In any case, time doesn't pass for particles that move at light speed.
Actually, from their perspective, time passes just fine for particles moving at the speed of light. From their perspective, it is we who are frozen in time.
And, of course, from our pespective, time flows just fine for us and the particles travelling at the speed of light are the ones frozen in time.
Contradictory? Yes. That's why the theory is called 'of relativity': it tells you that, in order to have a coherent, non-contradictory image of the universe, you must look at it from only one frame of reference. If you try to look at the universe from two frames of reference at the same time, you will inevitably encounter such paradoxes.
If the universe would be composed only of particles moving at light speed, FAR from being frozen in time, time would flow just fine for such an universe, from his perspective.
And, of course, this is not the only weak point of Cox's speculation about entropy ceasing.
Another one - extraordinary claim require extraordinary proof - and considering just how 'extraordinary' his claim is, Cox didn't even come close to meeting the level of proof necessary. All in all, I find this speculation quite unconvincing.