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Boltzmann Average

The Boltzmann average (sometimes known as the thermal average) for a given quantity or observable, let us say A, is given by

$\langle A \rangle= \frac{\sum_{i}Ae^{-E_i/k_BT}}{\sum_{i}e^{^{-E_{i}/k_BT}}}$

where kB is the Boltzmann constant, and T is the temperature. This provides the expected value of the property in question at a given temperature. This equation assumes non-degenerate states.