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# Canonical probability distribution

In thermal physics, the canonical probability distribution is a statistical function which equates to the Boltzmann factor divided by the partition function. The function was introduced by Willard Gibbs in his 1901 Elementary Principles in Statistical Mechanics.

$P(i)=\frac{e^{-\beta E_i}}{Z}=\frac{e^{-\beta E_i}}{\displaystyle\sum_{i} e^{-\beta E_i}}$
Where $\beta = \frac{1}{k_B T}$ and kB is the Boltzmann Constant.