Could entropy remain the same overall?

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I have read a bit from the book Cycles of Time(Penrose), and I wondered whether an increase in entropy in one part of the Universe, lead to a decrease in entropy in other parts, and maybe the universe's expansion is an attempt by the Universe to keep entropy at the same level.
And eventually you get another big bang...I like to think of this process, in the context of the Universe being a 3-sphere, or 3-torus, or some such...ie finite at any one time, but boundless.

So even with stars shining in one universe, you might get many cycles, all the while entropy staying the same.

I hope this isn't too non-mainstream..?
 
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and I wondered whether an increase in entropy in one part of the Universe, lead to a decrease in entropy in other parts
It doesn't.
and maybe the universe's expansion is an attempt by the Universe to keep entropy at the same level.
I don't see how you got that impression. No.
 

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