Bounds on fluctuations for ensembles of quantum thermal machines

TL;DR

This paper establishes universal bounds on fluctuations in ensembles of quantum thermal machines, showing that both upper and lower bounds on fluctuation measures hold under certain conditions, with implications for quantum thermodynamics.

Contribution

It proves that bounds on fluctuations for individual quantum thermal machines extend to ensembles, and demonstrates existence of bounds in specific quantum refrigerator models.

Findings

Ensemble fluctuations are upper-bounded by the Carnot efficiency raised to the power n.

For certain quantum refrigerators, lower bounds on fluctuations are established.

Numerical simulations support the existence of lower bounds beyond special cases.

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 upper-bounded, $\eta^{(n)}\leq \eta_C^n$ 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 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.