Quantile-DRT: A Model-Free Framework for Regime Detection and Degradation Diagnosis via Electrochemical Impedance Spectroscopy

We present Quantile-DRT, a model-free analytical framework that extracts physically interpretable regime indicators from Electrochemical Impedance Spectroscopy (EIS) spectra via the Distribution of Relaxation Times (DRT). The framework defines four core metrics — τ₆₃, M_slow, spread, and Π — as quantile statistics of the DRT cumulative distribution function, requiring no a priori equivalent circuit model. Validated on PEM fuel cells (GIANTLEAP H2020, 10,000h) and lithium-ion batteries (NMC622/C-SiO, 228 cells, Luh & Blank 2024). Extended to real-time optimisation via τ-based control signals for regime-aware operation, including adaptive purge control in dead-end anode systems. Cross-domain consistency with neural network training dynamics supports a Critical Slowing Down hypothesis for complex systems near regime transitions. Core metrics τ₆₃, M_slow, and spread were first formalised in internal working files dated 5–17 February 2026, prior to the publication of related preprints in March 2026. Supporting files included in this deposit. Methodological preprint deposited for priority establishment prior to peer-reviewed journal submission. Full access will be made available upon publication or upon request to the corresponding author.