We define a spatial field entropy S(t)S(t)S(t) as a measure of phase and amplitude disorder over a finite domain:
S(t)=P(I(x,t))logP(I(x,t))dxS(t) = - \int P(I(x,t)) \log P(I(x,t)) \, dxS(t)=P(I(x,t))logP(I(x,t))dx
Where P(I(x,t))P(I(x,t))P(I(x,t)) is the probability density of field intensity values at time ttt.
Simulation results:
Immediately after blink excitation, entropy spikes due to random field spreading.
Over time, entropy decreases sharply, correlating with:
Soliton formation
Vortex stabilization
Phase alignment across regions
Plateauing of entropy indicates transition to quasi-stable coherent regimes
This mirrors self-organization and dissipation-driven ordering, consistent with non-equilibrium thermodynamics in open systems.
2. Information Density and Coherent Structures
We define local information density I(x,t)\mathcal{I}(x,t)I(x,t) as:
I(x,t)=I(x,t)2+(x,t)2\mathcal{I}(x,t) = \left| \nabla I(x,t) \right|^2 + \alpha \left| \nabla \phi(x,t) \right|^2I(x,t)=I(x,t)2+(x,t)2
Where (x,t)\phi(x,t)(x,t) is the phase component, and \alpha weights the contribution from phase gradients.
Findings:
Localized peaks in I(x,t)\mathcal{I}(x,t)I(x,t) correspond to:
Solitons
Curvature spikes
Vortex cores
These zones store and trap information, maintaining their profile across time steps
Suggests a form of field memory, analogous to localized encoding in condensed matter or topological quantum computing
This supports the information-first cosmology view---where structure emergence arises from densification and stabilization of information content, not mass or energy alone.
