The Boltzmann factor is not a probability by itself, because it is not normalized. To normalize the Boltzmann factor into a probability, one divides it by the sum Z of the Boltzmann factors of all possible states of a system, which is called the partition function. This gives the Boltzmann distribution.
From the Boltzmann factor it is possible to derive the Maxwell-Boltzmann statistics, Bose-Einstein statistics, and Fermi-Dirac statistics that govern classical particles as well as quantum mechanical bosons, and fermions, respectively.
- Boltzmann relation (plasma physics)
- Charles Kittel and Herbert Kroemer, Thermal Physics, 2nd ed. (Freeman & Co.: New York, 1980).