Bounds on fluctuations for ensembles of quantum thermal machines
Abstract
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 upperbounded, $\eta^{(n)}\leq \eta_C^n$ with $n\geq 2$ 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 threelevel quantum absorption refrigerators and resonantenergy 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.03526
 Bibcode:
 2021arXiv210903526G
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 Na'im Kalantar and Matthew Gerry contributed equally to this work and are joint "first authors"