Editing Ensemble (mathematical physics) (section)

== Ensembles in statistics ==
{{main|Principle of maximum entropy|Markov random field}}
The formulation of statistical ensembles used in physics has now been widely adopted in other fields, in part because it has been recognized that the [[canonical ensemble]] or [[Gibbs measure]] serves to maximize the entropy of a system, subject to a set of constraints: this is the [[principle of maximum entropy]]. This principle has now been widely applied to problems in [[linguistics]], [[robotics]], and the like.

In addition, statistical ensembles in physics are often built on a [[principle of locality]]: that all interactions are only between neighboring atoms or nearby molecules. Thus, for example, [[lattice model (physics)|lattice models]], such as the [[Ising model]], model [[ferromagnetic material]]s by means of nearest-neighbor interactions between spins.  The statistical formulation of the principle of locality is now seen to be a form of the [[Markov property]] in the broad sense; nearest neighbors are now [[Markov blanket]]s. Thus, the general notion of a statistical ensemble with nearest-neighbor interactions leads to [[Markov random field]]s, which again find broad applicability; for example in [[Hopfield network]]s.