Can dynamic considerations apply to the statistical mechanics? I'm learning statistic mechanics this semester, but some intuitive questions haunted me  all the time.  
First, according to the Ergodic Theorem, all states of a system is equally possible. Let's imagine the universe as an isolated system. One particle A is at one end of the universe, which is state S1. There is another state S2, in which A appear at the other end  of universe (I just want the distance to be large enough). There is no restriction on the sequence of states. In other words, there is no restriction that some specific states can happen after S1, and some other can't. Thus, there is a possibility that S2 happens after S1 and the particle travel through the whole universe. This cannot happen, so which part of my arguments is wrong? 
Second, are time intervals between different states measurable? are they all equal?    
Thanks in advance!  
 A: Ergodicity is subtle and complex. Not only does it lead to difficult (and still unresolved) mathematical problems, it's not even clear whether affirmative answers would stop physicists debating with each other.
What you say is exactly right. It's ridiculous to assume that any old state S2 is as likely to follow S1 as any other. But it turns out that in many systems this is a very good approximation. If you've got a box of gas at 300 Kelvin, the gas particles are shooting around at 100's-1000's of km/h. Over the time you make your measurement of the gas' pressure (or whatever you want to measure) the particles have moved around so much their final state is practically independent of their initial configuration. And over the time the measurement was taken we can assume the particles accessed all available states for equal periods of time: of course, they didn't in reality, but they accessed so many so uniformly that the error is negligible.
Of course, you're free to ask: why should we expect a uniform distribution over all accessible states? Why shouldn't the probability of reaching a given state depend on some property of that state, like it's energy? The ergodic hypothesis is essentially the claim that the uniform distribution is the right distribution. It has been proven (and so is now the ergodic theorem) in a few special cases, such as for an infinite universe made of bouncing billiard balls. In our universe it remains a hypothesis, but it is an hypothesis that works, and that's good enough for most physicists.
