Boltzmann average

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

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 \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