Upvoted from -1 to 0 because the question is interesting and important; the fact that the answer seems clear to some is not cause for downvoting, in my view. (This is the Discussion section; would you have downvoted this post if it had been an Open Thread comment?)
As it happens, I don't think the answer is necessarily a settled matter, any more than time travel in general (of which this can be considered a special case) is. It seems quite possible that the universe may contain much more information about its past than we can currently envision being able to extract. (One might for instance compare the old belief that determining the chemical composition of stars was hopeless due to their distance.) Yes, thermodynamics may imply that not all of the past can be reconstructed, but it may not be necessary to extract all of it in order to reconstruct a few human minds. Presumably a huge (by present standards) expenditure of negentropy would be involved, but as far as I know the universe seems to contain a whole lot of "wasted" negentropy at the moment.
If someone gets cremated or buried long enough for eir brain to fully decompose into dirt, it becomes extremely difficult to revive em. Nothing short of a vastly superhuman intelligence would have a chance of doing it. I suspect that it would be possible for a superintelligence to do it, but unless there's a more efficient way to do it, it would require recomputing the Earth's history from the time the AGI is activated back to the death of the last person it intends to save. Not only does this require immense computational resources that could be used to the benefit of people who are still alive, it also requires simulating people experiencing pain (backwards). On the other hand, this saves people's lives. Does anyone have any compelling arguments on why an FAI would or would not recreate me if I die, decompose, and then the singularity occurs a long time after my death?
Why do I want to know? Well, aside from the question being interesting in its own right, it is an important factor in deciding whether or not cryonics is worth-while.