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The Big Phzzt
Would the universe end in a state of zero information?..... Nope!
...the Uncertainty principle would not allow a state of 'no information exchange' - i think if the universe expands to such a degree that particles can only exist in a quantum state, then each point in the universe would exist in its own universe, with 'our' observable universe a cloud of collected possibilities of all points, or rather, their observations....
... and information exchange would then be the effect of each such possible cloud on every other cloud,i.e., where no effect would be a null set, thereby giving us both a zero as well as preserving uncertainty!!!
....so we would never be able, in fact, to say that there is such a thing as the end of the universe, as we can never observe with certainty a position where there is no cloud i.e. a null set, nor can we isolate a single cloud as representative of the universe....