the figure of merit for delivering electric power by supplying heatfrom a phonon bath, beyond the one for producing the electric power byinvesting thermal power from the electronic heat current. The efficiency ofsuch a device is bounded by the non-negativity of the entropy production of theoriginal three-terminal junction. The efficiency at maximal power can be quiteclose to the Carnot efficiency, but then the electric power vanishes.

Efficiency bounds on thermoelectric transport in magnetic fields: The role of inelastic processes