Thanks greatly Tom,
Astute observations about the short scale vs long scale activity within a system. This appears to be more or less universal. As you say, the most drastic changes often happen on a short interval, and go unnoticed if one's observation considers only longer time scale phenomena.
Non-linear entropy is observed mostly when you take things that appear to happen instantaneously, and re-examine that behavior in terms of reciprocal exchanges. It's not instant at all, and involves a lot of back and forth activity, but it does happen very fast. Decoherence happens quicker still, but a closer examination shows us that is a dance as well.
However one would never know it is a complex phenomenon, without examining large excursions that happen in a short time more closely.
All the Best,
Jonathan