Eg, rolling a dice is deterministic, and I imagine an algorithm exists that could recover the value of a dice throw from a recording of the sound of it rolling and it's initial position. But once that sound has turned into heat, and that heat has conducted itself about the walls and into the air, I don't think it's possible to recover the sound.
See also:
"Is flipping a coin random?" (Numberphile)
There’s nothing in the laws of physics that prohibits us turning burned paper smoke back into a document and recover the information.
When you burn a document, all the matter might be transferred into the smoke, but you've rendered it into a stream of particles which is small enough to be effected by Brownian motion. Reversing the process (figuring out the initial position of each soot particle) involves knowing the position and momentum of the air molecules impacting the soot particles. In principle, you could take the current position and momentum of those particles and extrapolate backwards - but you can't actually measure that, not even in theory.