$ S \equiv k_B \ln \Omega $

S = k_B * ln( Omega )

$ S + S_h =max$

S + S_h =max

$\displaystyle\frac{1}{T}=\displaystyle\frac{\partial S}{\partial E}$

\displaystyle\frac{1}{T}=\displaystyle\frac{\partial S}{\partial E}

$\ln\Omega(E)=\ln\Omega(\bar{E})+\beta\eta-\displaystyle\frac{1}{2}\lambda\eta^2\ldots$

\ln\Omega(E)=\ln\Omega(\bar{E})+\beta\eta-\displaystyle\frac{1}{2}\lambda\eta^2\ldots

$P(E)=P(\bar{E})e^{-\lambda_0(E-\bar{E})^2/2}$

P(E)=P(\bar{E})e^{-\lambda_0(E-\bar{E})^2/2}

$\lambda_0\equiv-\displaystyle\frac{\partial^2\ln\Omega}{\partial E^2}=-\displaystyle\frac{\partial\ln\beta}{\partial E}$

\lambda_0\equiv-\displaystyle\frac{\partial^2\ln\Omega}{\partial E^2}=-\displaystyle\frac{\partial\ln\beta}{\partial E}