@Bracewell,
I would agree that it's an awful lot of potential volume, but that does not mean that it is infinite. Given a finite space, a system must be closed at some point. It might not be at a point that we can easily conceive, but without a nullspace randomly generating energy/matter, the system is closed. The ocean is an awfully big place to a single amoeba floating around; it is so vast as to seem infinite, but it's not. I suggest that we're dealing with a finite space because a finite amount of matter would seem to suggest a finite space, although it's true that it would not prove it.
In terms of entropy, I don't see how it's dead. We still see the effects in a localized manner; if not to perfection (due to changes outside the given system affecting the system) then enough to see the truth of it. My basic thought runs like this:
Regardless of entropy tending to increase in systems, we are aware that there is no such thing as a perfect engine. Some energy is also lost to heat. Eventually, as long as there is motion, all energy will have been lost to heat. There are only two ways this scenario can be avoided.
One, an input of energy from an outside source. The difficulty with this scenario is that the heat is still there. Our heat never dissipates(as one thing gets hotter, another, necessarily, gets colder). Since Einsteinian physics relies on the idea that energy is never created or destroyed, it simply changes form, this solution would also invalidate what seems to be a very workable set of physics.
Two, we reverse the general theory of relativity. If E=MC2[I have no idea how to get superscript, my apologies] then necessarily M=E/C2. If you can turn matter into it's correspondant energy, then it should be possible, if the laws of mathematics are to be believed, to turn energy into matter. If, under certain circumstances, this useless heat can be transformed into matter, we've solved our problem. Entropy can exist and at the same time not be relevant in the grand scheme of things.
Of course, I'm not nearly as up to date on a lot of astronomy and physics as I ought to be, I'm just chipping my 2 cents in.