There has been some discussion about the problem of entropy in a cosmos that is infinite in time and yet closed in space. I think this is true, and so therefore, anybody proposing a cosmoc infinite in time would also have to propose one infinite in space. In an open system, entropy doesn't apply. I know this is a bit abstract, but there are two questions I have.

First, how would entropy work in an open system? Would the system be constantly becoming closer to entropy, without every reaching it, or would it be meaningless even to speak of entropy?

The second is a bit more concrete. It seems to me that the cosmological redshift would be a problem in such a cosmos. I can think of three solutions:
(1) the redshift is not a doppler redshift.
(2) the redshift is a doppler redshift, but is only a local phenonomenon (I think that Eric Lerner adopted this position).
(3) the redshift is a doppler redshift, but has something to do with an expansion or contraction of space itself.

The question I have in this case concerns the third option. Would it be possible, in an infinitely sized and timed cosmoc, to have a doppler redshift based on a change in space itself? On one hand, it seems contradictory -- how can everything be expanding in an infinitely large universe?

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