Boltzmann factor: Definition from Answers.com

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 $T$ .

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

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. The normalization factor is one divided by the Partition Function (denoted as Z), the sum of the Boltzmann factors for all states of the system. 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.

References

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

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Boltzmann factor

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References