While my daughter was learning some basics of entropy, I realize a Big Crunch would reduce entropy as the universe becomes more ordered. And, since the system in question IS the environment, entropy would reduce or the change in entropy would be zero, at best…both are violations of the laws of thermodynamics. How do scientists explain this one away? There’s an increase in entropy in a parallel universe?
Mostly they don’t because Big Crunch theories are out of style.
Entropy can be a subtle concept in gravitationally interacting systems. Consider two lumps of stuff in free space, initially at zero velocity, that attract each other. If they fall towards one another, miss (say, because they don’t interact, because one has a hole the size of the other, or something like that), then separate again, at some point, they’ll reverse, and the same process starts again—so what we have here is clearly a reversible process, thus, entropy ought to be constant.
But what about the case when the two lumps do interact, and hit each other, at quite high speed, perhaps? Well, here things get complicated: what you’ll end up with is some messy lump, perhaps some shrapnell, with all kinds of internal dynamics happening—the impact will produce pressure waves in the material, the material will heat up, and so on. In the end, there won’t really be a possibility to reverse the process—the energy will have been dispersed into heat, sound waves, radiation, etc. Thus, in this process, entropy goes up, even though the system’s total volume decreases—the opposite of what you’d expect, given that there appear to be many more states corresponding to the system being dispersed, than to it being confined.
Now take a thinly, nearly uniformly dispersed gas: simple statistical reasoning on such a volume of gas would indicate that it should continue to expand, and thus, dilute itself—and that’s indeed what happens, say, if you open a pressurized container in an evacuated volume. But if the gas has enough total mass, what you’ll instead observe is that if becomes more clumpy—initial inhomogeneities tend to concentrate more and more of the gas, until we have instead a configuration of lumps of matter. Indeed, this is the process by which stars and planets form.
So, if one considers gravitational interactions, high entropy stated don’t conform to diluted matter distributions, but rather, to very clumpy ones, even though, superficially, this seems in violation of the second law—but if you do the calculations carefully enough, you’ll see that on average, the entropy of the matter configuration plus any kind of radition produced in the collapse process, like everything else in the universe, obeys thermodynamics. In fact, it can even be shown that the ultimate end product of any gravitational collapse, a black hole, has the highest possible entropy that can be stuffed into the volume of space it occupies. Thus, the end product of gravitational collapse is, in fact, a very high entropy state, and we need not appeal to any exotica to solve the apparent paradox.
Now, perhaps you’re wondering how, then, a Big Bang could ever work—it seems like it’s the reverse of the Big Crunch, which I’ve just explained is an entropy increasing process, thus, it would seem to decrease entropy! But in fact, a Big Bang is not the time reverse of a Big Crunch. Rather, the Big Bang state (just after the initial singularity; what happens there, of course, nobody really knows yet) is in fact a very homogeneous, low-entropy state, as a look at the tiny variations in the Cosmic Microwave Background shows. It’s from these tiny variations that, ultimately, the observed matter distribution of the universe developed, in just the sort of entropy-increasing gravitational clumping process I described. All is well!
Now, of course, the question is: how did the universe get into the initial low-entropy state in the first place? Well, I’m gonna leave that one as an exercise for the reader… 
(But seriously, if you do find out, please tell me.)
Are they?
Wiki says that systems “tend to maximize their entropy over time” – adding that, “in equilibrium, each microstate that the system might be in is equally likely to occur, and when this assumption is made, it leads directly to the conclusion that the second law must hold in a statistical sense. That is, the second law will hold on average, with a statistical variation on the order of 1/√N where N is the number of particles in the system. For everyday (macroscopic) situations, the probability that the second law will be violated is practically zero.”
Given enough time, “practically zero” is pretty good odds.
It’s hard to see how they would work with the evidence that the expansion of the universe is accelerating, instead of decelerating as we used to think it was. Of course, we don’t know what is causing the acceleration or how it works. We call it “dark energy”, but really, we don’t know what the hell it is. If you can figure it out, you’d probably be a candidate for a Nobel Prize in physics. I suppose we can’t rule out that it could possibly change sign at some point and make the universe start contracting. There’s no evidence to date that this is likely to happen, but it can’t be ruled out.
Big Rip theories are more in vogue than Big Crunch theories, currently.