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. Statistical mechanics is the application of Probability theory, which includes mathematical tools for dealing with large populations to the field of Mechanics Josiah Willard Gibbs ( February 11, 1839 &ndash April 28, 1903) was an American theoretical Physicist, Chemist Year 1878 ( MDCCCLXXVIII) was a Common year starting on Tuesday (link will display the full calendar of the Gregorian calendar (or a Common In Mathematical physics, especially as introduced into Statistical mechanics and Thermodynamics by J In Statistical mechanics, a microstate describes a specific detailed microscopic configuration of a system that the system visits in the course of its thermal fluctuations In Thermodynamics, a thermodynamic system, originally called a working substance, is defined as that part of the universe that is under consideration Macroscopic is commonly used to describe physical objects that are measurable and observable by the Naked eye. 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. In Statistical mechanics, the grand canonical ensemble is a Statistical ensemble (a large collection of identically prepared systems where each system is in (See also partition function). In Statistical mechanics, the partition function Z is an important quantity that encodes the statistical properties of a system in Thermodynamic
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. Claude Elwood Shannon (April 30 1916 – February 24 2001 an American Electronic engineer and Mathematician, is "the father of Information Information theory is a branch of Applied mathematics and Electrical engineering involving the quantification of Information. Year 1957 ( MCMLVII) was a Common year starting on Tuesday (link displays the 1957 Gregorian calendar) Edwin Thompson Jaynes ( July 5, 1922 &ndash April 30, 1998) was Wayman Crow Distinguished Professor of Physics at Washington University The principle of maximum entropy is a postulate about a universal feature of any Probability assignment on a given set of Propositions ( Events hypotheses In Physics the Maximum entropy school of thermodynamics (or more colloquially the MaxEnt school of thermodynamics initiated with two papers published in the Physical
This general result of the Gibbs algorithm is then a maximum entropy probability distribution. In Statistics and Information theory, a maximum entropy probability distribution is a Probability distribution whose entropy is at least as great Statisticians identify such distributions as belonging to exponential families. In probability and Statistics, an exponential family is a class of Probability distributions sharing a certain form which is specified below
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. In Mathematics and Physics, Gibbs sampling is an Algorithm to generate a sequence of samples from the joint probability distribution of two or In Mathematics and Physics, the Metropolis-Hastings algorithm is a method for creating a Markov chain that can be used to generate a sequence of
See also
External links
In Mathematics, the Gibbs measure is a Probability measure frequently seen in many problems of Probability theory and Statistical mechanics.Dapyx Software network: MP3 Explorer | Ebook Manager | Zenithic