We study the dual variants of the Erdős's distinct distances and unit distance problems. Instead of considering distances determined by points, we consider simplex volumes determined by hyperplanes. We investigate: (1) the maximum number of unit $d$-volume $d$-simplices determined by an arrangement of $n$ hyperplanes in $\mathbb{R}^d$, (2) the maximum number of minimum/maximum $d$-volume $d$-simplices determined by an arrangement of $n$ hyperplanes in $\mathbb{R}^d$, and (3) the maximum number $D_d(n)$ such that any arrangement of $n$ hyperplanes in $\mathbb{R}^d$ in general position contains $D_d(n)$ hyperplanes forming $d$-simplices of distinct $d$-volumes.

The study of dependence between random variables under external influences is a challenging problem in multivariate analysis. We address this by proposing a novel semi-parametric approach for conditional copula models using Bayesian additive regression trees (BART) models. BART is becoming a popular approach in statistical modelling due to its simple ensemble type formulation complemented by its ability to provide inferential insights. Although BART allows us to model complex functional relationships, it tends to suffer from overfitting. In this article, we exploit a loss-based prior for the tree topology that is designed to reduce the tree complexity. In addition, we propose a novel adaptive Reversible Jump Markov Chain Monte Carlo algorithm that is ergodic in nature and requires very few assumptions allowing us to model complex and non-smooth likelihood functions with ease. Moreover, we show that our method can efficiently recover the true tree structure and approximate a complex conditional copula parameter, and that our adaptive routine can explore the true likelihood region under a sub-optimal proposal variance. Lastly, we provide case studies concerning the effect of gross domestic product on the dependence between the life expectancies and literacy rates of the male and female populations of different countries.

Let $[\,\cdot\,]$ denote the floor function. In this paper, we show that whenever $η$ is real and the constants $λ_i$ satisfy some necessary conditions, then for any fixed $\frac{63}{64}<γ<1$ and $θ>0$, there exist infinitely many prime triples $p_1,\, p_2,\, p_3$ satisfying the inequality \begin{equation*} |λ_1p_1 + λ_2p_2 + λ_3p^2_3+η|<\big(\max \{p_1, p_2, p^2_3\}\big)^{{\frac{63-64γ}{52}}+θ} \end{equation*} and such that $p_i=[n_i^{1/γ}]$, $i=1,\,2,\,3$.

The fundamental question of when a static or dynamic system should be deemed intrinsically quantum remains a challenge to address in absolute terms. In this regard, a critical requirement lies in the certification (ideally, in real-time) of the emergence and persistence of genuine quantum features, principally entanglement and quantum superposition. Quantum Non-Demolition Measurements (QNDM) serve as the appropriate instrument for this certification, both from a theoretical and experimental standpoint. In this review paper, we explain, with accessible clarity, how the implementation of QNDM can be directly linked to a necessary and sufficient condition for the presence of genuinely quantum features in the system's state monitored over time in finite-dimensional systems, establishing a conceptual parallel with Leggett-Garg inequalities. Using concrete examples that detail the detection of negative terms in the quasi-probability density function resulting from QNDM, we introduce the core concepts for quantumness certification. As specific examples, we discuss an application where the quantum-to-classical transition due to the interaction with an environment can be tracked by QNDM. Moreover, we argue about the robustness of QNDM protocols in the presence of noise sources and their advantages with respect to standard Leggett-Garg inequalities defined by two-time correlators.

In an Earth-analogue atmosphere, water vapour is a key carrier of hydrogen in the lower atmosphere with its transport above the tropopause controlling the atmospheric hydrogen escape rate. On the Earth, this escape is limited by transport though the tropospheric cold trap where water vapour condenses. However, on a tidally-locked exoplanet, the strong day-night temperature gradient drives a global-scale circulation. This circulation could rapidly transport water through the cold trap, potentially increasing hydrogen escape and impacting the composition of potentially habitable worlds. We couple cometary impact and planetary atmospheric models to simulate water-depositing impacts with both a tidally-locked and Earth-analogue atmosphere and quantify how atmospheric circulations transport water from the impact site to high altitudes where it can potentially drive escape. The global nature of the atmospheric circulations on a tidally-locked world enhances hydrogen escape, with both our unimpacted tidally-locked and Earth-analogue atmospheres exhibiting similar mass loss rates despite the tidally-locked atmosphere being bpth cooler and drier near the surface. When considering the effects of a cometary impact, we find an order of magnitude difference in peak escape rates between impacts on the day-side ($Φ_{\mathrm{escape}}=1.33\times10^{10}\,\mathrm{mol\,mth^{-1}}$) and night-side ($Φ_{\mathrm{escape}}=1.51\times10^{9}\,\mathrm{mol\,mth^{-1}}$) of a tidally-locked atmosphere, with the latter being of the same order of magnitude as the peak escape rate found for an impact with an Earth-analogue atmosphere ($Φ_{\mathrm{escape}}=2.7\times10^{9}\,\mathrm{mol\,mth^{-1}}$). Our results show the importance of understanding the underlying atmospheric circulations when investigating processes, such as hydrogen escape, which depend upon the vertical advective mixing and transport.

