Bounds on fluctuations for ensembles of quantum thermal machines

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, $η^{(n)}$, are upper-bounded, $η^{(n)}\leq η_C^n$ with $n\geq 2$ and $η_C$ 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, $η_N^{(n)}\leq η_C^n$. 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 $η_N^{(n)}$ 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 $η_N^{(2)}$ for an ensemble of quantum refrigerators is demonstrated by numerical simulations.

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