Have you heard of Poincar̩ recurrence times? Basically, the second law of thermodynamics gives us an arrow of time that says the entropy of a closed system must strictly increase over time. In other words, a system moves from states of order to states of disorder in an irreversible way Рonce it leaves the sheltered world of order, there is no return. However, if you take a look at a system evolving in phase space, the ergodic hypothesis tells you that systems uniformly sample their microstates. That is, a system will eventually return to a state arbitrarily similar to its original state given enough time. This time is the so-called Poincar̩ recurrence time.

So we’re trying to marry these points of view in a satisfactory way. Right now, I’m still collecting bits of theory I need to even understand the problem, so I can’t claim any progress yet. But time and chaos are such fascinating issues that I’m in no rush.

I’ll be sure to post more thoroughly on the research as I understood more.

Love,
Aunt MaryPat