I think the issue is if there are any changes in inputs when the tape is
replayed.
If not, if the process is deterministic (chaotic or otherwise), then the
results will be exactly the same.
Few scientists are determinists today in an ultimate sense, because of the
indeterminacy in quantum mechanics (though some see that indeterminacy as
only apparent, and not real).
Quantum theory mightn't be as relevant for the issue of freedom as it seems,
in that on the typical indeterministic interpretation, the indeterminacy is
purely random -- a matter of chance, not choice. But one could
(speculatively) interpret it otherwise, when it's involved with the physical
states that correlate with consciousness, e.g.
John