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## Main Question or Discussion Point

Hello! I'm trying to do a satisfactory derivation of the boltzmann distribution. By using lagrange multipliers I've come as far as to prove that

[tex]P(i) = \frac{1}{Z} e^{-\beta E(i)}[/tex]

where

[tex]Z = \sum_i e^{-\beta E(i)},[/tex]

but how does one actually establish that

[tex]\beta = 1/kT?[/tex]

[tex]P(i) = \frac{1}{Z} e^{-\beta E(i)}[/tex]

where

[tex]Z = \sum_i e^{-\beta E(i)},[/tex]

but how does one actually establish that

[tex]\beta = 1/kT?[/tex]