  We examine the efficiency of an effective two-terminal thermoelectric device
under broken time-reversal symmetry. The setup is derived from a three-terminal
thermoelectric device comprising a thermal terminal and two electronic
contacts, under a magnetic field. We find that breaking time-reversal symmetry
in the presence of the inelastic electron-phonon processes can significantly
enhance the figure of merit for delivering electric power by supplying heat
from a phonon bath, beyond the one for producing the electric power by
investing thermal power from the electronic heat current. The efficiency of
such a device is bounded by the non-negativity of the entropy production of the
original three-terminal junction. The efficiency at maximal power can be quite
close to the Carnot efficiency, but then the electric power vanishes.
