Boltzmann average

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

$⟨A⟩=\frac{{\sum }_i{A}_i\exp (-E_i/k_{B}T)}{{\sum }_i\exp (-E_i/k_{B}T)}$

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.

See also

• Boltzmann distribution