ARROW OF TIME = CAUSALITY
An extremely simple and direct answer to the question of what determines the arrow of time is as follows. If the cosmos and everything in it strictly obeys the law of causality (i.e., if something happens it is because something physical caused it to happen) then there is always a chain of causality linking all events that take place, and this provides a definitive and unalterable arrow of time.
For example, scrambled eggs cannot unscramble themselves and jump back into their original eggs, etc. because that grossly violates causality. There is an inviolable causal chain and arrow of time that links selecting the eggs, cracking them open into the bowl, stirring them, cooking them, etc.
The same would be true for everything that occurs in the real physical universe, as opposed to the Platonic pipe-dream world of more than a few theoretical physicists. Einstein said he would skeptically question virtually anything and everything, but causality was the one principle he would never give up. Quantum theorists think he was wrong about this, but I would bet the farm that eventually he will be vindicated.
RLO