# 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.