Entropic Resonance Principle: A Unified Informational Framework for Persistence

This paper develops the Entropic Resonance Principle (ERP) as a unified informational framework for understanding how organized systems persist across physical, biological, cognitive, and engineered domains. ERP proposes that stability arises not from resisting entropy but from a regulated co-variation between coherence (R) and entropy (H), expressed by the proportionality dR/dH≈ λ ,where the resonance parameter λ=ln⁡φ≈0.4812 is derived from a minimal self-similar renewal model. This proportionality admits both a flux form and a variational form, δ(R- λH)=0 ,which together define persistent trajectories in an informational state space. ERP does not modify microphysical laws; rather, it functions as a meta-theoretical constraint that may emerge under appropriate coarse-graining. The paper clarifies the mathematical structure of ERP, analyzes its conceptual implications, and outlines empirical predictions that render the framework testable and falsifiable. Applications are explored in quantum decoherence, non-equilibrium chemistry, neural dynamics, adaptive computation, and complex engineered systems. A methodological protocol is proposed for estimating effective slopes dR/dH in real data using sliding-window regression, bootstrap uncertainty quantification, and model comparison. ERP is ultimately positioned as the nucleus of a research programme whose validity hinges on whether λ-like proportionalities recur across systems and scales. If supported, ERP may reveal a previously unrecognized informational invariant governing the persistence of structure; if not, it offers a precise template for evaluating how coherence and entropy jointly shape organized behavior.