Including phonon-assisted inelastic process in thermoelectric devices is able
to enhance the performance of nonequilibrium work extraction. In this work, we
demonstrate that inelastic phonon-thermoelectric devices have a fertile
functionality diagram, where particle current and phononic heat currents are
coupled and fueled by chemical potential difference. Such devices can
simultaneously perform multiple tasks, e.g., heat engines, refrigerators, and
heat pumps. Guided by the entropy production, we mainly study the efficiencies
and coefficients of performance of multitask quantum thermal machines, where
the roles of the inelastic scattering process and multiple biases in
multiterminal setups are emphasized. Specifically, in a three-terminal
double-quantum-dot setup with a tunable gate, we show that it efficiently
performs two useful tasks due to the phonon-assisted inelastic process.
Moreover, the cooperation between the longitudinal and transverse
thermoelectric effects in the three-terminal thermoelectric systems leads to
markedly improved performance of the thermal machines. While for the
four-terminal four-quantum-dot thermoelectric setup, we find that additional
thermodynamic affinity furnishes the system with both enriched functionality
and enhanced efficiency. Our work provides insights into optimizing
phonon-thermoelectric devices.Comment: 14 pages, 7 figure