“…Since the last century, with the maturity of quantum theory and its related technologies, people started to pay attention to the performance of quantum heat engines working in micro-scale within the framework of quantum thermodynamics [ 4 , 5 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 ]. Series of the quantum effect, such as coherence, entanglement, quantum phase transition, etc., of the working substance or heat source have been studied to realize better heat engines [ 13 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 ]. On the other hand, with the development of non-equilibrium thermodynamics [ 2 , 3 , 28 ], the optimization of actual heat engines under the framework of finite-time thermodynamics attracted a wide range of attention [ 29 , 30 , 31 , 32 , 33 ].…”