Boltzmann Distribution
- Page ID
- 1874
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.