The thermodynamic cost of driving quantum systems by their boundaries

TL;DR

This paper develops a thermodynamic framework for quantum systems actively driven at their boundaries, analyzing heat, work, and entropy production, and demonstrating how such systems can function as engines, heaters, or refrigerators.

Contribution

It introduces a boundary-driven Lindblad equation framework for quantum thermodynamics, extending existing models to actively controlled systems and analyzing their thermodynamic behavior.

Findings

XX chain relaxes to thermodynamic equilibrium with a single heat bath.

XY chain does not relax to equilibrium under the same conditions.

XX chain with two heat baths can operate as an engine, heater, or refrigerator.

Abstract

The laws of thermodynamics put limits to the efficiencies of thermal machines. Analogues of these laws are now established for quantum engines weakly and passively coupled to the environment providing a framework to find improvements to their performance. Systems whose interaction with the environment is actively controlled do not fall in that framework. Here we consider systems actively and locally coupled to the environment, evolving with a so-called boundary-driven Lindblad equation. Starting from a unitary description of the system plus the environment we simultaneously obtain the Lindblad equation and the appropriate expressions for heat, work and entropy-production of the system extending the framework for the analysis of new, and some already proposed, quantum heat engines. We illustrate our findings in spin 1/2 chains and explain why an XX chain coupled in this way to a single heat bath relaxes to thermodynamic-equilibrium while and XY chain does not. Additionally, we show that an XX chain coupled to a left and a right heat baths behaves as a quantum engine, a heater or refrigerator depending on the parameters, with efficiencies bounded by Carnot efficiencies.