I understand that the 2nd law of thermodynamics roughly states that, if you have a body (or a gas in a chamber) that is hot at one end and cold on the other, the heat will always flow from the hot to the cold part and to get the opposite effect, one has to put energy in from the outside (through a machine or something).
Now, I don't understand why this fact cannot be explained just through probabilities (of the velocities of the gas molecules, say).
It would seem to me that it is simply very, very, very unlikely that faster moving molecules all end up in (approximately) one spot at any time.
But from all the fuzz about the 2nd law, I'm led to believe that there has to be more behind it than probability. So where am I wrong? Why is the second law beyond probability? How is the 2nd law tested? (so that one can rule out simple probability?)
ps.: I haven't yet had a course on probability theory. So my understanding of it is limited.