# 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 *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. This equation assumes non-degenerate states.