> Eventually, though, the theory of quantum mechanics showed why it wouldn't work.
I was familiar with the information theory arguments (the same presented in Wikipedia[1]). Is that why they mean here by "quantum mechanics" or is there another counterargument to Maxwell's daemon?
1: https://en.m.wikipedia.org/wiki/Maxwell's_demon#Criticism_an...
https://en.m.wikipedia.org/wiki/Maxwell%27s_demon#Criticism_...
http://www.av8n.com/physics/thermo/entropy-more.html#sec-pha...
With 'entropy' being an obsolete term for (lack of) information, and
> “classical thermodynamics” is a contradiction in terms.
I think practically though, even before you hit anything "quantum", the requirement that you physically interact with the system is what dooms you.
The main requirement for the hole is that it's small enough that (with high enough probability) only at most one or a handful of molecules will make its way through.
And that size is completely independent of the size of your molecules, and only depends on how many there are per unit volume. There's a lot of 'empty space' between molecules in a gas.
> In the middle of the divider was a tiny gate, just large enough to admit one molecule of gas.
Still, that's quite a small hole relatively speaking. So you'd have to be fairly precise about both position and velocity. Potentially more than is allowed by Plank's constant. I dunno though, this isn't one of the counterarguments in the Wikipedia page, so probably you're right.
Searching for them did bring me to an interesting discussion :
https://www.lesswrong.com/posts/YSFRazdoWXKHgNakz/link-the-b... (2015)
and then to :
https://bayes.wustl.edu/etj/articles/second.law.pdf (1998)
Which confirms my suspicions, but also sheds lights on how old the confusion is !
There are a bunch of assumptions that are easy to make (because they almost always are true), but very hard to get rid of when they aren't :
- that entropy is objective/ontological rather than subjective/epistemic
- that entropy is equivalent to disorder
- that temperature can always be defined
- that entropy is extensive
(- I think there was at least another one, but I had to do something else in-between and I don't remember now)
- oh yeah, maybe it was that there's a difference between a distribution and a macrostate ? (not sure about it myself)
Now, I don't know what the Bayesian framework can bring to the table here (not being sufficiently familiar with it down to the nuts and bolts of calculations), but if it can prevent us (and future students) from making these mistakes over and over and over again, it would be real progress.
https://arxiv.org/abs/1508.02421v3 (updated, 2017)
They claim to fix the criticisms, see the section "The Bayesian arrow of time."
Who knows how well they did though.
As far as I can tell they're still making impossible assumptions, because certain Bayesian problems can't be calculated under a certain amount of energy, and some can't be calculated at all while embedded in spacetime (excepting time travel, and sometimes even then).
I think it's necessary to increase (on expectation) the entropy in a closed system when measuring, unless you take measuring to be magic and not a physical process.
So all in all, a classic description would work reasonably well. (Remember that quantum uncertainty is related more to de Boglie wavelength than physical size.)