Partition function (statistical mechanics) In physics, a
partition function describes the statistical properties of a
system in thermodynamic equilibrium. They are functions of
temperature and other parameters, such as the volume enclosing a
gas. Most of the aggregate thermodynamic variables of the
system, such as the total energy, free energy, entropy, and
pressure, can be expressed in terms of the partition function or
its derivatives. There are actually several different types of
partition functions, each corresponding to different types of
statistical ensemble (or, equivalently, different types of free
energy.) The canonical partition function applies to a canonical
ensemble, in which the system is allowed to exchange heat with
the environment at fixed temperature, volume, and number of
particles. The grand canonical partition function applies to a
grand canonical ensemble, in which the system can exchange both
heat and particles with the environment, at fixed temperature,
volume, and chemical potential.