Yes, almost any coarse graining can lead to an arrow of time unless the map that represents a step forward in time aligns with the coarse graining perfectly. Also, yes, there are often equilibria, but that's the heat death of the universe, and admittedly time is hard to define even macroscopically if everything is at the same temperature.
Chaos isn't even necessary, it just gets you there faster.
The collisionless case is that way for boring reasons: the map aligns with the coarse graining.
Thanks for explaining. I went and wrote a bunch of simulations of billiard ball dynamics with coarse-graining schemes applied and watched this stuff happening in front of my eyes. Pretty cool to see how entropy, energy and time are all directly related in these toy systems - the idea of a clock as a meter for entropy is making a lot more sense to me now =)
Chaos isn't even necessary, it just gets you there faster.
The collisionless case is that way for boring reasons: the map aligns with the coarse graining.