We study dynamic relationships in which one party extracts current surplus in ways that degrade the future state, while the counterparty cannot exit but adjusts effort in response. Standard stationary Markov equilibria may sustain collapse paths in which short-run extraction dominates strictly positive continuation gains. We introduce the Sustainable Exploitation Equilibrium (SEE), a refinement for dynamic games with irreversible failure modeled as an absorbing boundary that eliminates continuation value. When a survival-preserving action exists and failure destroys future surplus, equilibria assigning positive probability to collapse are sequentially irrational. Equilibrium analysis can therefore be restricted, without loss, to continuation-preserving stationary Markov equilibria. Within this restricted domain, viable renegotiation-proofness becomes structural: because failure truncates future surplus, any jointly improving survival-preserving deviation is credible prior to collapse. SEE selects the viable, renegotiation-stable equilibrium that maximizes the exploiter's value. Existence is established under standard conditions, and the refinement is illustrated in a hegemon-client setting.

We use sub-Doppler optical-optical double-resonance (OODR) spectroscopy with a 3.3 $μ$m single-frequency pump and a cavity-enhanced 1.65 $μ$m comb probe to measure 33 ladder-type (3$ν$${_3}$ ${\leftarrow}$ $ν$${_3}$) and 8 V-type (2$ν$${_3}$) transitions in the 5880-6090 cm$^{-1}$ range of methane, reaching states with rotational E symmetry in the region of the P6 and P4 polyads, respectively. We assign the ladder-type transitions using new Hamiltonian predictions and the ExoMol line list, and the V-type transitions using the new Hamiltonian, ExoMol, HITRAN2020, and the WKLMC line lists. While 7 of the states in the 3$ν$${_3}$ range have been previously observed either in earlier OODR work (without cavity enhancement) with 1.5 MHz accuracy or in FTIR measurements of cold bands with 150 MHz resolution, the states reported here have uncertainties down to 150 kHz (5 $\times$ 10$^{-6}$ cm$^{-1}$). The E-symmetry states exhibit first-order Stark splitting, which will be reported in our future work.

The first part of this paper deals with unipotent and reductive groups over finite fields with $q$ elements in which either $q$ goes to infinity or $G=GL_n(q)$ and $n$ goes to infinity. The second part of the paper deals with the symmetric group $S_n$. The main conclusion that we want to bring out in the case of reductive groups $G(q)$, $q$ varying, is that the dimension data, resp. the size of conjugacy classes, is in a statistical sense, ``roughly'' constant and the same (up to taking the squares). We introduce the notion of {\it asympototically constant}, and {\it asympototically log constant} to make precise these notions, which we apply to various groups discussed in this paper including the symmetric groups $S_n$.

Understanding and classifying multipartite entanglement is fundamental to quantum information processing. This work focuses on absolutely maximally entangled (AME) states, a class of highly entangled states characterized by their maximal entanglement across any bipartitions. To analyze and classify AME states, we employ the minimal decomposition entropy, defined as the minimum Rényi entropy $S_q$ associated with the state's decomposition over all local product bases. This quantity identifies the product bases in which the state is maximally localized, thereby yielding optimal representations for analyzing properties of AME states. We develop an efficient algorithm for computing the minimal decomposition entropy for finite $q>1$ and compare AME and Haar-random states for \( q = 2 \) and \( q = \infty \) in qubit, qutrit, and ququad systems. For \( q = 2 \), AME states of four qutrits and ququads show lower minimal entropy than generic states, indicating sparser optimal forms. For \( q = \infty \) -- related to the geometric measure of entanglement -- AME states exhibit higher entanglement. The algorithm also simplifies known AME states into sparser representations, aiding in distinguishing genuinely quantum AME states from those constructible from classical combinatorial designs. Our results advance the classification of AME states and demonstrate the utility of minimal decomposition entropy as both a local unitary invariant and a tool for state simplification.

