Thermoelectric transport is traditionally analyzed using relations imposed by time-reversal symmetry, ranging from Onsager's results to fluctuation relations in counting statistics. In this paper, we show that a recently discovered duality relation for fermionic systems-deriving from the fundamental fermion-parity superselection principle of quantum many-particle systems-provides new insights into thermoelectric transport. Using a master equation, we analyze the stationary charge and heat currents through a weakly coupled, but strongly interacting single-level quantum dot subject to electrical and thermal bias. In linear transport, the fermion-parity duality shows that features of thermoelectric response coefficients are actually dominated by the average and fluctuations of the charge in a dual quantum dot system, governed by attractive instead of repulsive electron-electron interaction. In the nonlinear regime, the duality furthermore relates most transport coefficients to much better understood equilibrium quantities. Finally, we naturally identify the fermion-parity as the part of the Coulomb interaction relevant for both the linear and nonlinear Fourier heat. Altogether, our findings hence reveal that next to time-reversal, the duality imposes equally important symmetry restrictions on thermoelectric transport. As such, it is also expected to simplify computations and clarify the physical understanding for more complex systems than the simplest relevant interacting nanostructure model studied here.

We perform a detailed study of the effect of finite bias and magnetic field on the tunneling‐induced decay of the state of a quantum dot by applying a recently discovered general duality [Phys. Rev. B 93, 81411 (2016)]. This duality provides deep physical insight into the decay dynamics of electronic open quantum systems with strong Coulomb interaction. It associates the amplitudes of decay eigenmodes of the actual system to the eigenmodes of a so‐called dual system with attractive interaction. Thereby, it predicts many surprising features in the transient transport and its dependence on experimental control parameters: the attractive interaction of the dual model shows up as sharp features in the amplitudes of measurable time‐dependent currents through the actual repulsive system. In particular, for interacting quantum dots, the time‐dependent heat current exhibits a decay mode that dissipates the interaction energy and that is tied to the fermion parity of the system. We show that its decay amplitude has an unexpected gate‐voltage dependence that is robust up to sizable bias voltages and then bifurcates, reflecting that the Coulomb blockade is lifted in the dual system. Furthermore, combining our duality relation with the known Iche‐duality, we derive new symmetry properties of the decay rates as a function of magnetic field and gate voltage. Finally, we quantify charge‐ and spin‐mode mixing due to the magnetic field using a single mixing parameter.

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