The Windmill
What makes the blades of a windmill turn?

From the viewpoint of a human farmer or windmill engineer, it's the wind.

But from the viewpoint of a bunch of air molecules, who are actually doing the work, "the wind" doesn't mean very much.  Molecules are constatnly tearing about, bouncing off each other and anything else in their path, inlcuding barn walls and windmill blades.  When a molecule bounces off one side of a windmill blade, it gives a little push to the blade.  Not a big push, but there are an awful lot of molecules bouncing off the blades.

And those molecules are moving pretty fast: about 700 miles per hour on the average.  If they would all get together and push in unison, all at once and in the same direction on the same side of the blades, the force would be devastating to the windmill.  A lot of work would get done on the blades.  Enough to shred them.

But the molecules don't get together.  Their motions are not, in general, correlated.  They are pretty much random.  So, when one molecule give a little push to one side of the blade by bouncing off of it, another is bouncing off the other side and pushing in the opposite direction.  They balance each other. What the human farmer or engineer sees as "no wind" is when the balance is exact.  There are a lot of forces acting on the blades, but they all exactly cancel each other out.

It's correlation that moves the blades.  It's a little more movement in one direction than in other directions.  Then, they don't quite cancel each other out.  Then, there is a little more force on the blades in one direction than in the other.  Then, work can get done on the windmill blades.  (Work is done on them when they move—and only when they are moved, by whatever is doing work on them.)  Then, the farmer and the engineer see "a wind."  A mere 10% correlation would be seen as a 70 mph "wind," a hurricane.
      ......Hey, didn't a square root get left out somewhere...??
This "correlation" is correlation of motions of molecules with themselves: autocorrelation.

Left to themselves—no outside influence, such as heating of the air by the sun, for example—any "winds" in the system of air molecules will die down.  The big winds will stir up eddies and swirls, waves and undulations, and even heat things up a bit here and there.  The eddies and waves will intermix and become dampened, and all the motions will eventually get mixed up, all the way down to the level of the individual molecules.  And that is what the farmer and engineer see as "a calm."  The air molecules are still moving pretty much as fast and furious as they were in the hurricane, but their motions are all mixed up; they are not acting coherently.  No coherence; no work.

That process is irreversible.  A calm cannot spontaneously become a hurricane;  winds out of calms happen only by outside influence.  A calm cannot transmit energy in an organized fashion.  A calm cannot do work on a windmill blade.

That irreversiblity is a human observation.  Back in the mid 19th century it was put into language and theory as The Second Law of Thermodynamics. When it refers to all energy transfers—not just to the energy transfers of air molecules bouncing off each other and windmill blades—it becomes the observation that the autocorrelation always tends toward zero.

In this observation, we are looking at one of the most important concepts of modern science:

"Entropy always increases in a system left to itself."
(in unusual circumstances, it might remain the same)


It's correlation that counts: autocorrelation. 

That's something out of statistics.

Correlation tends to decrease when there's no influence from outside the system.