Does this suggest that the 2nd law of thermodynamics has a quantum mechanical origin?
No, since thermodynamics can be derived from statistics of ideal classical bodies (and quantum evolution is time symmetric).
People have indeed shown such a relation. I noticed a professor here has posted a popularized article about this on his door (I think it may be scientific american, so I may be able to provide a link). I'll check next time I pass by his door.
Yes, quantum evolution is time symmetric. But that doesn't prevent entropy from increasing in one direction. Hence the notion of "thermodynamic arrow of time" (time increases in the direction of entropy increase).
Also, statistical mechanics is usually taught as a quantum theory (working with the multiplicity of states having the same macroscopic state values of, for instance, the total energy). So this doesn't need to be an issue of "ideal classical bodies".
Usually ideas relating entropy increase and quantum mechanics use the fact that as things interact their states become entangled.
What does "this" mean?! You haven't described any statement/fact/experiment/theory to refer to!
The Second Law is derivable from classical systems, so no, I wouldn't say it has a quantum mechanical origin.
Did you read the other posts?
Anyway, I checked the professor's door and it is still up. I can't find a free link to it, but googling I did find someone who put up an editorial of the article and goes over the main points:
You can get the reference to the main article from there.
Thanks for the link. OK, I see what you mean; the behavior on which the Second Law relies has a QM origin (because the behavior of all matter has a QM origin). My point was only that one can derive the Second Law from classical ensembles (as Gibbs did) and apply it to all sufficiently large systems with knowing any QM. But you're right; a deeper knowledge of randomness is valuable and will no doubt advance our science.
Separate names with a comma.