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# Boltzmann factor

In physics, the Boltzmann factor is a weighting factor that determines the relative probability of a state $i$ in a multi-state system in thermodynamic equilibrium at temperature $T$.

:$e^\left\{-frac\left\{E_i\right\}\left\{k_B,T$

Where $k_B$ is Boltzmann's constant, and $E_i$ is the energy of state $i$. The ratio of the probabilities of two states is given by the ratio of their Boltzmann factors.

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)

References

* Charles Kittel and Herbert Kroemer, "Thermal Physics", 2nd ed. (Freeman & Co.: New York, 1980).

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