Persistence Theory and The Persistence Equation

This manuscript introduces the Persistence Equation, a unifying framework developed from first principles in thermodynamics and information theory to explain how systems—biological, cognitive, physical, or scientific—maintain coherence or collapse under entropic pressure. Drawing on decades of translational research into thrombosis, autoimmunity, and neurodegeneration, the core insight is that system failure represents a phase transition, occurring at variable rates, and driven by the progressive loss of reversibility.The Persistence Equation is defined as:S(η) = exp[–α · (1 – η) · (Q / T)]Where:η is reversibility efficiency (0–1),Q is entropy-generating energy dissipation,T is environmental volatility (temperature or informational noise),α is a system-specific scaling or sensitivity factor,and S(η) is the persistence score, representing the probability of structural survival over time.This equation acts as a general filter, identifying which structures—whether molecular, cognitive, institutional, or epistemic—can persist in high-entropy environments. The manuscript develops this framework across multiple levels:A step-by-step derivation from thermodynamic and informational first principlesWorked examples demonstrating compounding entropic selection through iterationBiological application to redox reversibility and brain agingEpistemological extensions, offering a model for scientific fragility and reproducibilityOntological implications connecting to Noether’s theorem, entropy, and Terence Tao’s mathematical universeThis theory reframes what we mean by survival, cognition, knowledge, and scientific integrity—proposing that what endures across time is what minimizes irreversibility under entropy. The Persistence Equation offers a scalable, testable model for phase transitions in systems, and a possible bridge between physics, biology, consciousness, and the stability of truth itself.