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In 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 average
classical statistical mechanics
For 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 mechanics
For 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 limit
Ensemble average in other ensembles
|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.|