Partition function (statistical mechanics): Difference between revisions

Revision as of 03:56, 25 October 2020

Revision as of 03:56, 25 October 2020

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{{About|statistical mechanics|other uses|partition function (disambiguation)}}

{{Use American English|date = February 2019}}

{{Short description|Function in thermodynamics and statistical physics}}

{{statistical mechanics}}

In [[physics]], a '''partition function''' describes the [[statistics|statistical]] properties of a system in [[thermodynamic equilibrium]].{{Citation needed|reason=definition of partition function requires referencing|date=December 2016}} Partition functions are [[function (mathematics)|functions]] of the thermodynamic [[state function|state variables]], such as the [[temperature]] and [[volume]]. Most of the aggregate [[thermodynamics|thermodynamic]] variables of the system, such as the [[energy|total energy]], [[Thermodynamic free energy|free energy]], [[entropy]], and [[pressure]], can be expressed in terms of the partition function or its [[derivative]]s. The partition function is dimensionless, it is a pure number.

Each partition function is constructed to represent a particular [[statistical ensemble]] (which, in turn, corresponds to a particular [[Thermodynamic free energy|free energy]]). The most common statistical ensembles have named partition functions. The '''canonical partition function''' applies to a [[canonical ensemble]], in which the system is allowed to exchange [[heat]] with the [[Environment (systems)|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]]. Other types of partition functions can be defined for different circumstances; see [[partition function (mathematics)]] for generalizations. The partition function has many physical meanings, as discussed in [[#Meaning and significance|Meaning and significance]].

== Canonical partition function ==