# Boltzmann Factor & Distribution

November 20, 2008

The Boltzmann factor gives the *unnormalised relative probability* for a state of energy of being occupied at temperature .

The partition function is the proportional factor between the probability (for a state of energy of being occupied at temperature ) and the Boltzmann factor:

equivalently:

If the system can exchange particles, it is necessary to introduce the *chemical potential* by which it is possible to define the *Boltzmann distribution function* that represents the classical limit* (high energies) of the Fermi-Dirac and the Bose-Einsten distributions:

*in despite of the term “classical” the Boltzmann distribution is valid for quantum particles.

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