I have a hollow enclosed 1cm-sided cube. It is filled with N mols of an ideal gas.
(1) What is the probability that for one infinitesimal moment, all the gas will occupy half of the box, leaving a vacuum at the other side.
(2) What is the probability that it will stay this way for a specified length of time?
Are these meaningful questions? Are they two very different questions? Can either or both be calculated and, if so, what is the result?
We choose a desired volume in advance that is half the volume of the entire space. It is a specific half of the cube with the dividing plane being parallel to one of the sides.
It seems to me intuitively that to maintain this state, rather than just reach it for an instant, is going to be next to impossible because reflections from the sides will tend to refill the other half immediately. This is why I'm asking if the question is meaningful.
In order to make this easier to answer, please feel free to specify any extra conditions that will make calculations simpler.