Scaling law of asymptotic freedom in collective charging of quantum batteries

• URL: http://arxiv.org/abs/2606.10054v1
• Date: Mon, 08 Jun 2026 18:30:29 GMT
• Title: Scaling law of asymptotic freedom in collective charging of quantum batteries
• Abstract summary: We prove that the ergotropy-to-energy ratio approaches unity at least as fast as $sim N-1$ with the number of batteries $N$.<n>We show how the universal $1/N$ scaling can be overcome.
• Score: 21.415030687915948
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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