[ithkuil]

I guess what's confusing me in this scenario is that we're not saying that the two halves of the cylinder contain particles with different properties (e.g. different velocities) but only that we can "tell them apart" as if they were coloured differently, but otherwise behaving in exactly the same way.

The former scenario is famously the setting for Maxwell's daemon. I was assuming this scenario is something else.

I'm confused because on one hand I can see that it requires work to reorder the particles once they have been shuffled around. On the other hand I don't see how one could extract work while they get shuffled around if they all have the same momenta.

Perhaps the answer is that we cannot have a system where the microscopic entities are at the same indistinguishable but also distinguishable. Perhaps if they had different "colours' it means they do interact differently with the environment? I'm still confused frankly

[FiatLuxDave]

Historically this caused a lot of confusion, so you aren't the only one. You may find E. Jaynes' classic paper on the Gibbs mixing paradox helpful, especially from page 7 onwards:

https://www.mdpi.org/lin/entropy/cgibbs.pdf

[Lichtso]

> only that we can "tell them apart"

That is irrelevant, we don't need to be able to tell them apart, the membrane needs to be able to. Besides that, they can be completely identical.

> I'm confused because on one hand I can see that it requires work to reorder the particles once they have been shuffled around. On the other hand I don't see how one could extract work while they get shuffled around if they all have the same momenta.

In the illustration with the cylinder from Wikipedia you can see that the level of the one fluid (which the other fluid is selected into) rises. It performs work against gravity and builds up potential energy / increases the pressure. You can harvest that.

> The former scenario is famously the setting for Maxwell's daemon. I was assuming this scenario is something else.

In Maxwell's daemon you start with a substance which is already mixed and separate it into its components. That requires work and is the exact opposite of what is happening here. In fact it is called reverse Osmosis [0]. Osmosis gives you pressure which you can harvest, so reverse osmosis needs pressure back to operate. That completes the cycle.

[0] https://en.wikipedia.org/wiki/Reverse_osmosis

[jimmySixDOF]

>That is irrelevant, we don't need to be able to tell them apart

There is some speculation that intelligent behavior evolved as a response to entropy as a way to exert control over future events in the environment.

https://www.santafe.edu/news-center/news/dedeo-intelligent-b...