A Gibbs state in probability theory and statistical mechanics is an equilibrium probability distribution which remains invariant under future evolution of the system (for example, a stationary or steady-state distribution of a Markov chain, such as that achieved by running a Markov Chain Monte Carlo iteration for a sufficiently long time). Probability theory is the mathematical study of probability. ... Jump to: navigation, search Statistical mechanics is the application of statistics, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ... Jump to: navigation, search In mathematics, a (discrete-time) Markov chain, named after Andrei Markov, is a discrete-time stochastic process with the Markov property. ... Markov chain Monte Carlo (MCMC) methods, sometimes called random walk Monte Carlo methods, are a class of algorithms for sampling from probability distributions based on constructing a Markov chain that has the desired distribution as its stationary distribution. ...

In physics there may be several physically distinct Gibbs states in which a system may be trapped, particularly at lower temperatures. Since antiquity, people have tried to understand the behavior of matter: why unsupported objects drop to the ground, why different materials have different properties, and so forth. ...

They are named after J. Willard Gibbs, for his work in determining equilibrium properties of statistical ensembles. Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was an American physical chemist. ... In physics, a statistical ensemble is a very large set of similar systems, considered all at once. ...