Examples of “Ordered state from disordered state”

A thought experiment -

Imagine two containers joined to each other with a stopcock between them. One container initially has only two molecules of a gas and other is empty. Now, if we open the stopcock, it is quite likely that after some time, each container would have 1 molecule each. But it is surely possible that we can see both the molecules in one container, although not for much time.

Now if it were a real experiment as shown in figure:

Now, there are many molecules, the number being in powers of ten. If the stopcock is opened, the molecules diffuse uniformly in both the containers. So, owing to large numbers of molecules, it would be correct to say that if the both containers were of the same volume, both will have almost the same amount of molecules.

But there surely is non-zero (very less, negligible but not zero, a finite positive number) probability that at some instant in time, such that all the molecules are in one container. For around 1 mole or $6 \times 10^{23}$ molecules, it is about $10^{-(2 \times 10^{23})}$. So, if I can see the containers for many, millions of years, I should be able to see all the molecules in one container for at least an instant.

So, are there any examples in the real world where we actually see this? Can we actually see that short amount of time where order is obtained from disorder?

• When you say we, there are 7 billion of us, so possibly someone has seen a blatant contravention of the probabilies behind the second law, but as even a single mole has $10^{23}$ particles, it seems extremely unlikely that this behaviour has been seen without some outside intervention. – user146020 Mar 9 '17 at 19:32
• @Countto10 Isn't there any, a single phenomenon in the entire universe which has been actually seen and recorded? With so many possibilities in the universe, something of creating order out of disorder must have created in so many trillion years. – Apoorv Potnis Mar 9 '17 at 19:45
• Off the top of my head, there is one definite observation, that is that the universe started in an extremely ordered, low entropy state, apologies if you have mentioned this or already aware of it. So that is one example we need to explain. My other, purely amateur guess, is that the existence of the universe itself, due/related to the Big Bang, might be considered as an example of your point. As Feynman said, it's not just amazing that the universe can be explained by simple laws, it's far more amazing it's here at all, that would be the simplest outcome of probability laws. – user146020 Mar 9 '17 at 20:11
• @Countto10 Your explanation looks quite solid. – Apoorv Potnis Mar 12 '17 at 20:39
• In a word, yes. See: journals.aps.org/prl/abstract/10.1103/PhysRevLett.89.050601 – Rococo Mar 14 '17 at 5:15