Boltzmann average

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

$\langle A\rangle ={\frac {\sum _{i}A_{i}\exp(-E_{i}/k_{B}T)}{\sum _{i}\exp(-E_{i}/k_{B}T)}}$

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