Axiom 4: Non-Equilibrium Information Physics

We hypothesize that physical reality can be reformulated with an Information Field $\Psi$ as the fundamental ontological substrate, from which mass, energy, spacetime, and thermodynamic entropy emerge as phenomenological manifestations. Building on rigorously proven Lyapunov energy decay $(\dot{E} \le 0)$ in gauge-coupled dissipative field dynamics, we construct a Non-Equilibrium Information Physics (NEIP) framework satisfying the generalized second law $\Delta S_{\text{total}} + \Delta I_{\text{Fisher}} \ge 0$.

Key postulates:
(1) Mass represents stable, low-entropy information patterns with locked phase coherence;
(2) Energy represents propagating information updates as temporal coherence waves;
(3) Vacuum is a high-entropy, uncorrelated informational state.

We define information rigorously through Shannon entropy $H[\Psi]$, Fisher information $I[\Psi]$, and a coherence measure $\rho_c$ with observability threshold at $\rho_c \simeq 0.95$, empirically constrained from decoherence experiments. The framework predicts testable deviations from standard physics in quantum decoherence rates, thermodynamic-to-optical coherence transitions, and cosmological evolution. We present experimental protocols (P-suite: P1–P4) spanning EEG $\alpha$-wave synchrony, laser ring-down dynamics, and CMB power-spectrum modifications.

This work offers a conservative extension of quantum mechanics and general relativity, grounded in information geometry and dissipative gauge theory, with explicit falsification criteria.