A lesswrong attempts to explain physics using Information Theory!. This irritates me.

If we instead have a lot of particles in our first box, we might describe it as a box full of gas. If we connect this to another box and forget where the particles are, we would expect to find half in the first box and half in the second box. This means we can explain why gases expand to fill space without reference to anything except information theory.

No, you can't, because you're still presuming that gases do expand, i.e., that merely connecting two containers is enough to mix their contents. Otherwise, you're saying that if you fill one bottle with orange juice and another with vodka, and then forget which is which, you've made a screwdriver.

Then it gets weird and confused, talking about a box divided in two parts, with green particles on one side and pink ones on the other.

We might expect the partition to move some, but not all, of the way over, when we forget as much as possible.

Forgetting where things are doesn't give you psychoflexitive powers!

And from the comments:

My current understanding is that QM is not-at-all needed to make sense of stat mech.

No. If you don't incorporate quantum mechanics (or at the very least take some results of quantum mechanics as valid), you will get statistical mechanics very wrong rather quickly. Your results for the thermal properties of gases will get worse the more you calculate. You'll convince yourself that magnets are impossible. Etc.

For all that Yud has been praising the Feynman books ever since HPMOR at least, he doesn't seem to have inspired his fans to actually read the Lectures on Physics.