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Register a new userBounds on fluctuations for ensembles of quantum thermal machines
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We study universal aspects of fluctuations in an ensemble of noninteracting continuous quantum thermal machines in the steady state limit. Considering an individual machine, such as a refrigerator, in which relative fluctuations (and high order cumulants) of the cooling heat current to the absorbed heat current, $eta^{(n)}$, are upper-bounded, $eta^{(n)}leq eta_C^n$ with $ngeq 2$ and $eta_C$ the Carnot efficiency, we prove that an {it ensemble} of $N$ distinct machines similarly satisfies this upper bound on the relative fluctuations of the ensemble, $eta_N^{(n)}leq eta_C^n$. For an ensemble of distinct quantum {it refrigerators} with components operating in the tight coupling limit we further prove the existence of a {it lower bound} on $eta_N^{(n)}$ in specific cases, exemplified on three-level quantum absorption refrigerators and resonant-energy thermoelectric junctions. Beyond special cases, the existence of a lower bound on $eta_N^{(2)}$ for an ensemble of quantum refrigerators is demonstrated by numerical simulations.
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