Joel Lebowitz has worked for years on Ergodic Theory. I got interested in Quantum Chaos, via Classical Chaos. Intuitively I did not feel comfortable with two different sources of randomness. In Classical Statistical Mechanics the source is our lack of information on the system, in Quantum Chaos I thought the source was deeper, with uncertainty measured by Planck's Constant. Two classical billiards colliding will go in random ways afterwards. Lebowitz studied problems like those.
Now I am considering a proposal: Randomness comes from Quantum Entanglement.
I do not like this proposal much, unless the wave function is a real physical field, a la de Broglie-Bohm interpretation.
Lebowitz's Rutgers group, might have cracked the problem open.