# Boltzmann average

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The Boltzmann average (sometimes known as the thermal average) for a given quantity or observable, let us say $A$, is given by
$\langle A \rangle = \frac{\sum_i A_i \exp(-E_i/k_B T)}{\sum_i\exp(-E_i/k_B T)}$
where $k_B$ is the Boltzmann constant, and T is the temperature. This provides the expected value of the property in question at a given temperature.