...

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?

--pretty well. It obeys a set of axioms like Shannon entropy... it basically IS Shannon entropy if interpreted right...

...

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 Poincar? 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.

--hmm. Well, that pdf just makes an undefined claim without a proof. I think with appropriate words it is true though. There is an entropy bound in a bounded region with bounded energy. But in my picture we are NOT in a "bounded region" we are infinite spatial extent (my proof of the no-gravity-wave-absorber theorem requires plane gravity waves to exist to even be able to talk about it, which requires infinite space which is asymptotically flat... the "positive energy theorem" about positive mass in GR, proven by Witten et al, also requires asymptotic flatness as an assumption).

...

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

--Well, imagine you are a hot body. (Actually a true fact.) Your atoms bounce around hence accelerate. Hence they emit gravity waves. (At a very low rate.) If you lived inside a perfect reflecting wall mirror box, your emissions of photons, even neutrinos in principle, would not act as "measurements" of you so you'd be able maybe to be quantumly weird. Also, the space of modes inside the box with bounded total energy, would actually be finite-dimensional, hence recurrence would apply. BUT gravitons cannot be shielded even in principle. When you emit them, they fly away right thru the box walls. Bingo -- you've been measured by an "external environment." You now cannot be too weird. Note this happens no matter how good your shielding, refrigeration etc are. Also note, you lost info to that external environment, it "measured" something about you, and hence you gain Von Neumann entropy (at least to the degree the approximation of this emission as a "measurement" is correct). This happens forever. It cannot be avoided. Not even in principle.