Earlier quoted context omitted.
I suggest you read Prigogine's book if you're really interested but his work demonstrates that the problem isn't having detailed enough information about state, it's the irreversibility of time, which makes physics fundamentally non-deterministic.
What has irreversibility got to do with it? There are cellular automata that are irreversible but obviously deterministic.
The math behind is pretty gnarly but if you want to understand it I recommend his book: http://www.amazon.com/End-Certainty-Ilya-Prigogine/dp/068483... .
A CA is not a good model for this.