  Periodically driven coherent conductors provide a universal platform for the
development of quantum transport devices. Here, we lay down a comprehensive
theory to describe the thermodynamics of these systems. We first focus on
moderate thermo-electrical biases and low driving frequencies. For this linear
response regime, we establish generalized Onsager-Casimir relations and an
extended fluctuation-dissipation theorem. Furthermore, we derive a family of
thermodynamic bounds proving that any local matter or heat current puts a
non-trivial lower limit on the overall dissipation rate of a coherent transport
process. These bounds do not depend on system-specific parameters, are robust
against dephasing and involve only experimentally accessible quantities. They
thus provide powerful tools to optimize the performance of mesoscopic devices
and for thermodynamic inference, as we demonstrate by working out three
specific applications. We then show that physically transparent extensions of
our bounds hold also for strong biases and high frequencies. These generalized
bounds imply a thermodynamic uncertainty relation that fully accounts for
quantum effects and periodic driving. Moreover, they lead to a universal and
operationally accessible bound on entropy production that can be readily used
for thermodynamic inference and device engineering far from equilibrium.
Connecting a broad variety of topics that range from thermodynamic geometry
over thermodynamic uncertainty relations to quantum engineering, our work
provides a unifying thermodynamic theory of coherent transport that can be
tested and utilized with current technologies.
