Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory (arxiv.org)

I found https://www.quantamagazine.org/epic-effort-to-ground-physics... much more informative. Sometimes you can't digest everything in 10min.

In my perception Sabine’s quality degraded over the last year or so.

Maybe it’s also the topics she covers. I’m not sure why she is getting into fantasies of AGI for example.

I liked the skeptical version of her better.

Shan Gao's review on this is really nice and accessible, thanks.

I've been puzzling about this as well. The best answer I have (as an interested maths geek, not a physicist, caveat lector) is that it sneaks in under the assumption of "molecular chaos", i.e. that interactions of particles are statistically independent of any of their prior interactions. That basically defines an arrow of time right from the get-go, since "prior" is just a choice of direction. It also means that the underlying dynamics is not strictly speaking Newtonian any more (statistically, anyway).

Strictly speaking, naturally on its own, it doesn't. Detailed equations remain reversible. Even for very big N, typical isolated classical mechanical systems are reversible. However, typical initial conditions imply transitions to equilibrium, or very long stay in it. The reversed process (ending in Poincare return) will happen eventually, but the time is so incredibly long, it can't be verified.

This has been known for a long time: the irreversibility comes from the assumption that the velocities of particles colliding are uncorrelated, or equivalently, that particles loose the "memory" of their complete trajectory between one collision and another. It's called the molecular chaos hypothesis.

See https://en.wikipedia.org/wiki/Molecular_chaos