Cadmium zinc telluride (CZT) detectors offer excellent room-temperature energy resolution, making them well suited for X- and $γ$-ray spectroscopy in challenging environments. Within the SIDDHARTA-2 program at the DA$Φ$NE collider, a new CZT-based detection system has been developed to enable precision measurements of kaonic atom transitions in the intermediate mass range. In this work, we report the results of a calibration campaign performed with the collider operating, aimed at assessing the detector performance. A dedicated setup, including an array of quasi-hemispherical CZT sensors and a $^{152}$Eu source, was used to characterize the spectral response. The reconstructed emission lines were fitted with a model accounting for Gaussian response and incomplete charge recollection tails, and the detector linearity was evaluated by comparing the measured peak positions with their nominal energies. The results demonstrate that the CZT detector exhibits excellent linearity and stable operation with the collider on, confirming its suitability for future kaonic-atom spectroscopy at DA$Φ$NE.

Simulating large quantum circuits on hardware with limited qubit counts is often attempted through methods like circuit knitting, which typically incur sample costs that grow exponentially with the number of connections cut. In this work, we introduce a framework based on Cluster-level Light-cone analysis that leverages the natural locality of quantum workloads. We propose two complementary algorithms: the Causal Decoupling Algorithm, which exploits geometric disconnections in the light cone for sampling efficiency, and the Algebraic Decomposition Algorithm, which utilizes algebraic expansion to minimize hardware requirements. These methods allow simulation costs to depend on circuit depth and connectivity rather than system size. Together, our results generalize Lieb-Robinson-inspired locality to modular architectures and establish a quantitative framework for probing local physics on near-term quantum devices by decoupling the simulation cost from the global system size.

While mergers between massive galaxies and their dwarf satellites are well studied, the properties of dwarf - dwarf satellite mergers are not well constrained. Stellar streams trace satellite disruption and, in the dwarf galaxy regime, are predicted to provide novel constraints on low-mass galaxy evolution and dark matter. However, the mass ratios required to form these streams make them challenging to detect. We present a preview of the Stellar Stream Legacy Survey (SSLS) in the dwarf galaxy regime. The SSLS aims to produce a statistically large, homogeneous sample of stellar streams for comparison with galaxy evolution theory. We visually inspect dwarf galaxies using the DESI Legacy Imaging Survey (DES and DECaLS footprints, r-band 29 mag arcsec^-2 within 4 - 35 Mpc. We develop a classification metric to categorise accretion debris around dwarf galaxies, and measure the frequency of accretion features in the DES footprint only. We present the first release of accretion features around dwarf galaxies collected from the DES and DECaLS footprints, including 1 stream, 11 shells, and 8 asymmetric stellar halos, of which 17 constitute new identifications. In the DES footprint, we inspect 730 dwarfs and find that 5.1% (37/730) show accretion features. Although this frequency measurement is lower than the SSLS result for massive galaxies, we discuss the observational biases behind detecting streams in the dwarf galaxy regime. Our results highlight the difficulty of detecting streams around dwarfs, and identify the need for improved theoretical modelling of low-mass merger morphologies. Nevertheless, they place constraints on hierarchical mass assembly in this regime.

The Galactic Center GeV Excess (GCE) remains a compelling but enigmatic signal from the inner region of our galaxy. Muonphilic dark matter (DM), which couples exclusively to muons via a new mediator, provides a viable explanation for the GCE and relic density while naturally evading constraints from direct detection, collider searches and other multi-messenger observations. Based on the viable non-resonant parameter space identified in previous global fits, we perform a comprehensive study exploring the prospects for discovering such muonphilic DM in the context of a future $3$ TeV muon collider, focusing on simplified models with a $Z_2$-even mediator. Four distinct search strategies are investigated: visible on-shell mediator decays ($μ^{+}μ^{-}γ$ final state), invisible on-shell mediator decays (mono-photon plus missing energy), mono-photon production via off-shell mediators, and vector boson fusion production.Through a detailed signal-background analysis using cut-and-count methods, we project the exclusion limits at $95\%$ confidence level for seven representative models across a wide range of mediator masses. Our results demonstrate that the projected limits cover a significant portion of the viable parameter space that explains the GCE, establishing a muon collider as a decisive machine for testing the muonphilic DM hypothesis.

