Ensemble

An ensemble is an imagined infinite collection of identical copies of a system, each in one of its accessible microstates, distributed according to some probability rule. Rather than follow one system through time, statistical mechanics averages over the ensemble at a single instant; under the ergodic hypothesis the two procedures give the same answer for equilibrium quantities.

Different physical situations call for different ensembles. The microcanonical ensemble describes an isolated system of fixed energy, with every accessible microstate equally probable (the fundamental postulate). The canonical and grand canonical ensembles describe systems exchanging energy, or energy and particles, with a large reservoir, and weight microstates by the Boltzmann factor. This is a stub entry; the specific ensembles and the partition function that ties them together are developed in the statistical-mechanics module.

The ensemble idea reframes thermodynamic quantities as averages and fluctuations over probability distributions, making the link between microscopic mechanics and macroscopic thermodynamics quantitative.

The ensemble formalism is due to J. Willard Gibbs, who introduced the term and the canonical/grand-canonical machinery in 1902, building on Boltzmann's and Maxwell's statistical methods.