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 12:54, 17 July 2008
I think that the current definition of Boltzmann distribution is misleading. The probability of a microsate, say Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle X_i } , is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \propto \exp \left[ - E(X_i) \right] } . but a given energy can be degenerate, so I think that it should be written something like
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(E) \propto \Omega(E) \exp \left[ - E/k_B T \right] } ,
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Omega \left( E \right) }
is the degeneracy of the energy Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E }
; therefore
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(E) = \frac{1}{Z} \Omega(E) \exp \left[ -E/k_B T \right] } .
--Noe 10:32, 17 July 2008 (CEST)