We extend thermodynamics-grounded anomaly detection to directed dependency structure learning, framing tumorigenesis as a progressive rewiring of biological interaction networks alongside deviation from physiological equilibrium. We introduce the Causal Entropic Response (CER) — formalised as a graph-perturbation Fisher sensitivity functional — which quantifies how perturbations to the directed dependency graph propagate through distributional dynamics, connects to the score function, and admits a Lipschitz continuity bound providing formal noise robustness. The unified detection functional Phi(t) is derived from a generalised free energy decomposition rather than arbitrary linear combination. Edge importance scores are equipped with bootstrap confidence intervals (B=1000) and stability selection, replacing heuristic thresholds. Pseudotime ordering (Monocle2) is validated against Slingshot. Through synthetic multi-node dynamical systems and single-cell gene expression datasets, structural first-passage anticipates critical transitions earlier than state-based detectors by ~1.5 time units (synthetic) and ~0.12 pseudotime units (~18-24 months, real data).
Karimov et al. (Sun,) studied this question.