A Canonical Coherence Functional Across Physical Scales

Critical phenomena appear across a wide range of physical domains, from quantum chromodynamics to condensed matter and complex macroscopic systems. Despite this ubiquity, there is currently no canonical observable capable of quantifying coherence and coherence breakdown in a directly comparable manner across such disparate regimes. In this work, we introduce a canonical coherence functional, denoted K, defined as a normalized spectral-entropy measure over modal power distributions. The index satisfies a set of strict constraints required for cross-domain applicability, including normalization, scale invariance, robustness to noise, and sensitivity to modal redistribution rather than absolute amplitudes. We compute K across multiple physical domains using publicly available datasets and show that it exhibits pronounced minima or inflection points coincident with known critical transitions, including chiral symmetry restoration in QCD and coherence breakdown in molecular energy landscapes. These features persist under robustness tests and are absent in randomized or synthetic null models. Importantly, we do not propose a new dynamical model nor a unified field theory. Instead, we demonstrate the existence of a measurable, domain-independent functional that captures structural coherence and its loss across physical systems. The recurrence of similar K-profiles suggests that critical phenomena may share a common organizational signature, distinct from conventional dynamical universality classes and independent of microscopic details.