The macroscopic transformation is time asymmetric (the balls will not sort themselves back again) even though the microscopic transformations are time symmetric

The macroscopic transformation is time asymmetric (the balls will not sort themselves back again) even though the microscopic transformations are time symmetric (elastic collisions and frictionless movement). I agree with your observation of what happens to the black and white billiards. My question is - if the interactions are all time-symmetric (implies conservation of entropy), where does the entropy come from in the macroscopic system? My belief is that the microscopic model is flawed; if we simply introduce some randomness into the collision dynamics of two particles (which is believable given particle accelerator experiments / QM), then microscopic interactions are no longer T-symmetric. It comes down to a philosophical interpretation of whether you can treat a system of two particles probabilistically (i.e. thermodynamically in aggregate) or not.