Local master equations are a widespread tool to model open quantum systems, especially in the context of many-body systems. These equations, however, are believed to lead to thermodynamic anomalies and violation of the laws of thermodynamics. In contrast, here we rigorously prove that local master equations are consistent with thermodynamics and its laws without resorting to a microscopic model, as done in previous works. In particular, we consider a quantum system in contact with multiple baths and identify the relevant contributions to the total energy, heat currents, and entropy production rate. We show that the second law of thermodynamics holds when one considers the proper expression we derive for the heat currents. We confirm the results for the quantum heat currents by using a heuristic argument that connects the quantum probability currents with the energy currents, using an analogous approach as in classical stochastic thermodynamics. We finally use our results to investigate the thermodynamic properties of a set of quantum rotors operating as thermal devices and show that a suitable design of three rotors can work as an absorption refrigerator or a thermal rectifier. For the machines considered here, we also perform an optimization of the system parameters using an algorithm of reinforcement learning.

中文翻译：

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量子热力学一致的局部主方程

局部主方程是建模开放量子系统的广泛工具，尤其是在多体系统的情况下。但是，这些方程被认为会导致热力学异常并违反热力学定律。相反，在这里，我们严格地证明了局部主方程与热力学及其定律是一致的，而无需像以前的工作那样采用微观模型。特别是，我们考虑了与多个镀液接触的量子系统，并确定了对总能量，热流和熵产生率的相关贡献。我们表明，当人们考虑我们为热流得出的正确表达式时，热力学第二定律成立。我们使用类似于经典随机热力学的方法，通过将量子概率电流与能量流联系起来的启发式论证，来确认量子热电流的结果。我们最终使用我们的结果来研究一组用作热装置的量子转子的热力学性质，并表明三个转子的合适设计可以用作吸收式制冷机或热整流器。对于此处考虑的机器，我们还使用强化学习算法对系统参数进行了优化。我们最终使用我们的结果来研究一组用作热装置的量子转子的热力学性质，并表明三个转子的合适设计可以用作吸收式制冷机或热整流器。对于此处考虑的机器，我们还使用强化学习算法对系统参数进行了优化。我们最终使用我们的结果来研究一组用作热装置的量子转子的热力学性质，并表明三个转子的合适设计可以用作吸收式制冷机或热整流器。对于此处考虑的机器，我们还使用强化学习算法对系统参数进行了优化。