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Display information for equation id:math.2497.40 on revision:2497
* Page found: Thermodynamische Stabilität (eq math.2497.40)
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Hash: 737c3463c4dfa9f9b7b3a77e503e41b3
TeX (original user input):
\begin{align}
& \rho ={{e}^{\left( \Psi -{{\lambda }_{\nu }}{{M}^{\nu }} \right)}} \\
& \Rightarrow b=-\Psi +{{\lambda }_{\nu }}{{M}^{\nu }} \\
& \Rightarrow \Delta b:=b-\left\langle b \right\rangle ={{\lambda }_{\nu }}\left( {{M}^{\nu }}-\left\langle {{M}^{\nu }} \right\rangle \right)={{\lambda }_{\nu }}\Delta {{M}^{\nu }} \\
& \left\langle {{\left( \Delta b \right)}^{2}} \right\rangle ={{\lambda }_{\nu }}{{\lambda }_{\mu }}\left\langle \Delta {{M}^{\nu }}\Delta {{M}^{\mu }} \right\rangle \\
\end{align}
TeX (checked):
{\begin{aligned}&\rho ={{e}^{\left(\Psi -{{\lambda }_{\nu }}{{M}^{\nu }}\right)}}\\&\Rightarrow b=-\Psi +{{\lambda }_{\nu }}{{M}^{\nu }}\\&\Rightarrow \Delta b:=b-\left\langle b\right\rangle ={{\lambda }_{\nu }}\left({{M}^{\nu }}-\left\langle {{M}^{\nu }}\right\rangle \right)={{\lambda }_{\nu }}\Delta {{M}^{\nu }}\\&\left\langle {{\left(\Delta b\right)}^{2}}\right\rangle ={{\lambda }_{\nu }}{{\lambda }_{\mu }}\left\langle \Delta {{M}^{\nu }}\Delta {{M}^{\mu }}\right\rangle \\\end{aligned}}
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<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>ρ</mi><mo>=</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi mathvariant="normal">Ψ</mi><mo>−</mo><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇒</mo><mi>b</mi><mo>=</mo><mo>−</mo><mi mathvariant="normal">Ψ</mi><mo>+</mo><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇒</mo><mi mathvariant="normal">Δ</mi><mi>b</mi><mi>:</mi><mo>=</mo><mi>b</mi><mo>−</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>b</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>=</mo><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><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><mo>−</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub><mi mathvariant="normal">Δ</mi><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi mathvariant="normal">Δ</mi><mi>b</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>=</mo><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi mathvariant="normal">Δ</mi><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><mi mathvariant="normal">Δ</mi><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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