3. Field Coherence Length
The coherence length \xi is estimated from the two-point correlation function:
C(r,t)=I(x,t)I(x+r,t)C(r, t) = \langle I(x,t) I(x + r,t) \rangleC(r,t)=I(x,t)I(x+r,t)
with (t)\xi(t)(t) defined by:
C(,t)=C(0,t)e1C(\xi, t) = C(0, t) e^{-1}C(,t)=C(0,t)e1
Results:
Prior to blink: \xi is minimal, field is uncorrelated
Post-blink: \xi grows with time, peaking at stable pattern formation
Long coherence lengths coincide with:
Phase-locking across domains
Vortex lattice regularity
Suppression of random fluctuations
This mirrors cosmological inflation models, where quantum fluctuations become coherent seeds of structure.
4. Entropy Gradient and Geometric Flow
Interestingly, entropy gradients within the simulation correlate with spatial curvature distributions. We define an effective information-geometric flow:
Js(x,t)=S(x,t)J_s(x,t) = - \nabla S(x,t)Js(x,t)=S(x,t)
This entropy flux vector field tends to align with:
