Canonical probability distribution

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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.

The probability of an element of the canonical ensemble having energy Ei is given by:

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.

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