Also, simply starting with a prior and evolving the distribution in accord with the laws will not work (even ignoring what I say in the next paragraph). The entropy of the probability distribution won't change if you follow that procedure, so you won't recover the Second Law asymmetry. This is a consequence of Liouville's theorem. In order to get entropy increase, you need a periodic coarse-graining of the distribution. Adding this ingredient makes your derivation even further from a pure reduction to the fundamental laws.

Dang, you're right. I'm still not entirely convinced of your point in the original post, but I think I need to do some reading up in order to:

• Understand the distinction in approach to the Second Law you're proposing is not sufficiently explored
• See if it seems plausible that this is a result of treating physics as rules instead of descriptions.

This has been an interesting thread; I hope to continue discussing this at some point in the not super-distant future (I'm going to be pretty busy over the next week or so).