# 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 $$\Omega(E)$$ 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.

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