Topological superconductors represent a fruitful playing ground for fundamental research as well as for potential applications in fault-tolerant quantum computing. Especially Josephson junctions based on topological superconductors remain intensely studied, both theoretically and experimentally. The characteristic property of these junctions is their 4π-periodic ground-state fermion parity in the superconducting phase difference. Using such topological Josephson junctions, we introduce the concept of a topological Josephson heat engine. We discuss how this engine can be implemented as a Josephson–Stirling cycle in topological superconductors, thereby illustrating the potential of the intriguing and fruitful marriage between topology and coherent thermodynamics. It is shown that the Josephson–Stirling cycle constitutes a highly versatile thermodynamic machine with different modes of operation controlled by the cycle temperatures. Finally, the thermodynamic cycle reflects the hallmark 4π-periodicity of topological Josephson junctions and could therefore be envisioned as a complementary approach to test topological superconductivity.

拓扑超导体为基础研究以及容错量子计算的潜在应用提供了丰硕的基础。特别是基于拓扑超导体的约瑟夫森结，无论在理论上还是实验上都得到了深入的研究。这些结的特征是它们的4π超导相差中的-周期基态费米子平价。使用这种拓扑约瑟夫森结，我们介绍了拓扑约瑟夫森热机的概念。我们讨论了该引擎如何在拓扑超导体中实现为约瑟夫森-斯特林循环，从而说明了拓扑与相干热力学之间有趣而富有成果的结合的潜力。结果表明，约瑟夫森-斯特林循环构成了一种高度通用的热力学机器，具有受循环温度控制的不同操作模式。最后，热力循环反映了标志4 π拓扑约瑟夫逊结的-periodicity，因此可以设想为一个互补的方法进行测试拓扑超导性。