Why are the relative fluctuations of intensive properties so small?

[heyhey281]

I get that the relative fluctuations of extensive properties (in thermodynamics) are tiny because you can divide the whole system in many subsystems and apply the central limit theorem, but I just dont get it with intensive properties. Could someone explain?

 

[andrewkirk]

Intensive properties are are often calculated by dividing one extensive property by another. So if the extensive properties have small fluctuations, so will the associated intensive ones.
You can think of an intensive property of a large system as an average across the whole system of intensive properties of component parts. So the same central limit tendencies will apply.

 

[sophiecentaur]

So if the extensive properties have small fluctuations, so will the associated intensive ones.

In addition to that, in order to be relied upon, the quoted value of an intensive property needs to be the limit as the population goes to infinity. That implies a smaller variation because it would be the product of two peaked distributions of huge populations.