A Critical Review of the Theory of Entropicity (ToE) on Original Contributions, Conceptual Innovations, and Pathways towards Enhanced Mathematical Rigor: An Addendum to the Discovery of New Laws of Conservation and Uncertainty

The Theory of Entropicity (ToE) proposes a paradigm in which entropy is not merely a statistical measure but a fundamental, dynamical field that shapes the behavior of all physical systems. By extending symmetry‐breaking concepts beyond traditional operators, ToE links intrinsic irreversibility to fundamental CP violations and offers a thermodynamic perspective on the universe’s matter–antimatter asymmetry. The “No-Rush Theorem” establishes a universal lower bound on interaction durations, encapsulating the principle that physical processes cannot occur instantaneously. In open quantum systems, ToE predicts an entropy-driven decoherence rate proportional to the norm of the interaction operator, thereby unifying collapse dynamics with entropy flow. A generalized entropic postulate recasts information itself as an entropy carrier subject to context-dependent thresholds that govern measurement irreversibility and wavefunction collapse. The Self-Referential Entropy (SRE) formalism introduces novel Clone Theorems at both quantum and macroscopic scales, alongside an SRE Index that quantifies a system’s internal entropic feedback. New conservation laws and principles—such as Entropic Probability, Entropic CPT symmetry, an Entropic Noether principle, a universal Speed Limit, and a Thermodynamic Uncertainty relation—emerge naturally. Applications range from quantum information theory and AI architecture design to clinical biomarkers of consciousness. The paper concludes by outlining key directions for mathematical formalization and experimental tests of entropic thresholds.