Thermodynamic limit

There will still be detectable fluctuations (typically at microscopic scales) in some physically observable quantities, such as Mathematically an asymptotic analysis is performed when considering the thermodynamic limit.

Thus for a macroscopic volume with perhaps the Avogadro number of molecules, fluctuations are negligible, and so thermodynamics works.

In general, almost all macroscopic volumes of gases, liquids and solids can be treated as being in the thermodynamic limit.

That is, the entropy of two systems or objects taken together (in addition to their energy and volume) is the sum of the two separate values.

In some models of statistical mechanics, the thermodynamic limit exists, but depends on boundary conditions.