Advances in mid-infrared (MIR) dual-comb spectroscopy (DCS) have significantly enhanced molecular detection in recent years. The capability of DCS to precisely identify and quantify atmospheric trace gases makes it attractive for field applications across the environmental, agricultural, energy, and industrial sectors. In particular, there is a growing demand for mobile and continuous gas monitoring in outdoor environments where emission sources and sinks are often episodic and spatially heterogeneous. However, the practical field-deployment of DCS on mobile platforms under realistic field conditions has remained limited. This study demonstrates for the first time a vehicle-mounted MIR DCS system that enables continuous mobile atmospheric sampling across multiple outdoor sites and road environments. The system exhibited a stable signal-to-noise performance during on-road operation, including expressway driving at speeds up to 100 km/h. Furthermore, natural-gas leakage sources were successfully located and a two-dimensional methane concentration field was reconstructed around a controlled release source. In the future, the system can be integrated into more mobile platforms, such as unmanned aerial vehicles, enabling flexible trace gas detection over urban-scale regions.

The purpose of this paper is twofold. We explore higher property T as an abstract group-theoretic property. In particular, we provide new operator-algebraic characterizations of higher property T. Then we turn to lattices in semisimple Lie groups. We relate higher property T to other cohomological, rigidity and geometric phenomena below the real rank. The second part outlines a conjectural framework that unifies these aspects and reviews recent advances.

We investigate behavior of brane backgrounds under poly-vector deformations in Type IIB and D=11 supergravities. We find that the standard bi-vector deformations add dissolved F1 string charge to a Dp-brane background, quadri-vector deformations add D3-brane charge, tri- and six-vector deformations in D=11 add M2- and M5-brane charges respectively. We discuss these results in the context of NRCS and OM theories.

Predicting real-time dynamics in correlated systems is demanding: exact two-time Green's function methods are accurate but often too costly, while the Generalized Kadanoff-Baym Ansatz (GKBA) offers time-linear propagation at the risk of uncontrolled behavior. We examine when and why GKBA fails in a minimal yet informative setting, the Holstein dimer that describes electron-phonon coupling. Using a conserving, fully self-consistent electron-phonon self-energy, we map out parameter regions where GKBA dynamics is stable and where it becomes unstable. We trace the onset of these failures to qualitative changes in the model's ground-state solutions obtained from the full nonequilibrium Green's function theory, thereby providing practical stability bounds for GKBA time evolution. We further show that coupling the dimer to electronic leads can damp and, in part, cure these instabilities. The results supply simple diagnostics and guidelines for reliable GKBA simulations of electron-phonon dynamics.

Motivated by the recent interest in conformal and duality invariant nonlinear electrodynamics, we study the non-Abelian extension of ModMax electrodynamics. The theory is parameterized by a single dimensionless constant, and it is continuously connected to Yang-Mills theory in its vanishing limit. We show that the theory admits (anti-)self-dual instantons, despite the additional nonlinearities that characterize the non-Abelian ModMax theory. For $SU(2)$, we construct the generalization of the BPST instanton and extend this solution to Euclidean de Sitter and anti-de Sitter backgrounds. In the latter case, the Chern-Pontryagin index depends on the instanton size since the configuration is not a pure gauge at infinity; a property already pointed out in Yang-Mills on negative-curvature backgrounds by Callan and Wilczek. We compute the contribution of the latter to the spectrum of the Dirac operator at the boundary, which is crucial for determining the non-local contributions to the Dirac index. Then, we show that the ansatz constructed with 't Hooft symbols accommodates multi-instantons in the non-Abelian ModMax theory. The system of (anti-)self-dual equations reduces to a single nonlinear equation, which can be perturbatively solved order by order in the parameter that controls the nonlinearity. Following such a strategy, we provide a formal solution for the $N$-instanton configuration to first order in the expansion. Then, we couple non-Abelian ModMax theory to gravity with a conformally coupled scalar field and construct new gravitating solutions that describe Euclidean wormholes and other smooth configurations with secondary hair.

