Is the arrow of time only given from initial conditions? I am not a physicist, but I have tried to sort out where the arrow of time comes from or how it fits into our physical models. 
Harvey Brown, a philosopher, physicist, and professor emeritus at Oxford says the laws of physics are entirely reversible with respect to time, and the only way to get a direction of time is to insert some other explanation beyond the equations of physics. The actual direction of time comes from prior conditions, not the physical equations themselves. So, separate from the laws, our universe started in a state of lower entropy. The laws acted upon those conditions which lead to an increase in entropy. 
And (not Harvey's direct worlds at this point but others) at some point in the infinite future, because of our light cone, recurrence will happen because the horizon has a temperature due to increasing expansion and finite lightspeed (i.e. universe in box). Thus, in the far future the conditions will allow for the arrow backwards with the same laws of physics, if recurrence to some arbitrary accuracy is guaranteed in a finite system. (Which we have because of our horizon in an expanding universe).
So is this the current, state of the art explanation for the arrow of time? Not the experience of time or related stuff, just the direction. If not where did I go wrong?  Also how does CP  breaking fit in here? I suppose an experiment looks different forwards and backwards but nonetheless can be run either way with no privileged direction?
 A: If you want to learn about the arrow of time, I think the best place is to just go to the source: The Nature of the Physical World by Arthur Eddington in 1928 (it looks like the first mention of "Time's Arrow" happens on page 46 of the PDF). 
Essentially, the "arrow of time" is just a restatement of the Second Law of Thermodynamics being applied to human perception: we perceive entropy increase as time "moving forward". So when you say 

So is this the current, state of the art explanation for the arrow of time? Not the experience of time or related stuff, just the direction.

I think there is a misunderstanding here, because the arrow of time depends on the "experience of time". There isn't really a way to separate those two ideas. If you did want to separate them, then just go back to the Second Law of Thermodynamics without bringing in human perception.
So I would say yes, the arrow of time depends on "initial conditions". For example, if a system starts at its maximum entropy, then there is no arrow of time anymore.
I cannot understand what you are saying about time's arrow reversing.
