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Periodically driven coherent conductors provide a universal platform for thedevelopment of quantum transport devices. Here, we lay down a comprehensivetheory to describe the thermodynamics of these systems. We first focus onmoderate thermo-electrical biases and low driving frequencies. For this linearresponse regime, we establish generalized Onsager-Casimir relations and anextended fluctuation-dissipation theorem. Furthermore, we derive a family ofthermodynamic bounds proving that any local matter or heat current puts anon-trivial lower limit on the overall dissipation rate of a coherent transportprocess. These bounds do not depend on system-specific parameters, are robustagainst dephasing and involve only experimentally accessible quantities. Theythus provide powerful tools to optimize the performance of mesoscopic devicesand for thermodynamic inference, as we demonstrate by working out threespecific applications. We then show that physically transparent extensions ofour bounds hold also for strong biases and high frequencies. These generalizedbounds imply a thermodynamic uncertainty relation that fully accounts forquantum effects and periodic driving. Moreover, they lead to a universal andoperationally accessible bound on entropy production that can be readily usedfor thermodynamic inference and device engineering far from equilibrium.Connecting a broad variety of topics that range from thermodynamic geometryover thermodynamic uncertainty relations to quantum engineering, our workprovides a unifying thermodynamic theory of coherent transport that can betested and utilized with current technologies.

Thermodynamic Bounds on Coherent Transport in Periodically Driven Conductors