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| {{Unreferenced|date=December 2009}}
| | The writer's title is Christy. Distributing manufacturing is exactly where her primary earnings comes from. Mississippi is the only location I've been residing in but I will have to move in a yr or two. The favorite hobby for him and his children is to play lacross and he would never give it up.<br><br>Also visit my web page ... [http://kjhkkb.net/xe/notice/374835 tarot readings] |
| {{Disputed|date=March 2008}}
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| In [[statistical mechanics]], the '''Gibbs algorithm''', first introduced by [[J. Willard Gibbs]] in 1878, is the injunction to choose a [[statistical ensemble]] (probability distribution) for the unknown [[microstate (statistical mechanics)|microscopic state]] of a [[thermodynamic system]] by minimising the average log probability
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| :<math> H = \sum_i -p_i \ln p_i \, </math>
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| subject to the probability distribution satisfying a set of constraints (usually expectation values) corresponding to the known [[macroscopic]] quantities. Physicists call the result of applying the Gibbs algorithm the [[Gibbs distribution]] for the given constraints, most notably Gibbs's [[grand canonical ensemble]] for open systems when the average energy and the average number of particles are given. (See also ''[[Partition function (mathematics)|partition function]]'').
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| In the light of [[Claude E. Shannon|Claude Shannon]]'s [[information theory]], in 1957 [[E.T. Jaynes]] re-interpreted the Gibbs algorithm as a much more general, more widely applicable inference technique, leading to the [[principle of maximum entropy]], and the [[Maximum entropy thermodynamics|MaxEnt view of thermodynamics]].
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| This general result of the Gibbs algorithm is then a [[maximum entropy probability distribution]]. Statisticians identify such distributions as belonging to [[exponential family|exponential families]].
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| ==Not to be confused with==
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| The [[Gibbs sampler]], an update algorithm used in [[Markov chain Monte Carlo]] iterations, a special case of the [[Metropolis-Hastings algorithm]].
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| {{DEFAULTSORT:Gibbs Algorithm}}
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| [[Category:Statistical mechanics]]
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| [[Category:Particle statistics]]
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| [[Category:Entropy and information]]
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