4 ms·

Interesting, so if I understand right you are saying that coarse-graining your states can produce an arrow of time on its own? Given some fixed coarse-graining,

Interesting, so if I understand right you are saying that coarse-graining your states can produce an arrow of time on its own? Given some fixed coarse-graining, I can see that entropy would initially increase, since your coarse-graining hides information from you. The longer you evolve the system under this coarse graining the less certain you will be about the micro-states. But I would expect this to eventually reach an equilibrium where you are at "maximum uncertainty" with respect to your coarse graining. Does that sound right at all? And if so, then there must be something else responsible for the global arrow of time, right? > If you set the collision probability to zero it's time reversible even with molecular chaos Is this true for boring reasons? If nothing interacts then you just have a bunch of independent particles in free motion, which is obviously time-reversible. And also obviously satisfies molecular chaos because there are no correlations whatsoever. Maybe I misunderstand the terminology.

whatshisface 1y ago
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.
- bubblyworld 1y ago
  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 =)

whatshisface 1y ago

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.

bubblyworld 1y ago
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 =)