# General linear thermodynamics for periodically driven systems with multiple reservoirs

## TL;DR

This paper develops a linear thermodynamics framework for Markov systems with periodic driving and multiple reservoirs, providing explicit formulas for thermodynamic quantities and verifying Onsager relations, with applications to quantum dots.

## Contribution

It introduces a comprehensive linear thermodynamics theory for periodically driven Markov systems, including explicit formulas and verification of Onsager relations, applicable to quantum systems with multiple reservoirs.

## Key findings

- Derived explicit formulas for thermodynamic quantities.
- Verified Onsager-Casimir reciprocal relations.
- Applied theory to a quantum dot system.

## Abstract

We derive a linear thermodynamics theory for general Markov dynamics with both steady-state and time-periodic drivings. Expressions for thermodynamic quantities, such as mechanical and chemical work, heat and entropy production are obtained in terms of equilibrium probability distribution and the drivings. The entropy production is derived as a bilinear function of thermodynamic forces and the associated fluxes. We derive explicit formulae for the Onsager coefficients and use them to verify the Onsager-Casimir reciprocal relations. Our results are illustrated on a periodically driven quantum dot in contact with two electron reservoirs and optimization protocols are discussed.