# What is the probability of ice in boiling water?

Ice crystals are spatially ordered, and in every randomness there is a low possibility of temporarily order. If given enough boiling water, and sufficient time, could local clusters water molecules happen to be in a crystalized state?

This may seem absurd, but I believe it must be possible, imagine dropping an ice cube in boiling water(and water vapor) in a perfect closed system, the ice cube melts while the water keeps boiling (because of the water vapor), then because of Poincare recurrence theorem, there will be an similar ice cube after a sufficiently long but finite time.

EDIT: The temperature is 100 Celsius and 1 atm (not at triple point)

• Do not hold your breath. It is the same answer to "what is the probability that all the air ends up in the upper right corner of the room and we suffocate". Jan 12, 2014 at 15:29
• @Jitter, no it'll snow in the lower left corner, so we'll die w/o even getting a single run down the slope :-) Jan 12, 2014 at 15:57
• At the triple point of water, the probability is quite high. Jan 12, 2014 at 15:58
• @OlinLathrop true, but I don't think you can convince water to boil at the triple point. Jan 12, 2014 at 17:13
• @Carl: At the triple point is right on the edge between all three phases of water. Any liquid will boil with just little extra heat or lower pressure, or will freeze with just a little less heat. Jan 13, 2014 at 0:06