If our comoving patch defines an approximately closed system, the next step is to think about its space of states. General relativity tells us that space itself, the stage on which particles and matter move and interact, evolves over time. Because of this, the definition of the space of states becomes more subtle than it would have been in if spacetime were absolute. Most physicists would agree that information is conserved as the universe evolves, but the way that works is quite unclear in a cosmological context. The essential problem is that more and more things can fit into the universe as it expands, so—naively, anyway—it looks as if the space of states is getting bigger. That would be in flagrant contradiction to the usual rules of reversible, information-conserving physics, where the space of states is fixed once and for all.
Of course we've already looked a bit at the life of the universe, way back in Chapter Three. The difference is that we're now focusing on how entropy evolves, given our hard-acquired understanding of what entropy is and how it works for black holes. This is where we review Roger Penrose's well-known-yet-still-widely-ignored argument that the low entropy of the early universe is something that needs to be explained. In a sense, this is pretty straightforward stuff, following directly from what we've already done in the book. But it's also somewhat controversial among professional cosmologists. The reason why can be found in the slightly technical digression that begins on page 292, "Conservation of information in an expanding universe." The point is that physicists often think of "the space of states in a region of spacetime" as being equal to "the space of states we can describe by quantum field theory." They know that's not right, because gravity doesn't fit into that description, but these are the states they know how to deal with. This collection of states isn't fixed; it grows with time as the universe expands. You will therefore sometimes hear cosmologists talk about the high entropy of the early universe, under the misguided assumption that there were fewer states that could "fit" into the universe at that time. (Equivalently, that gravity can be ignored.) This approach has, in my opinion anyway, done great damage to how cosmologists think about fine-tuning problems. One of the major motivations for writing the book was to explain these issues, not only to the general reader but also to my scientist friends.
At the end of the chapter I deviate from Penrose's argument a bit. He believes that a high-entropy state of the universe would be one that was highly inhomogeneous, full of black holes and white holes and what have you. I think that's right if you are thinking about a very dense configuration of matter. But matter doesn't have to be dense -- the expansion of the universe can dilute it away. So I argue that the truly highest-entropy configuration is one where space is essentially empty, with nothing but vacuum energy. This is also very far from being widely accepted, and certainly relies on a bit of hand-waving. But again, I think the failure to appreciate this point has distorted how cosmologists think about the problems presented by the early universe. So hopefully they read this far in the book!