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 ∼ 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 ∼ N^-b with b>1 and even exponential scaling in N². 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.