Principles of Infodynamics Force, Entropy and the Jahangirian Limit - Formalization of the Intelligence-Entropy Ratio (Jh) and the SynapticString-Q Architecture

Introduction: Infodynamics is developed in this monograph as a rigorous theoretical framework unifying structural coherence, entropy production, and informational dynamics within physical systems. The central construct of the theory is the Infodynamic Ratio I = \frac{F}{E}, where F denotes informational force—the rate at which a system increases its structural coherence—and E denotes entropy production. This dimensionless ratio characterizes whether a system tends toward informational decay, equilibrium maintenance, or structural growth. The work introduces the Jahangirian Limit, defined by the condition I = 1, which marks the critical threshold between inert, homeostatic, and synergistic regimes. The manuscript develops this concept through mathematical physics, information geometry, variational principles, and non‑equilibrium thermodynamics. The treatment is intentionally rigorous and avoids speculative claims, focusing instead on deriving general principles that apply across diverse physical and informational processes. The text is structured as a complete theoretical foundation for Infodynamics, suitable for researchers in physics, mathematics, information theory, and complex systems. It aims to provide a durable conceptual basis for future empirical, mathematical, and interdisciplinary work. Keywords: Infodynamics, Entropy production, Information theory, Non‑equilibrium thermodynamics, Structural coherence, Information geometry, Variational principles, Dynamical systems, Critical thresholds, Jahangirian Limit, Theoretical physics, Mathematical physics