Would it be fair to say that the second law of thermodynamics is only "a law" given our human perspective of the direction of time? If time has no "arrow", but a memory is only possible in non-decreasing entropy which is our perspective, there can be another perspective in which the big bang is the future and our future is the past, only we cannot comprehend it because a memory is not possible in decreasing entropy?
The second law of thermodynamics is about entropy, which is an observer dependent quantity. It is the discrepancy between what one knows about a system (e.g. its temperature) and its state (e.g. the position and momentum of every particle in a classical gas). A being that knows the exact state of a system does not observe entropy increasing or decreasing. At least classically.
Digging deep into my memory of classical mechanics, I think this is along the right lines. However, I believe (seem to recall) entropy is an actual measure of the number of ways a system can be ordered in its details and still produce the same generalized outcome.
A crystalline solid has relatively low entropy because you can be reasonably sure where each nucleus is, as they are highly ordered. A gas or plasma can have the nuclei distributed nearly randomly. Both systems can be measured generally (stochastically, or of their overall or average properties) but the number of ways you can organize all the nuclei to get those results very different between the two systems.
Feel free for someone more knowledgeable to correct or expand.
That's basically the gist of it. The entropy of a system is proportional (via Boltzmann's constant) to the natural log of the number of available microstates, where microstates are configurations the system could be in, and available denotes that they have the same total value for all conserved quantities as the aggregate system. Consequentially the system is free to spontaneously transition between any of its available microstates.
Even if we were not able to tell which is which between the past and the future (as in Feynman's dropped egg though experiment), it would still be paradoxical that we could still easily _distinguish_ them in most macroscopic changes, given that's supposed to be caused by a superposition of time symmetrical microscopic changes. Even with no observer, no past and no future, why are most macroscopic events asymmetric?
