Carbonate compensation depth: Difference between revisions

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{{Unreferenced|date=December 2009}}
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{{Disputed|date=March 2008}}
 
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
 
:<math> H = \sum_i -p_i \ln p_i \, </math>
 
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]]'').
 
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]].
 
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]].
 
==Not to be confused with==
The [[Gibbs sampler]], an update algorithm used in [[Markov chain Monte Carlo]] iterations, a special case of the [[Metropolis-Hastings algorithm]].
 
{{DEFAULTSORT:Gibbs Algorithm}}
[[Category:Statistical mechanics]]
[[Category:Particle statistics]]
[[Category:Entropy and information]]

Revision as of 22:36, 19 February 2014

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