Isn't the classical definition of Arrow of time is from the system with less entropy to a system with more entropy? What is lacking in this definition of Arrow of time that we need to take it to Quantum level?
How the entropy spreads on a microscopic level, rather than a statistical one.
Again, probability is just a model that can predict something, but not explain how it works. Take a pseudorandom number generator and do rand() > 0.5. Your probability is 50%, and that is a pretty good model to predict how the subroutine will behave, but it may also be useful to understand what algorithm the PRNG is using.
In physics, a "model" is the same as "how something works", unless and until you can uncover details (like the precise order of generated numbers) that the old model can't express.