I'm having difficulties understanding what liouville's theorem is all about. I was "meditating" over an adiabatic free expansion and i got stuck because of a contradiction in my reasoning so it seems i still don't have a clue what liouville actually wants me to understand :) So imagine an ideal gas in volume V that adiabatically expands (free) to a volume 2V. This means more microstates. Then my contradiction: liouville says that the volume of the microstates (of the macrostate) in phase space under hamiltonian flow stays the same. And as the energy of an ideal gas after free expansion also remains the same, this would mean that the volume of the microstates corresponding to the first macrostate would stay the same So i get the same "amount" of microstates for the final macrostate which is in contradiction with the above statement and is just plain wrong Clearly there's a fundamental flaw in my reasoning, and it would mean a lot if someone could give me a nudge in the right direction! Thanks! *edit* okay i meditated a little more and i guess it's because you have to find a reversible path between the initial and final state because it's an irreversible process, so you can't use Q=0 (and then E won't be constant). Is this right?