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Ensemble averageIn statistical mechanics, the ensemble average is defined as the mean of a quantity that is a function of the microstate of a system (the ensemble of possible states), according to the distribution of the system on its microstates in this ensemble. Since the Ensemble average is dependent of the ensemble chosen, its mathematical expression varies from ensemble to ensemble. However, the mean obtained for a given physical quantity doesn't depend on the ensemble chosen at the thermodynamic limit. Statistical ensemble (mathematical physics) Additional recommended knowledge
Canonical ensemble averageclassical statistical mechanicsFor a classical system in thermal equilibrium with its environment, the ensemble average takes the form of an integral over the phase space of the system:
The denominator in this expression is known as the partition function, and is denoted by the letter Z. quantum statistical mechanicsFor a quantum system in thermal equilibrium with its environment, the weighted average takes the form of a sum over quantum energy states, rather than a continuous integral: characterization of the classical limitEnsemble average in other ensemblesMicrocanonical ensembleMacrocanonical ensemble 

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Ensemble_average". A list of authors is available in Wikipedia. 