Beyond Entropy Magnitude: Directional Symmetry Breaking, Temporal Memory, and Entropy Production Rate as Early Warning Signals in Complex System Collapse

The Kerimov-Alekberli (KA) framework Karimov and Alekberli, 2026 detects imminent collapse in complex systems by monitoring KL-divergence accumulation relative to a stable reference distribution via a rst-passage time (FPT) trigger. Prior work established that incorporating directional asymmetry accelerates detection fourfold. The present paper extends the KA model with three additional structural components: (1) directional asymmetry A(t); (2) temporal memory M(t) via lag-1 autocorrelation deviation; and (3) a symmetrized entropy production rate proxy σˆ(t). A multi-scale detection architecture is introduced, separating wide-window (Φ, WΦ = 40) and narrow-window (A, σˆ, Wfast = 12) components to ensure mechanistic independence. Monte Carlo validation across three collapse scenarios (N = 200 each, FAR = 5%) yields scenario-dependent gains: 15.9× in Hopf bifurcation, 1.02× in 3-phase drift, 0.98× in TAR model. A 300-sample Dirichlet weight search identies optimal weights w∗ = Φ : 0.220, A : 0.425, M : 0.269, σˆ : 0.086, with default weights achieving 98.7% of optimal. Ablation study conrms M(t) provides the largest marginal gain (+41.1 steps in Hopf). Phase-randomized surrogate testing conrms the Hopf memory gain is not a calibration artifact (Mann-Whitney p < 0.0001, rank-biserial r = 0.952). Bootstrap 95% CI for composite lead time: 50.1, 59.3 steps. Cohen's d = 2.65 (very large) for the memory extension. Empirically-calibrated real-domain validation demonstrates: BTC ash crash composite achieves 24.7 days lead (1.08×, 100% DR); ICU sepsis onset composite achieves 12.1 hours lead (+2.0 h absolute gain, 82% DR). The central nding is that gain is mechanism-dependent: memory M(t) is most valuable in oscillatory/CSD systems; KL divergence is near-sucient for distributional-shift collapses. The EPR proxy σˆ(t) is grounded as a symmetrized KL rate with O(∆t) relative error to true Onsager EPR.