QM vs. the second law of thermodynamics

[zhermes]

One of the most classical and verified principles of physics is that entropy never decreases. E.g. gas occupying half of a 1L container will quickly disperse quite-evenly throughout the container. It seems however, that QM easily allows momentary violations of this principle. For instance (the classical QM-for-the-laymen idea) is that such a collection of particles (gas in a 1L container) could spontaneously arrange itself into half of the container, with some small probability.
If that happened, wouldn't it be a drastic decrease in entropy?

 

[xepma]

Entropy is an averaged quantity -- averaged with respect to time. There will always be fluctuations with respect to the 'average' state of the system (the so-called Gibbs state). You cannot speak of the entropy at a specific instance of time, because at any given time the system will be in a definite state which would imply zero entropy. Rather, the entropy arises as a measure of the number of states accessible to the system. As the system evolves it will explore, for lack of a better word, the space of accessible states. The size of this space determines the entropy. If the specific state you mentioned is part of this space of accessible states, then the system will -- at some point -- sit in this state.

But even if the particles arrange themself into half of the container, you're guarenteed that at a later time the system will be in some other state. Averaged over time, the entropy hasn't decreased.