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ThomasT said:None, imho. I don't know of any compelling reason to think that the time asymmetry of our experience is not rooted in the fundamental dynamics of our universe, and in quantum level phenomena that aren't amenable to our sensory perception.
However, time asymmetry is a somewhat easy solution to some foundational problems. So, some philosopers and physicists adopt this approach.
The truth is, currently, anybody's guess. But it's good to keep in mind that the basic equations of motion of physics aren't correctly identified as time symmetric. Rather, they're time independent. They're equations of 'motion', not of 'time'. And insofar as they might describe a real 'time evolution', then that evolution proceeds in a particular 'direction' and is time asymmetric.
Everything that's actually known about the evolution of our universe suggests that its evolution is asymmetric (which would necessarily apply to the evolution of any of our universe's subsystems).
This might sound weird to you and I am not going to explain myself any further, but my guess is that microscopic physics is fundamentally time symmetric, but macroscopic physics might be *fundamentally* time assymetric. So, as I said, I am not going to explain the mechanism I have in mind to cause such a ''phase'' transition.