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LucasBrown (talk | contribs) Adding local short description: "Generalization of the concept from statistical mechanics", overriding Wikidata description "which generalizes its use in statistical mechanics and quantum field theory" |
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{{Short description|Generalization of the concept from statistical mechanics}}
{{For|the partition function in number theory|Partition function (number theory)}}
The '''partition function''' or '''configuration integral''', as used in [[probability theory]], [[information theory]] and [[dynamical systems]], is a generalization of the definition of a [[partition function in statistical mechanics]]. It is a special case of a [[normalizing constant]] in probability theory, for the [[Boltzmann distribution]]. The partition function occurs in many problems of probability theory because, in situations where there is a natural symmetry, its associated [[probability measure]], the [[Gibbs measure]], has the [[Markov property]]. This means that the partition function occurs not only in physical systems with translation symmetry, but also in such varied settings as neural networks (the [[Hopfield network]]), and applications such as [[genomics]], [[corpus linguistics]] and [[artificial intelligence]], which employ [[Markov network]]s, and [[Markov logic network]]s. The Gibbs measure is also the unique measure that has the property of maximizing the [[entropy (general concept)|entropy]] for a fixed expectation value of the energy; this underlies the appearance of the partition function in [[maximum entropy method]]s and the algorithms derived therefrom.
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