“…The self-contained thermal devices were originally proposed as refrigerators to cool the cold bath [ 12 , 13 , 14 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 ], or as thermal engines to extract work [ 46 , 47 ]. Later, they were widely extended to a variety of cases, including the different interaction mechanisms, or for achieving various functions, such as heat current amplification [ 9 , 24 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 ], thermal rectification [ 19 , 20 , 21 , 54 , 55 , 56 , 57 , 58 , 59 , 60 ], thermal batteries [ 61 , 62 , 63 ], and thermometers [ 64 , 65 , 66 ]. It is a quite fundamental question for quantum thermodynamics as to...…”