Coherence in the Leak and Storage Kurtosis control Ergotropy in Quantum Batteries

TL;DR

This work develops a cavity-mediated quantum battery model where noise-induced coherences and nonreciprocal energy flow enable enhanced ergotropy. By combining full counting statistics with machine learning, the authors quantify higher-order fluctuations via cumulants and identify that the fourth cumulant (kurtosis) $C^{(4)}$ and leakage-mode coherence $p_c$ are the strongest predictors of high ergotropy. A data-driven pipeline reveals that a minimal feature set including $C^{(4)}$, $T_h$, $Q_h$, $p_c$, and $T_\ell$ can classify ergotropy regimes with MCCs near 0.96 on TEST data, rivaling more feature-rich models. The results demonstrate that non-Gaussian energy exchange fluctuations, captured by higher-order cumulants, are central to optimizing open quantum batteries and can guide design toward higher work extraction.

Abstract

We introduce a cavity-coupled finite quantum system which can act as a quantum battery by harnessing noise induced coherences. We apply the methodology of full counting statistics to capture higher-order fluctuations of quanta exchange in the storage station. Together with the thermodynamic parameters, the fluctuations constitute a training platform for unsupervised as well as supervised learning models in predicting ergotropy. We identify a minimal predictive feature set from the battery's operating parameters that can classify the ergotropy into different regimes with great accuracy.Our results show that the usual quantum and thermodynamic variables are inadequate for the purpose of identifying high ergotropy regimes in isolation. Rather, it is the kurtosis of quanta exchange in the storage and the noise-induced coherence in the leakage mode that become the dominant quantities in controlling the magnitude of ergotropy.

Figures (9)

• Figure 1: (a) Schematic representation of the cavity-mediated quantum battery model. (b) Illustration of the charging, leakage, and storage pathways. (c--e) Time evolution of the storage-to-charging, leakage-to-storage, and leakage-to-charging ratios for the parameters $\epsilon_1=\epsilon_2=0.1$, $\epsilon_b=0.4$, $\epsilon_a=1.5$, $r=1$, $g=1$, $p_h=0.61$, $p_c=0.97$, $T_c=5$, $T_\ell=1$, $T_h=6.36$, and $\tau=0.95$. (f) Normalized ergotropy $\mathcal{E} / \mathcal{E}_{0}$ plotted as a function of the scaled time $rt$. The blue curve corresponds to the parameters used in panels (c--e), with the reference ergotropy $\mathcal{E}_{0}$ computed at $p_c=p_h=0$ and $\tau=0$. The grey curve uses the same parameters as (c--e) except $p_h=0.9$, $p_c=0.1$, $T_c=0.1$, and $T_h=2$, with $\mathcal{E}_{0}$ evaluated at $p_c=p_h=0$ and $\tau=0$. All quantities shown are dimensionless.
• Figure 2: (a) Dataset divided into DEV and TEST splits; the histograms of normalized energy $\mathcal{E}/\mathcal{E}_0$ exhibit comparable right-skewed distributions. (b) On the DEV set, samples with ( $\mathcal{E}/\mathcal{E}_0$$<$ 1) are manually assigned to class 0, while the remaining data undergo unsupervised clustering. Both the silhouette score and the within-cluster sum of squares (WCSS) identify $K = 2$ as the optimal number of clusters, yielding two additional learned classes. (c) The resulting three-class structure, is visualized through class-wise histograms of $\mathcal{E}/\mathcal{E}_0$.
• Figure 3: Scaling of performance with dataset size for five parameter mappings. Panels (a-e) show the validation macro-F1, $F1_V$, versus dataset size for $f_T$, $f_E$, $f_{Th}$, $f_Q$, and $f_C$; panel (f) shows the train-to-validation ratio $F1_T/F1_V$ for $f_C$ to diagnose overfitting. Curves compare MLP (red), HistGradientBoosting (green), and Random Forest (blue). The x-axis in all panels is dataset size ($\times 10^{5}$).
• Figure 4: Cumulants mapping $f_C:\{C^{(i)}\}\rightarrow \mathcal{E}/\mathcal{E}_0$ on the TEST set for the MLP model. (a) Confusion matrix, (b) one-vs-rest ROC curves (per-class AUCs shown), and (c) precision-recall (PR) curves (per-class APs shown). The three classes correspond to ergotropy regimes: class 0, $\mathcal{E}/\mathcal{E}_0 < 1$; class 1, mid; class 2, high. The model shows strong separability with most residual confusion between classes 1 and 2, yielding macro ROC-AUC $\approx 0.921\text{--}0.989$ and macro PR-AUC $\approx 0.739\text{--}0.950$.
• Figure 5: F1-based feature-importance comparison across three models multi layer perceptron (MLP), HistGradientBoosting (HGB), and Random Forest (RF). Bars correspond to the physical variables $\{p_c,\ \varepsilon_a,\ Q_h,\ T_h,\ Q_c,\ \varepsilon_b,\ C^{(4)},\ T_\ell,\ \varepsilon_1,\ p_h,\ W, F, \ C^{(2)},\ C^{(1)},\ \eta,\ \tau,\ T_c,\ C^{(3)}\}$. Consistently high importances of $p_c$, and $C^{(4)}$ indicate their dominant role in determining classification performance across all models.