Time is a dimension, but not like space

I only got my undergrad in physics, but I think there is something there to be mined between time as a dimension and the second law of thermodynamics. Why this one?

First, I will render a quote which never failed to amuse me: "The law that entropy always increases holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations -- then so much the worse for Maxwell's equations. If it is found to be contradicted by observation -- well, these experimentalists do bungle things sometimes. But if your theory is found to be against the Second Law of Thermodynamics I can give you no hope; there is nothing for it to collapse in deepest humiliation." (Eddington)

Why such honor? For one, in statistical physics, you can more or less derive the second law of thermodynamics, from scratch. No need for observation. It's just there the same way the quadratic equation is. Somewhere I have a cheap Dover reprint which contains a relatively easy to follow construction of the second law. It's the math. You can measure things badly, you can find one phenomenon creating the appearance of another, but you cannot fool The Math.

And so the statistical physics you can get from just math gives you this arrow of time, flying only one way, just as we see from spacetime.

To me, and again, I only got a few grad courses under my belt in it, this suggests not just a deep connection between entropy and spacetime, but the inevitability of it from the basic math (really, a talented high schooler could be coached through it) means that there is something about large (for n = ?) numbers of particles losing the reversibility which is so often present in particle interactions where n is smaller. What gives there? How do we go from this "trend" emerging to it being a property of spacetime even if no particles are sitting in said spacetime.

Not that I would have dared write the great Wheeler, but I have wondered if his "geon" concept would have fit in with this sort of thing. It seems so fundamental. One can imagine a universe with a different number of un-unified forces, or gravity dropping as the inverse-cube, or varying physical constants, but the math is still the same in these universes and it then suggests that there's no, uh, room for an option wherein the time facet of spacetime is anything but an arrow flying forever on towards entropy in its many masks.

A great task, or perhaps a very alluring windmill, for someone younger and brighter than I.

I'm in a similar boat, but I've always felt the opposite! I've always felt the second law is kind of a shoe-in and maybe even shouldn't be a law at all.

The first and third laws, "energy is never created or destroyed" and "for every action there's an equal and opposite reaction" are always true! To my knowledge, no process is ever allowed to break either law. (With exceptions for cosmological process like the expansion of the universe that we really don't purport to understand.)

The second, "entropy can only increase" isn't! That's right, I said it. The processes it describes (a cup unshuttering, or coffee unmixing, or particles all finding their way into the same side of a box) are totally legal process, albeit statistically unlikely. If you restrict your system to few enough particles (say, n=3), random processes that decrease entropy are not only possible, but something that happens with regularity!

Now, I make no claims to be right here. I suspect that Eddington fellow probably knows what he's talking about. But, this has been a longstanding thorn in my understanding of physics, so I'd be interested if anybody has any interesting insights!