What does the arrow of time and entropy say about the universe and repetition? This question What is the relationship between how time is viewed in thermodynamics and how time is viewed in general relativity? is close to what I was wondering, but it didn't get into repetition specifically.
I'm not a physicist, my Scientific American level of understanding is that the universe is constantly changing, I think that is specifically the changing state of entropy, and that constant change is what creates the arrow of time.
Nothing is ever truly unchanging and so the constant change is how we perceive time.
But doesn't repetition fit in somehow?
If some state of the universe repeated, wouldn't that be a reserving of the arrow of time?
I suppose the answer might simply be no, and if I am confused by the repetition, that's just a problem with my perception.
But, anyway, do these theories of arrow of time and entropy say anything about repetition?
 A: The arrow of time and the second law of thermodynamics are the same thing. They are just different ways to look at it. We basically associate increases in entropy with forward time. If you were to see a system whose entropy was decreasing, you would perceive time to be flowing backwards (think of coffee and creamer suddenly un-mixing).
There are definitely systems that undergo cycles. Just think about heat engines which operate on cycles. However, just because the entropy of the heat engine is increasing and decreasing in a cycle does not mean that the entropy of the entire universe is doing this as well. Indeed, heat engines have to pump heat out of the system, and hence increase the entropy of its surroundings (the rest of the universe).
If we assume the universe is an isolated system then the entire state of the universe actually cannot be repeated. It is statistically impossible e.g. the second law of thermodynamics. Perhaps if the universe was not isolated then some external factor could in fact cause the universe to truly repeat.
