I think some stuff about the universe is starting to come into view, thanks to some of my reading that's been broken down into lay terms, which is good since my knowledge in this area stops right after Trig and high school physics.
If I'm reading Greene correctly, entropy isn't a process confined to temporal movement towards the future, but also occurs when you move backwards in time. This seems strange because all of our day-to-day references seem to indicate the exact opposite. A slice of bread left on the side of the road decays into disorder and you never see slices of bread being composed by random movement of matter. Or, to use Greene's example, eggs dropped on the kitchen floor break and we never see them randomly form from the molecular constituents that make them up. That's because movement from states of high entropy (the chaos of dispersed particulate matter) very rarely moves towards states of low entropy (such as we often see in the order of day to day life... complete objects, ordered sets, and so on) are extremely rare.
This means that the assumption that entropy only increases towards the future is highly improbable. If that assumption is true, it would be required for the current, improbable, state of low entropy arose from a state of even lower entropy, something that is even more statistically unlikely. In fact, it's more likely that if you go far enough back, you'll find low entropy reverting to high entropy. The order that we see in the universe (galaxies, stars, life, and so on) was a random emergence from pure chaos. All such phenomena indicate that entropy can decrease (and it had to at some point in the past, otherwise we wouldn't be here), albeit on extremely rare occasions. This puts the Big Bang in a new light because it means that it was nothing more than a chance movement from a state of high entropy to one of low entropy. The universe has probably existed for an eternal amount of time. Given that infinite time span, it was inevitable that the universe would eventually be created. Who knows how long the universe sat in chaos, just waiting for that unlikely event to occur? Probably an amount of time that we can't even conceptualize. This is interesting because, in contrast to scientific eschatologists, like Tipler, who think that the Big Bang implies a "beginning" of the universe, this suggests that there was chaos prior to that beginning. Don't misunderstand me, the Big Bang was definitely the beginning of space-time in the way that we understand it, but entropy still existed before it occurred, which gives some credence to the Nietzschean theorists of eternal recurrence because it allows for an infinite span of time, allowing the occurence of every possible configuration of matter, no matter how unlikely.
It also forces us to reconceptualize time. Up until now, entropy was the best way to determine whether time was moving forwards or backwards from an absolute perspective; but if entropy increases when you move backwards, we lose that frame of reference and time becomes symmetrical. This suggests that, even though we seem to perceive time in a unidirectional fashion, there's no legitimate, empirical basis for assuming that that direction is an ontologically applicable feature of our universe. Separate from our specific apprehensions of time moving in one direction, there's no reason to assume it's any more of a forced sequence from past to future than there is to assume that one part of the curved space of the universe is any closer to the end than any other. Time certainly exists, but it's not linear in the fashion that we normally assume that it is.
This also has interesting implications for an open universe. It means that even if the universe continues to expand forever into a state of heat death and entropy, that state can be reversed, even if it's extremely improbable (after all, it was also unlikely when it happened last time). Maybe this is just one brief phase of low entropy among an infinite number of them throughout the infinite expanse of reality.