Boltzmann distribution

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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.

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