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Entropy isn't a problem as long as you have access to energy. Yes, billions or trillions of years from now, there might not be any more available energy (although I can't say for certain what our ancestors of a trillion years might be able to do), but that is an awfully long time. If you want to use a definition of immortality that means living for an infinite number of years, you may do so, but it is a bit of a narrow definition.
If we had immortality, limited only by catastrophic accidents or available energy (if you won't call that immortality, call it what you like) we would have to make major cultural changes. Children would have to be strictly limited to only replacement of those who were killed. We probably wouldn't like such controls, but the alternative would probably be worse.
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