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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 micro-state of a system (the ensemble of possible states), according to the distribution of the system on its micro-states 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 |
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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. |