[vizakenjack]

So, at 0°, H²O molecules will be escaping ice into the liquid portion of a cup:


as well as H²O molecules from liquid portion will enter the ice cube. Both of these processes happen at the same rate, so the exchange of molecules is said to be at equilibrium.

But, what if... you catch a few molecules that escaped the ice state, and then you collect them. Would this affect the overall state of water in a cup? Or will it still balance itself as its temperature is at 0°.

[Borek]

How are you going to catch these molecules?

[Arkcon]

But, what if... you catch a few molecules that escaped the ice state, and then you collect them. Would this affect the overall state of water in a cup? Or will it still balance itself as its temperature is at 0°.

Have you heard of the thought experiment -- Maxwell's Demon?  http://en.wikipedia.org/wiki/Maxwell%27s_demon  Or perhaps you are on your way to rediscovering it?  At any rate, recognizing that chemical equilibria may be simply a statistical observation is all well and good.  However, you have to deal sooner or later with Borek:'s question -- how will you achieve it.