We study a system of Fokker-Planck equations recently introduced to describe the temporal evolution of statistical distributions of population densities with predator-prey interactions. At the macroscopic level, the system recovers a Lotka-Volterra model and defines an explicit family of equilibrium densities that depend on the form of the diffusion coefficient. By introducing Energy-type distances, we rigorously establish exponential convergence to equilibrium in appropriate homogeneous Sobolev spaces, with a rate explicitly determined by the dissipative contribution of the interaction term. The analysis highlights the intrinsic energy dissipation mechanism governing the dynamics and clarifies how the evolution of expected quantities determines the emergence of a stable equilibrium configuration. This approach provides a new perspective on the convergence to equilibrium for problems with time-dependent coefficients.

In this paper, we establish dimension-free $L_p$-estimates for operator-valued maximal spherical means over cyclic groups $\Z_{m+1}^d$ for all $p>1$ and $m\geq1$. The key ingredient is a noncommutative extension of the spectral technique developed by Nevo and Stein. As an application, we obtain a noncommutative spherical maximal inequality for automorphism actions on von Neumann algebras, along with several concrete examples.

We develop a Fokker-Planck approach to describe the dynamics of staggered magnetization and thermal fluctuations in a two-dimensional antiferromagnetic system with uniaxial anisotropy. Beginning with a classical model for the antiferromagnetic system, we incorporate a Landau-Lifshitz-Gilbert equation augmented by Langevin fields to account for thermal fluctuations, and we derive the Fokker-Planck equation governing the probability distribution function of the spin configuration. Employing the mean-field approximation, we derive the equations of motion for the spin polarization and the two-time spin-spin correlation functions. The methodology is applied to the study of spin-wave dynamics and to the formulation of a phenomenological model for resistance fluctuations in two-dimensional antiferromagnetic semiconductors.

High-energy particle decays naturally realise informationally weak measurements of quantum spin. Decay kinematics act as continuous pointer variables whose overlapping angular distributions encode partial, non-projective information about the parent spin state. Ensemble averages of these pointers yield weak values, linking collider spin-density reconstruction to Aharonov-Vaidman measurement theory. This framework unifies spin tomography, entangled-decay correlations, and spin-correlation algorithms, showing that relativistic decays realise informationally weak measurements of spin and suggesting new ways to probe coherence and interference in high-energy processes.

We test screened dark energy with near-Earth, space-based measurements. In a post-Newtonian framework, we compute leading corrections to geodetic precession (Gravity Probe B), LAGEOS-2 pericenter advance, and the Sagnac delay in a prospective orbital configuration, yielding bounds on chameleon, symmetron, and dilaton models. LAGEOS-2 sets the strongest Earth-orbit limits on symmetron and dilaton, while a Sagnac setup at the projected sensitivity of state-of-the-art space clocks gives the tightest chameleon constraint. These results show that low-density, space-based experiments sensitively probe screened dark energy and exclude previously allowed parameter space. Notably, at nuclear-clock precision $\mathcal{O}\big(10^{-19}\big)$, a Sagnac test would exclude the entire chameleon parameter space considered.

We study theoretically a process of cooling electrons using a superconducting tunnel junction with a $π$ phase difference and a usual insulator or a ferroelectric in-between, and an array of such junctions with ferroelectric layers in-between. These setups have a complex structure of entropy due to nodal lines, where the density of states can be divergent or larger than for a free electron gas at a chemical potential level. We consider a small current running from the bath of electrons through the setup, where electrons have to have higher entropy, and thus remove heat from the bath.

The seminal work of Coleman, Glaser, and Martin established that, at zero temperature, any non-trivial solution to the equations of motion with the least Euclidean action is $O(D)$-symmetric. This paper extends their foundational analysis to finite temperature. We rigorously prove that for a broad class of scalar potentials, any saddle-point configuration with the least action is necessarily $O(D\!-\!1)$-symmetric and monotonic in the spatial directions. This result provides a firm mathematical justification for the symmetry properties widely assumed in studies of thermal vacuum decay and cosmological phase transitions.

