Scaling law of asymptotic freedom in collective charging of quantum batteries

Abstract:We establish a universal scaling law for collective charging of quantum batteries, independent of microscopic details. We prove that the ergotropy-to-energy ratio approaches unity at least as fast as $\sim N^{-1}$ with the number of batteries $N$, implying generic asymptotic freedom. We further show how the universal $1/N$ scaling can be overcome: when the battery state becomes asymptotically pure, the convergence can be substantially faster, including $\sim N^{-b}$ with $b>1$ and even exponential scaling in $N^2$. Rigorous finite-$N$ upper and lower bounds on the ergotropy-to-energy ratio are further derived, providing nonasymptotic guarantees for the universal $1/N$ scaling.

arXiv:2606.10054 [quant-ph]

(or arXiv:2606.10054v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2606.10054 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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