Prieto-Rodríguez Irene, Prados Antonio, Plata Carlos A
Department of Physics, Ludwig-Maximilians-Universität München, Schellingstr. 4, D-80799 Munich, Germany.
Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, Spain.
Entropy (Basel). 2025 Jan 15;27(1):72. doi: 10.3390/e27010072.
Heat engines transform thermal energy into useful work, operating in a cyclic manner. For centuries, they have played a key role in industrial and technological development. Historically, only gases and liquids have been used as working substances, but the technical advances achieved in recent decades allow for expanding the experimental possibilities and designing engines operating with a single particle. In this case, the system of interest cannot be addressed at a macroscopic level and their study is framed in the field of stochastic thermodynamics. In the present work, we study mesoscopic heat engines built with a Brownian particle submitted to harmonic confinement and immersed in a fluid acting as a thermal bath. We design a Stirling-like heat engine, composed of two isothermal and two isochoric branches, by controlling both the stiffness of the harmonic trap and the temperature of the bath. Specifically, we focus on the irreversible, non-quasi-static case-whose finite duration enables the engine to deliver a non-zero output power. This is a crucial aspect, which enables the optimisation of the thermodynamic cycle by maximising the delivered power-thereby addressing a key goal at the practical level. The optimal driving protocols are obtained by using both variational calculus and optimal control theory tools. Furthermore, we numerically explore the dependence of the maximum output power and the corresponding efficiency on the system parameters.
热机以循环方式将热能转化为有用功。几个世纪以来，它们在工业和技术发展中发挥了关键作用。从历史上看，只有气体和液体被用作工作物质，但近几十年来取得的技术进步使得扩大实验可能性并设计以单个粒子运行的发动机成为可能。在这种情况下，感兴趣的系统无法在宏观层面上进行研究，对它们的研究被纳入随机热力学领域。在本工作中，我们研究了由一个受简谐约束并浸没在作为热浴的流体中的布朗粒子构成的介观热机。我们通过控制简谐陷阱的刚度和热浴的温度，设计了一种类似斯特林热机的热机，它由两个等温分支和两个等容分支组成。具体而言，我们关注不可逆、非准静态的情况——其有限持续时间使发动机能够输出非零功率。这是一个关键方面，它能够通过最大化输出功率来优化热力学循环——从而在实际层面上实现一个关键目标。通过使用变分法和最优控制理论工具获得了最优驱动协议。此外，我们通过数值方法探索了最大输出功率和相应效率对系统参数的依赖性。
