Delt-IEt: A Domain-Agnostic Entropic Acceleration Index for Unsupervised Detection of Imminent Failure in Physical Systems

We introduce Delt-IEt (Delta-Entropic Index by Transition), a closed-form index based on the second-order temporal variation of Shannon entropy, designed to detect imminent failure precursors in physical systems without supervised training, failure labels, or domain-specific parameterization. The index tracks the acceleration of Shannon entropy computed over adaptive sliding windows. We validate the method across four physically unrelated engineering domains using public benchmark datasets: (i) power semiconductor aging (NASA IGBT), (ii) lithium-ion battery degradation (NASA Battery B0005/B0007), (iii) microalgae bioreactor dynamics (UCSD Algae Raceway), and (iv) turbofan engine run-to-failure trajectories (NASA CMAPSS FD001). In all domains, Delt-IEt detects early structural anomalies before conventional absolute thresholds are breached. A critical anomalous observation is reported: in lithium-ion cells, the index fires at cycle 8 (capacity 1.856 Ah, 99.5% of nominal), 116 cycles before End-of-Life, in a phase where no conventional metric indicates degradation. The same event pattern recurs at identical cycles in two independent battery units — consistent with the hypothesis of real-time detection of discrete electrochemical phase transitions, an open scientific question reported in the paper. The method establishes competitive utility in the zero-label predictive maintenance regime for energy, aerospace, and power electronics. Patent application: INPI Brazil, BR 10 2026 012158 4, filed 18 May 2026.