Whats confusing to me is the dual use of the word entropy in both the physical science and in communication. The local minimums are some how stable in a world of increasing entropy. How do these local minimums ever form when there's such a large arrow of entropy.

Certainly intelligence is a reduction of entropy, but it's also certainly not stable. Just like cellular automata (https://record.umich.edu/articles/simple-rules-can-produce-c...), loops that are stable can't evolve, but loops that are unstable have too much entropy.

So, we're likely searching for a system thats meta stable within a small range of input entropy (physical) and output entropy (information).

There are theories and evidence that your brain operates hovering on the edge of the phase transition to chaos

https://en.m.wikipedia.org/wiki/Critical_brain_hypothesis

If you have any system that tries to gravitate to a local minimum it is almost impossible to not make Newton's fractal with it. Classical feed forward network learning does pretty much look like newtons method to me. Please take a look into https://en.m.wikipedia.org/wiki/Newton%27s_method