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Display information for equation id:math.2279.14 on revision:2279

* Page found: Beispiel des Großkanonischen Ensenbles (eq math.2279.14)

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Beispiel des Großkanonischen Ensenbles Eq: math.2284.14

Hash: 309757cdb4f3d380f7afb27db4f1ed3d

TeX (original user input):

\begin{align}
  & k{{\lambda }_{\nu }}={{\partial }_{\left\langle {{G}_{\nu }} \right\rangle }}S\Rightarrow k\beta ={{\left( \frac{\partial S}{\partial E} \right)}_{V,\bar{N}\left( \left( \text{V},\text{N sind nicht anzufassen bei der partiellen Ableitung} \right) \right)}} \\
 & k\sum\limits_{\nu }{{{\lambda }_{\nu }}{{M}_{\nu ,\alpha }}={{\partial }_{{{h}_{\alpha }}}}S}\Rightarrow {{\left( \frac{\partial S}{\partial N} \right)}_{E,\bar{N}}}=-k\beta \operatorname{Tr}\left( \frac{\partial H}{\partial V}R \right)\quad \left( {{\partial }_{V}}N\to 0 \right) \\
\end{align}

TeX (checked):

{\begin{aligned}&k{{\lambda }_{\nu }}={{\partial }_{\left\langle {{G}_{\nu }}\right\rangle }}S\Rightarrow k\beta ={{\left({\frac {\partial S}{\partial E}}\right)}_{V,{\bar {N}}\left(\left({\text{V}},{\text{N sind nicht anzufassen bei der partiellen Ableitung}}\right)\right)}}\\&k\sum \limits _{\nu }{{{\lambda }_{\nu }}{{M}_{\nu ,\alpha }}={{\partial }_{{h}_{\alpha }}}S}\Rightarrow {{\left({\frac {\partial S}{\partial N}}\right)}_{E,{\bar {N}}}}=-k\beta \operatorname {Tr} \left({\frac {\partial H}{\partial V}}R\right)\quad \left({{\partial }_{V}}N\to 0\right)\\\end{aligned}}

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\begin{aligned} k λ_{ν} = \partial_{⟨ G_{ν} ⟩} S \Rightarrow k β = {(\frac{\partial S}{\partial E})}_{V, \bar{N} ((V, N sind nicht anzufassen bei der partiellen Ableitung))} \\ k \sum_{ν} λ_{ν} M_{ν, α} = \partial_{h_{α}} S \Rightarrow {(\frac{\partial S}{\partial N})}_{E, \bar{N}} = - k β Tr (\frac{\partial H}{\partial V} R) (\partial_{V} N \to 0) \end{aligned}

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Identifiers

$k$

$λ_{ν}$

$G_{ν}$

$S$

$k$

$β$

$S$

$E$

$V$

$\bar{N}$

$k$

$ν$

$λ_{ν}$

$M_{ν, α}$

$h_{α}$

$S$

$S$

$N$

$E$

$\bar{N}$

$k$

$β$

$H$

$V$

$R$

$V$

$N$

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