This is a dialogue between a Sophist and a Platonist. The topic of the dialogue is: What is the cause of the arrow of time?
The participants of this dialogue are: Socrates and Sean Carroll
Location: This dialogue takes place in a coffee shop near the ocean in California
Socrates: Sean, you seem to be saying that the laws of physics are all time reversible, but that the motion of particles can still be time asymmetric. If I understand your argument, then you are saying that we can tell past from future, at least right now, because the future will have higher entropy than the past. You seem to state that this is due to the fact that it is more probable for a system to be in a state of high entropy rather than low entropy.
Sean Carroll: That's right. You have stated my position correctly. The universe started in a state of low entropy and gradually the entropy is increasing. The most probably state of the universe in the future is for it to be in a high state of entropy than the past. Though, if in the future, the universe reaches complete equilibrium, then we will see small fluctuations about this maximum value of entropy. Well, that is of course if there is such a thing as maximum entropy, and there is also the caveat that there might not be a 'we' to measure the entropy that far in the future.
Socrates: You are saying that time will continue to increase even after we reach equilibrium. I think that I understand your position. Let me rephrase what I think that you're saying: If the state of the universe were probabilistic, and if you were to look at the state of the universe, then most of the time it should be in a state associated with the highest entropy. Though, if the state of the universe were probabilistic, then it might be possible for the universe to be far-from-this-maximum-entropy state. But tell me, Sean, why is the universe in a state so-very-far-from-this-maximum-entropy state?
Sean Carroll: That's because the universe started with a very-low entropy Big Bang. And the universe is still in the process of increasing its entropy. We are headed to a state of maximum entropy, but that is not for some time in the future, and perhaps, if the universe continues to expand, it might never happen. The entropy might just continue to increase as the universe increases.