[evouga]

What I really like about this explanation is that it highlights the fact that entropy is not a natural property of the physics system: entropy is only defined with respect to some coarse-graining operation applied by an imperfect observer of the system. So as Sabine points out it seems we should really be talking about multiple different entropies, each of which corresponds to a different mechanism for coarse-graining microstates into macrostates, with each different entropy changing at different rates depending on the coarse-graining mechanism and physical system. (And in particular, God observing the universe would not see entropy change at all; even if there were uncertainty in the initial conditions of the universe, God would see that uncertainty perfectly propagated with no loss of information, in a way made precise by Liouville's Theorem.)

But even this is not the full story, because I can take a mass-spring network, and no matter how I choose to coarse-grain it, I will not see the entropy corresponding to that coarse-graining increase, because the trajectory of a mass-spring system is periodic. Entropy increase requires that the system is ergodic with respect to the chosen coarse-graining operation, i.e. that over long times the trajectory visits the coarse-grained states in a "random" and uniform way. It's not at all obvious to me why the dynamics of particles bouncing around in a box have this property, and particles attached in a mass-spring network do not; and neither the Sabine nor the Veritaserum videos address this or why we should expect all practical real-world physical systems to be ergotic with respect to practical coarse-graining mechanisms.

[dist-epoch]

> mass-spring system is periodic

I don't pretend to understand this stuff, but wouldn't a real mass-spring system slowly stop, due to friction, air resistance, heat dissipation, ...? So a real system wouldn't be periodic.

[sidlls]

Periodic doesn't mean perpetual, perfect, constant periodic motion (in general).

[consilient]

Yes, but they're talking about an idealized harmonic oscillator, not a physical mass-spring system.