Warren Smith wrote:

--correct comment... for classical Hamiltonian mechanics (which is what Poincare Recurrence thm is about). But for Von Neumann formulation of quantum mechanics,

Okay, I accept that there exists a quantity that is invariant under the deterministic QM laws and strictly increases during probabilistic wavefunction collapse (for a rather crude example, you can simply define an integer N, which is the number of wavefunction collapses since the beginning of time). But is the von Neumann entropy compatible with the standard concept of entropy?

entropy stays same - except that during measurements it increases. Since quantum is more true theory of nature than classical... it would be you who "are wrong."

There are quantum-mechanical analogues of the Poincaré Recurrence Theorem, such as this one: http://elcent.shinshu-u.ac.jp/wakate/abstracts/sasaki.pdf Hence, I am not ready to accept defeat just yet.

In my picture of quantum mechanics & decoherence, the graviton sea serves as an infinite "entropy sink" (as Meeker was calling it). It actually is infinite dimensional

That comes as no surprise. Most phase-spaces in quantum mechanics are infinite-dimensional Hilbert spaces. Sincerely, Adam P. Goucher