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 first-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 $sighat(t)$. A multi-scale detection architecture is introduced, separating wide-window ($\Phi$, $W_\Phi=40$) and narrow-window ($A$, $sighat$, $W_{\mathrm{fast}}=12$) components to ensure mechanistic independence. Monte Carlo validation across three collapse scenarios ($N=200$ each, $FAR=5\%$) yields scenario-dependent gains: $15.9\times$ in Hopf bifurcation, $1.02\times$ in 3-phase drift, $0.98\times$ in TAR model. A 300-sample Dirichlet weight search identifies optimal weights $w^*=[\Phi:0.220,\,A:0.425,\,M:0.269,\,\hat{\sigma}:0.086]$, with default weights achieving $98.7\%$ of optimal. Ablation study confirms $M(t)$ provides the largest marginal gain ($+41.1$ steps in Hopf). Phase-randomized surrogate testing confirms 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 flash crash composite achieves $24.7$ days lead ($1.08\times$, $100\%$ DR); ICU sepsis onset composite achieves $12.1$ hours lead ($+2.0$,h absolute gain, $82\%$ DR). The central finding is that gain is mechanism-dependent: memory $M(t)$ is most valuable in oscillatory/CSD systems; KL divergence is near-sufficient for distributional-shift collapses. The EPR proxy $sighat(t)$ is grounded as a symmetrized KL rate with $O(\Delta t)$ relative error to true Onsager EPR.