The smallest absorption refrigerator: the thermodynamics of a system with quantum local detailed balance

TL;DR

This paper explores the thermodynamics of a quantum system interacting with multiple baths, deriving a Lindblad equation from a microscopic model, and introduces a quantum local detailed balance condition relevant for small absorption refrigerators.

Contribution

It derives a Lindblad equation from a repeated interaction model and establishes a quantum local detailed balance condition for systems with non-Gibbs equilibrium states.

Findings

External power is needed to reach steady state.

The system functions autonomously once in steady state.

Thermodynamics can be described by system properties under certain conditions.

Abstract

We study the thermodynamics of a quantum system interacting with different baths in the repeated interaction framework. In an appropriate limit, the evolution takes the Lindblad form and the corresponding thermodynamic quantities are determined by the state of the full system plus baths. We identify conditions under which the thermodynamics of the open system can be described only by system properties and find a quantum local detailed balance condition with respect to an equilibrium state that may not be a Gibbs state. The three-qubit refrigerator introduced in [N. Linden, S. Popescu and P. Skrzypczyk, Phys. Rev. Lett.$ {\bf 105}$, 130401 (2010)] is an example of such a system. From a repeated interaction microscopic model we derive the Lindblad equation that describes its dynamics and discuss its thermodynamic properties for arbitrary values of the internal coupling between the qubits. We find that external power (proportional to the internal coupling strength) is required to bring the system to its steady state, but once there, it works autonomously as discussed in [N. Linden, S. Popescu and P. Skrzypczyk, Phys. Rev. Lett. ${\bf 105}$, 130401 (2010)].