Thermodynamics of precision for ac-driven strongly-correlated quantum devices in linear-response

We study thermoelectric transport in quantum nanoelectronics devices comprising arbitrary interacting fermionic degrees of freedom coupled to macroscopic source and drain leads. Charge and heat currents flow between the leads through the interacting nanostructure due to a temperature gradient and/or ac bias voltage. However, measurement precision depends on current fluctuations, which are in turn bounded by so-called thermodynamic uncertainty relations (TURs). For generic interacting systems, the Landauer-Buttiker formulas cannot be used, and so we resort to the Kubo formula in linear response, generalized to the ac-driven case. Using the Green's function formalism, we show that the TUR lower-bound is exactly satisfied in linear response only in the dc limit. We also uncover TURs involving the charge-heat cross-correlation noise. In terms of using quantum transport measurements in such a nanoelectronics device for metrology, we take as the simplest concrete example the interacting Anderson impurity model of a quantum dot system. For this model we calculate the quantum Fisher information, which provides a measure of distinguishability between density matrices perturbed by an ac voltage bias, and relate it to the ac electrical conductance. We also examine more heuristic measures of sensitivity for quantum thermometry and magnetometry, seeing boosted performance when quantum many-body effects and Kondo entanglement come into play at low temperatures.