I've come across this explanation that the "arrow of time" is a consequence of the second law of thermodynamics, which says that the entropy of an isolated system is always increasing. The argument is that the past looks different from the future because of this increase in entropy. However, this still doesn't make time vanish, since a hypothetical clock could still be ticking in a completely uniform universe, but only this time there is no change in entropy because it is already at a maximum. In this maximum entropy universe, the past would look just like the future, but that need not mean that time isn't still flowing. It is just that we $\it{associate}$ the flow of time with a change that is recognizable.
But after having watched a few episodes of Professor Brian Cox's Wonders of the Universe, I want to know the deeper reason behind why people make the entropy argument. I've heard Sean Carroll make a similar argument to a group of physicists, so I get the idea it is not just a sloppy popularization.
Best Answer
The laws of physics are time reversible, so a clock could tick backwards as well as forwards. However in our current low entropy universe it is vastly more probable that the clock ticks forwards. In a maximum entropy universe the probablility of a backwards tick would be identical to a forwards tick, so on average the clock time wouldn't change.