We study the $T=0$ phase diagrams of models of bilayers of $S=1/2$ square lattices antiferromagnets with SU(2) Heisenberg symmetry that have 2, 4, and 6 spin exchanges. We study two families of bilayer models with distinct internal symmetries and, hence, different phase diagram topologies. A traditional bilayer model in which the interlayer interaction is Heisenberg so that the two layers can exchange spin (and energy) with each other, making it possible to achieve a simple dimerized valence bond liquid-like state. The resulting phase diagram is rich with Néel, valence bond solid and simple dimer phases, and both first-order and continuous transitions, which we demonstrate are consistent with the conventional Landau theory of order parameters. In the second family of models in which the layers can exchange only energy but no spin (reminiscent of the Ashkin-Teller coupling), the simple dimer state cannot occur. The phase diagrams reveal a number of phase transitions that are accessed for the first time. We find that the phase transition between Néel and VBS is first order in both the spin-spin and energy-energy coupled models, although they have strikingly distinct finite-size scaling behavior and that the transition from VBS to dimer in the spin-spin coupling model deviates from the expected scenario of an XY model with dangerously irrelevant four-fold anisotropy.

Audio watermarking is essential for verifying speech authenticity, yet single-watermark schemes often struggle against sophisticated distortions such as neural reconstruction and adversarial attacks. To address this limitation, we introduce a multiplexing paradigm that combines multiple watermarking techniques to leverage their inherent complementarities. We explore both parallel and sequential multiplexing strategies and propose perceptual-adaptive time-frequency multiplexing (PA-TFM), a robust training-free approach. To further enhance performance, we introduce MaskNet, a novel model-based framework designed to learn effective time-domain multiplexing. Experimental results on the LibriSpeech and Common Voice datasets under 14 diverse attack types, including high-strength white-box and neural reconstruction attacks, demonstrate that both PA-TFM and MaskNet considerably outperform existing single-watermark baselines, establishing a resilient paradigm for real-world audio protection.

Whispered speech lacks vocal-fold excitation, making intelligible conversion challenging. We propose WhisperVC, a three-stage framework for low-resource whisper-to-normal (W2N) conversion that decouples cross-domain alignment from speech generation. Stage 1 uses limited paired whisper-normal data with a content encoder and a Conformer-based variational autoencoder (VAE) with soft-DTW alignment to learn domain-invariant semantic representations. Stage 2, trained only on normal speech, employs a Length-Channel Aligner and a two-stage speaker-conditioned mel generator for timbre and prosody modeling. Stage 3 fine-tunes a HiFi-GAN vocoder for waveform synthesis. Experimental results on AISHELL6-Whisper show competitive quality (DNSMOS 3.07, UTMOS 2.83, CER 16.93%) and WavLM speaker similarity (0.95). The framework also supports privacy-preserving communication as well as non-vocal communication and a rehabilitation tool for post-surgical vocal-fold patients. Samples are available online.

We present a comparative analysis of warm dark matter (WDM) subhalo populations generated by the semi-analytic model {\sc Galacticus} and the COZMIC suite of dark matter-only $N$-body simulations. Using a range of thermal relic WDM particle masses (3--10 keV), we examine key summary statistics -- including the subhalo mass function, spatial distribution, maximum circular velocity $V_\text{max}$, and its corresponding radius $ R_\text{max} $ -- to evaluate the consistency between these two modeling frameworks. Both models predict a suppression of low-mass subhalos correlated with decreasing WDM particle mass, and that WDM subhalos tend to have lower $V_\text{max} $ and larger $ R_\text{max} $ values than their CDM counterparts at fixed mass. While {\sc Galacticus} provides more statistically precise results due to a larger sample size, the COZMIC simulations display similar qualitative trends. We discuss how differences in halo finder algorithms, simulation resolution, and modeling assumptions affect subhalo statistics. Our findings demonstrate that {\sc Galacticus} can reliably reproduce WDM subhalo distributions seen in $N$-body simulations, offering a computationally efficient tool for exploring the implications of WDM across astrophysical phenomena.

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 $\mathcal{O}(N)\!\sim\!N^α$ 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 $τ$, 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 $α_{E_{\mathrm{max}}}\!\in\![1.08,1.26]$, $α_τ\!\approx\!-0.49$, $α_{\bar{P}_{\mathrm{max}}}\!\in\![1.57,1.73]$, 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.