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For steady-state autonomous absorption refrigerators operating in the linearresponse regime, we show that there exists a hierarchy between the relativefluctuation of currents for cold, hot, and work terminals. Our proof requiresthe Onsager's reciprocity relation along with the refrigeration condition thatsets the direction of the mean currents for each terminal. As a consequence,the universal bounds on the mean cooling power, obtained following thethermodynamic uncertainty relations, receive a hierarchy. Interestingly, withinthis hierarchy, the tightest bound is given in terms of the work currentfluctuation. Furthermore, the relative uncertainty hierarchy hands overadditional bounds that can be tighter than the bounds obtained from thethermodynamic uncertainty relations. Interestingly, all of these boundssaturate in the tight-coupling limit. We test the validity of our results fortwo paradigmatic absorption refrigerator models: (i) a four-level working fluidand (ii) a two-level working fluid, operating, respectively, in the weak(additive) and in the strong (multiplicative) system-bath interaction regime.

Universal bounds on cooling power and cooling efficiency for autonomous absorption refrigerators