Is the entanglement "process" theoretically reversible in the same way that classical physics is theoretically reversible? Is it possible to describe the idea w

Is the entanglement "process" theoretically reversible in the same way that classical physics is theoretically reversible? Is it possible to describe the idea without using words that implicitly include the arrow of time? It's possible that I'm simply not understanding the concepts well enough, but I don't see how the "process" of entanglement is any less dependent on temporal ordering. Why wouldn't running it backwards make physical sense as a "disentanglement" phenomenon? For that matter, why is it right to conclude that the coffee cup has only become entangled with its exterior after it has cooled down? Is this only because the matter in the cup is supposedly the result of disentangled quantum fluctuations from the distant past? I realize that the coffee cup example is an imperfect one, but can someone explain why the process of entanglement is special in this regard where the process of increasing entropy is not? I'm sure that many smart people have been thinking about these questions, but the interpretations of QM still seem to be stuck in the realm of philosophy.