  The consistency with Onsager's theorem is examined for commonly used
perturbative approaches, such as the Redfield and second-order von Neumann
master equations, for thermoelectric transport through nanostructures. We study
a double quantum dot, which requires coherences between states for a correct
description, and we find that these perturbative approaches violate Onsager's
theorem. We show that the deviations from the theorem scale with the
lead-coupling strength in an order beyond the one considered systematically in
the respective approach.
