[fedorsapronov]

Nice writeup. One thing I've been exploring is how information-theoretic measures connect to physics — specifically, the KL divergence between a "true" vacuum distribution and a perturbed one gives you coupling constants. In the Fibonacci- structured potential V(s) = v⁴(s−s₀)²/(1−s−s²), the strong coupling αₛ = 1/(2φ³) emerges exactly as the curvature at the vacuum divided by 2. The information- geometric interpretation is that αₛ measures how "distinguishable" the vacuum is from the pole — a Fisher metric on the space of potentials.

Probably a stretch, but it's interesting how divergence measures keep showing up in unexpected places.

[chermi]

There's a lot of work, good and some really bad, about fisher information and physics. vijay balasubramanian and Jim Sethna may interest you, though sethna is more condensed matter. And of course amari.