Dear Inés,
thanks for the careful reading and for the comments. You write By all means, don't take this as a critique. Wouldn't it be rather boring if we all already agreed on every tiny little detail? ;-)
@2: I should have phrased that more carefully - this was mainly about my lack of knowledge. For instance, when reading Erik Hoel's essay and scanning the references I got the impression that there might be interesting models which I should learn about. I essentially agree with all you say here.
@1: You say Bolzmann derived irreversibility assuming particles had independent positions and velocities after each collision, which is ultimately not true. He thereby introduced irreversibility.
There is no such assumption in Boltzmann's derivation of irreversibilty, it doesn't even require the notion of collisions. I think I've retold the relevant parts almost completely in my essay. If you'd like more details I really recommend this article by Lebowitz.
Maybe you had some calculation from the kinetic theory of gases in mind?
There is only one way, in which you could claim that Boltzmann already introduced irreversibility through a backdoor, in order to then derive it: On a cosmic scale you have to assume that the universe started in a very special highly ordered state. However, Boltzmann was well aware of that. I recently had a nice discussion about this point with a friend back over at facebook.
@3: I agree. I only gave examples concerning the required rigidity and flexibility. I didn't define these concepts in a general and precise way. I'd love to, but so far I don't know how. And I'd also expect that one can frame those conditions in a substrate-independent fashion.
Thanks again for the stimulating comments!
Cheers, Stefan