[lisper]

> Of course it is trading one assumption for another.

Why "of course"? If would only be "of course" if it were impossible to derive the second law from Newton's laws. AFAIK that hasn't been proven impossible.

But I think you may have misinterpreted my objection. It's not that I object to substituting one axiom for another in general. That can often represent progress. For example: before Einstein, it was observed that inertial mass and gravitational mass were very close to each other, lending considerable weight to the reasonableness of assuming that they were in fact the same. It turns out that you don't have to assume this. There's another set of axioms that allow you to prove this, and these axioms are "better" because they provide a much larger scope of explanatory power for the same axiomatic price.

By way of contrast, Turing machines and the lambda calculus are "the same" in some deep sense that makes it silly to argue about which one is "the right model" of computation.

It's not clear to me whether adopting Liouville really represents progress a la relativity, or whether it's arguing potato-potahto a la Turing vs Church.

BTW, it just occurred to me that there is a fundamental difference between the thermodynamic and quantum arrows of time: the thermodynamic arrow of time is reversible in a non-isolated system. The quantum arrow is not.