# 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.

- ,

where is the degeneracy of the energy ; leading to

- .

where is the Boltzmann constant, *T* is the temperature, and the normalization constant *Z* is the partition function of the system.