# Thermodynamic Bounds on Coherent Transport in Periodically Driven Conductors

## TL;DR

This paper develops a comprehensive thermodynamic theory for periodically driven coherent conductors, establishing bounds and relations that enhance understanding and optimization of quantum transport devices.

## Contribution

It introduces generalized thermodynamic bounds and relations applicable to coherent conductors under periodic driving, including strong bias and high frequency regimes.

## Key findings

- Derived generalized Onsager-Casimir relations.
- Proved thermodynamic bounds independent of system specifics.
- Established a quantum-aware thermodynamic uncertainty relation.

## Abstract

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.