Core Relationship:
\[
\frac{dC}{dt} = -\frac{dF}{dt} \implies C(t) = F_0 - F(t)
\]
Coherence accumulation rate equals free energy reduction rate. Success creates rigidity.
Inverse Relationship: F(t) & C(t)
\(C(t) = F_0 - F(t)\): As free energy decreases, coherence accumulates
Phase Portrait: (C, dC/dt)
Trajectory shows approach to rupture threshold
Precision-Coherence: Π(t) ∝ eC/Ω
Exponential memory amplification with learning
Expected Free Energy: G(π)
Exploration vs Exploitation balance controlled by Ω
Memory Depth Evolution
\(\tau_{eff} = \int_0^t e^{C(\tau)/\Omega} d\tau\): Non-Markovian transition
Exploration-Exploitation Spectrum
Policy weighting: \(\text{Score}(\pi) = \Omega \cdot \text{Epistemic} + \frac{1}{\Omega} \cdot \text{Pragmatic}\)