Entanglement and Dynamical Scaling Laws in Quantum Superabsorption

Quantum batteries (QBs) exploit collective quantum resources to surpass the limits of classical energy storage and power delivery. We analyze $N$-qubit cavity-coupled QBs governed by Dicke and Tavis--Cummings models under Gaussian driving and open-system dynamics. Finite-size scaling laws $\mathcal{O}(N)\!\sim\!N^{\alpha}$ demonstrate an optimal region of relaxation and dephasing where coherent driving stabilizes entanglement entropy growth for thermodynamic observables (maximum energy $E_{\mathrm{max}}$, charging time $\tau$, and maximum power $\bar{P}_{\mathrm{max}}$) and for qubit and cavity entanglement entropies. The Dicke model exhibits entropy-suppressed extensive behavior, while the Tavis--Cummings model achieves super-extensive scaling with $\alpha_{E_{\mathrm{max}}}\!\in\![1.08,1.26]$, $\alpha_{\tau}\!\approx\!-0.49$, $\alpha_{\bar{P}_{\mathrm{max}}}\!\in\![1.57,1.73]$, supported by qubit-cavity entanglement. We demonstrate that dissipation can act as a stabilizer source, yielding scaling benchmarks that are relevant to several experimental platforms. Our findings connect entanglement, dissipation-enhanced scaling laws and superabsorption, outlining a pathway towards scalable quantum batteries offering practical quantum advantage.