- #71
Nullstein
- 313
- 201
You have a misunderstanding here. It's not that Gibbs' H-theorem is inapplicable. The idea of this route to thermal equilibrium is that you artificially coarse grain your state in order to apply Gibbs' H-theorem (without any physical justification). This is the unphysical step that I have been pointing out all along. The actual state of the system is always a delta state, but you have to introduce some artifical coarse graining in order to apply the theorem. And it doesn't even suffice to coarse grain once in the beginning. You have to do it over and over, because a single application of Gibbs' H-theorem doesn't suffice to reach ##S_\text{max}##. Gibbs' H-theorem only shows that ##S(t_1) > S(t_0)## and ##S(t_2) > S(t_0)##, but from this it doesn't follow that ##S(t_2) > S(t_1)## (from ##2 > 0## and ##1 > 0##, it doesn't follow that ##1 > 2##). In order to show that, you must again perform a coarse graining at ##t_1##, so you can apply Gibbs' H-theorem. Unless there is a physical source for these coarse graining steps (e.g. coupling to some heat bath), this route to thermal equilibrium is therefore excluded.