“…Combining optimal control theory and FTT theory, Erdman et al [ 49 ] optimized the two-level HE by a fast Otto-cycle and derived the closed formula of MPO and the corresponding efficiency. In addition, more genres of WM have been considered and studied recently [ 50 , 51 , 52 , 53 , 54 , 55 , 56 ]. To date, the research on quantum thermodynamic cycles has mainly focused on the optimal path and optimal performance in one-stage HEs, including Carnot HEs [ 37 , 38 , 39 , 44 , 55 , 56 , 57 , 58 ], Brayton HEs [ 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 ], Otto HEs [ 46 , 67 , 68 , 69 , 70 , 71 , 72 , 73 , 74 , 75 , 76 ], Stirling HEs [ 45 , 77 , 78 , 79 , 80 , 81 ], and other HEs and systems [ 43 , 82 , 83 , 84 , 85 , 86 , 87 ].…”