Time is a dimension, but not like space

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.

Formalising this intuition is another story though...

It's no wonder, because statistical physics was devised as a tool for the study of complex systems.

For the same reason I don't deem entropy to be a fundamental property of physics, but one of complex systems. As far as I remember from university, the 2nd law of thermodynamics simply arises from the fact, that there are exponentially more unordered than ordered states.

Though information itself may be a fundamental physical property. The recent interest in Quantum computers shines new light on the connection between information and Quantum Mechanics. It remains to be seen, how that point of view is compatible with relativity.

I hope, that one day someone finds out, that the "time dimension" arises in the macroscopic limit from a graph of discrete causal events.