Everything about Gibbs Algorithm totally explained
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
microscopic state of a
thermodynamic system by minimising the average log probability
»
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).
In the light of
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
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 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.
Further Information
Get more info on 'Gibbs Algorithm'.
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