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Display information for equation id:math.2268.92 on revision:2268

* Page found: Vorurteilsfreie Schätzung des statistischen Operators zu einem festen Zeitpunkt (eq math.2268.92)

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Vorurteilsfreie Schätzung des statistischen Operators zu einem festen Zeitpunkt Eq: math.2273.92

Hash: e9d08b00900119aa28a676ec408a4b8a

TeX (original user input):

\begin{align}
  & S=k\sum\limits_{\nu }{{{\lambda }_{\nu }}\left\langle {{G}_{\nu }} \right\rangle }+k\ln Z \\
 & dS=k\sum\limits_{\nu }{\left( d{{\lambda }_{\nu }}\left\langle {{G}_{\nu }} \right\rangle +{{\lambda }_{\nu }}d\left\langle {{G}_{\nu }} \right\rangle  \right)}+k\frac{dZ}{Z} \\
 & =k\sum\limits_{\nu }{\left( d{{\lambda }_{\nu }}\left( -\frac{\partial Z}{\partial {{\lambda }_{\nu }}}\frac{1}{z} \right)+{{\lambda }_{\nu }}d\left\langle {{G}_{\nu }} \right\rangle  \right)}+k\frac{dZ}{Z} 
\end{align}

TeX (checked):

{\begin{aligned}&S=k\sum \limits _{\nu }{{{\lambda }_{\nu }}\left\langle {{G}_{\nu }}\right\rangle }+k\ln Z\\&dS=k\sum \limits _{\nu }{\left(d{{\lambda }_{\nu }}\left\langle {{G}_{\nu }}\right\rangle +{{\lambda }_{\nu }}d\left\langle {{G}_{\nu }}\right\rangle \right)}+k{\frac {dZ}{Z}}\\&=k\sum \limits _{\nu }{\left(d{{\lambda }_{\nu }}\left(-{\frac {\partial Z}{\partial {{\lambda }_{\nu }}}}{\frac {1}{z}}\right)+{{\lambda }_{\nu }}d\left\langle {{G}_{\nu }}\right\rangle \right)}+k{\frac {dZ}{Z}}\end{aligned}}

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\begin{aligned} S = k \sum_{ν} λ_{ν} ⟨ G_{ν} ⟩ + k \ln Z \\ d S = k \sum_{ν} (d λ_{ν} ⟨ G_{ν} ⟩ + λ_{ν} d ⟨ G_{ν} ⟩) + k \frac{d Z}{Z} \\ = k \sum_{ν} (d λ_{ν} (- \frac{\partial Z}{\partial λ_{ν}} \frac{1}{z}) + λ_{ν} d ⟨ G_{ν} ⟩) + k \frac{d Z}{Z} \end{aligned}

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Identifiers

$S$

$k$

$ν$

$λ_{ν}$

$G_{ν}$

$k$

$Z$

$d$

$S$

$k$

$ν$

$d$

$λ_{ν}$

$G_{ν}$

$λ_{ν}$

$d$

$G_{ν}$

$k$

$d$

$Z$

$Z$

$k$

$ν$

$d$

$λ_{ν}$

$Z$

$λ_{ν}$

$z$

$λ_{ν}$

$d$

$G_{ν}$

$k$

$d$

$Z$

$Z$

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