Editing Ensemble (mathematical physics) (section)

=== Canonical ensemble average ===
The generalized version of the [[partition function (mathematics)|partition function]] provides the complete framework for working with ensemble averages in thermodynamics, [[information theory]], [[statistical mechanics]] and [[quantum mechanics]].

The [[microcanonical ensemble]] represents an isolated system in which energy (''E''), volume (''V'') and the number of particles (''N'') are all constant. The [[canonical ensemble]] represents a closed system which can exchange energy (''E'') with its surroundings (usually a heat bath), but the volume (''V'') and the number of particles (''N'') are all constant. The [[grand canonical ensemble]] represents an open system which can exchange energy (''E'') and particles (''N'') with its surroundings, but the volume (''V'') is kept constant.