Persistence Science
A First-Principles Framework for Complex System Resilience
Every complex open system—whether a biological organism, market architecture, physical universe, or digital network—operates under constant thermodynamic and operational degradation. Persistence Science establishes a unified mathematical framework explaining how systems preserve structural identity over time.
Fundamental Root Axiom
$$C(I) \cdot E > D$$
A system persists if and only if its Information-Control capacity ($C(I)$) multiplied by available Energy ($E$) strictly exceeds its total rate of Decay ($D$).
Persistence Capacity
$$C_p = C(I) \cdot E$$
Persistence Index ($\Omega$)
$$\Omega = \frac{C(I) \cdot E}{D}$$
Core Metrics & Theoretical Propositions
From the core condition of persistence, the framework introduces quantitative indicators for systemic health and collapse dynamics:
- The Persistence Index ($\Omega$): Defined as $\Omega = \frac{C(I) \cdot E}{D}$. A system exists in growth ($\Omega > 1$), equilibrium ($\Omega = 1$), or entropic collapse ($\Omega < 1$).
- Theoretical Proposition (System Boundary Integrity): Sustained structural bounds are maintained when energy capture scales proportionally with internal structural complexity.
Cross-Disciplinary Extensions
The framework translates directly across physical cosmology, biological organization, and macroeconomic network systems.