Thermodynamic limit

Summary

The thermodynamic limit lets the volume and the number of particles of a system grow to infinity while the density stays fixed. Extensive quantities, such as the energy or the logarithm of the partition function, are divided by the volume before the limit is taken. In this limit the different ensembles give the same thermodynamics, fluctuations of densities vanish, and sharp phase transitions can appear. Proving that the limit exists is one of the first results of rigorous statistical mechanics.