Boltzmann average

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

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \langle A\rangle ={\frac {\sum _{i}A_{i}\exp(-E_{i}/k_{B}T)}{\sum _{i}\exp(-E_{i}/k_{B}T)}}}

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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