Talk:Boltzmann distribution: Difference between revisions
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but a given energy can be degenerate, so I think that it should be written something like | but a given energy can be degenerate, so I think that it should be written something like | ||
:<math> f(E) \propto \Omega(E) \exp \left[ - E/k_B T \right] </math>, where | :<math> f(E) \propto \Omega(E) \exp \left[ - E/k_B T \right] </math>, | ||
<math> \Omega \left( E \right) </math> is the degeneracy of the energy <math> E </math> | where <math> \Omega \left( E \right) </math> is the degeneracy of the energy <math> E </math>; therefore | ||
:<math> f(E) = \frac{1}{Z} \Omega(E) \exp \left[ -E/k_B T \right] </math>. | :<math> f(E) = \frac{1}{Z} \Omega(E) \exp \left[ -E/k_B T \right] </math>. | ||
Revision as of 13:54, 17 July 2008
I think that the current definition of Boltzmann distribution is misleading. The probability of a microsate, say , is . but a given energy can be degenerate, so I think that it should be written something like
![{\displaystyle \propto \exp \left[-E(X_{i})\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2723c183e143d7747e97d16ab6b4a7bba6fd6023)
- ,
![{\displaystyle f(E)\propto \Omega (E)\exp \left[-E/k_{B}T\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/725f1e2b5447a4afad931d9e8e7df8b9f9de382f)
where is the degeneracy of the energy ; therefore
- .
![{\displaystyle f(E)={\frac {1}{Z}}\Omega (E)\exp \left[-E/k_{B}T\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/29989eb0fa666f3d8a3535c8e19c64d4ed203c45)
--Noe 10:32, 17 July 2008 (CEST)