The arrow of time doesn't move forward forever. There's a phase in the history of the universe where you go from low entropy to high entropy. But then, once you reach the locally maximum entropy you can get to, there's no more arrow of time.

The weird thing about the arrow of time is that it's not to be found in the underlying laws of physics. It's not there. So it's a feature of the universe we see, but not a feature of the laws of the individual particles. So the arrow of time is built on top of whatever local laws of physics apply.

The simplest way out of the puzzle of time travel is to say that it can't be done. That's very likely the right answer. However, we don't know for sure.

Sean M. Carroll Quotes