Boltzmann distribution
From SklogWiki
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.
