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Display information for equation id:math.2263.56 on revision:2263
* Page found: Vorurteilsfreie Schätzung des statistischen Operators zu einem festen Zeitpunkt (eq math.2263.56)
(force rerendering)Occurrences on the following pages:
Hash: f238960a0783b5971a0d7453329c0b78
TeX (original user input):
\begin{align}
& \eta \left( R \right)=-k\operatorname{Tr}\left( R\ln R \right)=-k\operatorname{Tr}\left( -R\sum\limits_{\nu }^{{}}{{}}{{\lambda }_{\nu }}{{G}_{\nu }}-R\ln Z \right) \\
& =-k\sum\limits_{\nu }^{{}}{{}}{{\lambda }_{\nu }}\left\langle {{G}_{\nu }} \right\rangle +k\ln Z \\
\end{align}
TeX (checked):
{\begin{aligned}&\eta \left(R\right)=-k\operatorname {Tr} \left(R\ln R\right)=-k\operatorname {Tr} \left(-R\sum \limits _{\nu }^{}{}{{\lambda }_{\nu }}{{G}_{\nu }}-R\ln Z\right)\\&=-k\sum \limits _{\nu }^{}{}{{\lambda }_{\nu }}\left\langle {{G}_{\nu }}\right\rangle +k\ln Z\\\end{aligned}}
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MathML (2.02 KB / 443 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mi>η</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>R</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mo>−</mo><mi>k</mi><mi data-mjx-texclass="OP" mathvariant="normal">Tr</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>R</mi><mi>ln</mi><mo>⁡</mo><mi>R</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mo>−</mo><mi>k</mi><mi data-mjx-texclass="OP" mathvariant="normal">Tr</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>−</mo><mi>R</mi><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub><msub><mi>G</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub><mo>−</mo><mi>R</mi><mi>ln</mi><mo>⁡</mo><mi>Z</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><mo>−</mo><mi>k</mi><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi>G</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>+</mo><mi>k</mi><mi>ln</mi><mo>⁡</mo><mi>Z</mi></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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