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Display information for equation id:math.2497.5 on revision:2497

* Page found: Thermodynamische Stabilität (eq math.2497.5)

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Thermodynamische Stabilität Eq: math.2497.5

Hash: 7aab937de7f8118cee204d32ae26d0b2

TeX (original user input):

\begin{align}

& K\left( \rho ,{{\rho }^{0}} \right)=K\left( {{\rho }^{0}},{{\rho }^{0}} \right)+\left( \frac{\partial I}{\partial \left\langle {{M}^{\nu }} \right\rangle }+{{\lambda }_{\nu }}^{0} \right)\delta \left\langle {{M}^{\nu }} \right\rangle +\frac{1}{2}\frac{{{\partial }^{2}}I}{\partial \left\langle {{M}^{\nu }} \right\rangle \partial \left\langle {{M}^{\mu }} \right\rangle }\delta \left\langle {{M}^{\nu }} \right\rangle \delta \left\langle {{M}^{\mu }} \right\rangle  \\

& \frac{\partial I}{\partial \left\langle {{M}^{\nu }} \right\rangle }=-{{\lambda }_{\nu }} \\

& K\left( {{\rho }^{0}},{{\rho }^{0}} \right)=0 \\

\end{align}

TeX (checked):

{\begin{aligned}&K\left(\rho ,{{\rho }^{0}}\right)=K\left({{\rho }^{0}},{{\rho }^{0}}\right)+\left({\frac {\partial I}{\partial \left\langle {{M}^{\nu }}\right\rangle }}+{{\lambda }_{\nu }}^{0}\right)\delta \left\langle {{M}^{\nu }}\right\rangle +{\frac {1}{2}}{\frac {{{\partial }^{2}}I}{\partial \left\langle {{M}^{\nu }}\right\rangle \partial \left\langle {{M}^{\mu }}\right\rangle }}\delta \left\langle {{M}^{\nu }}\right\rangle \delta \left\langle {{M}^{\mu }}\right\rangle \\&{\frac {\partial I}{\partial \left\langle {{M}^{\nu }}\right\rangle }}=-{{\lambda }_{\nu }}\\&K\left({{\rho }^{0}},{{\rho }^{0}}\right)=0\\\end{aligned}}

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\begin{matrix} K (ρ, ρ^{0}) = K (ρ^{0}, ρ^{0}) + (\frac{\partial I}{\partial ⟨ M^{ν} ⟩} + {λ_{ν}}^{0}) δ ⟨ M^{ν} ⟩ + \frac{1}{2} \frac{\partial^{2} I}{\partial ⟨ M^{ν} ⟩ \partial ⟨ M^{μ} ⟩} δ ⟨ M^{ν} ⟩ δ ⟨ M^{μ} ⟩ \\ \frac{\partial I}{\partial ⟨ M^{ν} ⟩} = - λ_{ν} \\ K (ρ^{0}, ρ^{0}) = 0 \end{matrix}

<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>K</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ρ</mi><mo>,</mo><msup><mi>ρ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</mo><mi>K</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>ρ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup><mo>,</mo><msup><mi>ρ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">+</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>I</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><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></mrow></mrow></mfrac></mrow><mo stretchy="false">+</mo><msup><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>δ</mi><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 stretchy="false">+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>I</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><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><mi>∂</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mrow></mrow></mfrac></mrow><mi>δ</mi><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><mi>δ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><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 class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>I</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><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></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mo stretchy="false">−</mo><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>K</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>ρ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup><mo>,</mo><msup><mi>ρ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</mo><mn>0</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

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Identifiers

$K$

$ρ$

$ρ$

$K$

$ρ$

$ρ$

$I$

$M$

$ν$

$λ_{ν}$

$δ$

$M$

$ν$

$I$

$M$

$ν$

$M$

$μ$

$δ$

$M$

$ν$

$δ$

$M$

$μ$

$I$

$M$

$ν$

$λ_{ν}$

$K$

$ρ$

$ρ$

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