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Display information for equation id:math.2416.49 on revision:2416
* Page found: Entropie von Gleichgewichtszuständen (eq math.2416.49)
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Hash: b9abeaef96751d7ff6fffd460a2cbab1
TeX (original user input):
\begin{align}
& \frac{\partial \Psi }{\partial {{\lambda }_{n}}}=\left\langle {{M}^{n}} \right\rangle \\
& \Psi \left( {{\lambda }_{n}} \right)=-\ln tr\left( {{e}^{-{{\lambda }_{n}}{{M}^{n}}}} \right) \\
\end{align}
TeX (checked):
{\begin{aligned}&{\frac {\partial \Psi }{\partial {{\lambda }_{n}}}}=\left\langle {{M}^{n}}\right\rangle \\&\Psi \left({{\lambda }_{n}}\right)=-\ln tr\left({{e}^{-{{\lambda }_{n}}{{M}^{n}}}}\right)\\\end{aligned}}
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MathML (1.674 KB / 416 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><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi mathvariant="normal">Ψ</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub></mrow></mrow></mfrac></mrow><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mo>−</mo><mi>ln</mi><mo>⁡</mo><mi>t</mi><mi>r</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup></mrow></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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