Boltzmann distribution

The Maxwell-Boltzmann distribution function is a function f(E) which gives the probability that a system in contact with a thermal bath at temperature T has energy E. This distribution is classical and is used to describe systems with identical but distinguishable particles.

$f(E)\propto \Omega (E)\exp \left[-E/k_{B}T\right]$,

where $\Omega \left(E\right)$ is the degeneracy of the energy $E$; leading to

$f(E)={\frac {1}{Z}}\Omega (E)\exp \left[-E/k_{B}T\right]$.

where $k_{B}$ is the Boltzmann constant, T is the temperature, and the normalization constant Z is the partition function of the system.

See also

• Boltzmann average