Entropy is generally considered to be an *emergent* property of matter - if
you look closely enough at matter, it becomes impossible to see it (e.g. in
single atom interactions). The source of the "entropy gradient"  appears to
be boundary conditions on the universe (e.g. the existence of the big bang
+ cosmic expansion). B ut is also as you say related to the existence of
gravity, which is a major constructor of gradients from which energy can be
derived -- in particular, stars. It's also related to nucleon binding
energy following the curve it does, and the fact that the big bang created
mainly the two lightest elements - thus allowing lots of scope for nuclear
reactions to move the contents of the universe towards the stablest
configurations. (This is all very fortuitous for us, or WAP related as the
case may be.)

However, contrariwise, black hole physics implies that entropy is a
*fundamental* property of space-time (Hawking's famous result, the
Beckenstein bound, etc). I don't know if this apparent dichotomy has been
resolved. You comment about a universal collapse reversing sign is
interesting, I can see that that could work as described - although I have
no idea how or why the sign reversal would occur.

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