When Noise Raises the Quantum Charging Advantage: Ratio Effects in Global and Dicke Batteries

The collective charging advantage Γ of a quantum battery is a ratio, and noise can raise it even while the battery’s own charging power falls. This paper shows how noise and its correlations set Γ in an idealized global N-body charger, a Dicke cavity battery and two all-to-all two-body chargers.Exact results: local pure dephasing maps the N-cell dynamics onto single-cell dynamics run N times faster, so Γ = N for equal rates. A common-mode share c of the dephasing enters as an effective rate γ_φ[1 + (N − 1)c], so Γ/N depends only on x = (N − 1)c and, for fixed c, levels off at a closed-form constant.Numerical results: local noise raises Γ while power per cell falls; collective dephasing does not. Γ alone therefore cannot rank batteries, and absolute power per cell should be reported with it.Code and data: https://doi.org/10.6084/m9.figshare.34989034