The discussion clarifies why the relative fluctuations of intensive properties in thermodynamics are minimal. It establishes that intensive properties are derived from extensive properties, which exhibit small fluctuations due to the central limit theorem. As extensive properties are averaged across subsystems, the resulting intensive properties inherit these small fluctuations. Furthermore, the reliability of an intensive property value is contingent upon it being the limit as the population approaches infinity, leading to reduced variation from two peaked distributions of large populations.
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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.andrewkirk said:So if the extensive properties have small fluctuations, so will the associated intensive ones.