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Display information for equation id:math.2282.13 on revision:2282
* Page found: Beispiel des Großkanonischen Ensenbles (eq math.2282.13)
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TeX (original user input):
k{{\lambda }_{\nu }}={{\partial }_{\left\langle {{G}_{\nu }} \right\rangle }}S\Rightarrow k\beta ={{\left( \frac{\partial S}{\partial E} \right)}_{V,\bar{N}}};\quad k\sum\limits_{\nu }{{{\lambda }_{\nu }}{{M}_{\nu ,\alpha }}={{\partial }_{{{h}_{\alpha }}}}S}\Rightarrow {{\left( \frac{\partial S}{\partial N} \right)}_{E,\bar{N}}}=-k\beta \operatorname{Tr}\left( \frac{\partial H}{\partial V}R \right)
TeX (checked):
k{{\lambda }_{\nu }}={{\partial }_{\left\langle {{G}_{\nu }}\right\rangle }}S\Rightarrow k\beta ={{\left({\frac {\partial S}{\partial E}}\right)}_{V,{\bar {N}}}};\quad k\sum \limits _{\nu }{{{\lambda }_{\nu }}{{M}_{\nu ,\alpha }}={{\partial }_{{h}_{\alpha }}}S}\Rightarrow {{\left({\frac {\partial S}{\partial N}}\right)}_{E,{\bar {N}}}}=-k\beta \operatorname {Tr} \left({\frac {\partial H}{\partial V}}R\right)
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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"><mi>k</mi><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub><mo>=</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><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></mrow></msub><mi>S</mi><mo>⇒</mo><mi>k</mi><mi>β</mi><mo>=</mo><msub><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>S</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>E</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>V</mi><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>N</mi><mo>¯</mo></mover></mrow></mrow></mrow></mrow></msub><mo>;</mo><mspace width="1em"></mspace><mi>k</mi><munder><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></munder><mrow data-mjx-texclass="ORD"><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub><msub><mi>M</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>ν</mi><mo>,</mo><mi>α</mi></mrow></mrow></msub><mo>=</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><msub><mi>h</mi><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msub></mrow></msub><mi>S</mi></mrow><mo>⇒</mo><msub><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>S</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>N</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>E</mi><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>N</mi><mo>¯</mo></mover></mrow></mrow></mrow></mrow></msub><mo>=</mo><mo>−</mo><mi>k</mi><mi>β</mi><mi data-mjx-texclass="OP" mathvariant="normal">Tr</mi><mo>⁡</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>H</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>V</mi></mrow></mrow></mfrac></mrow><mi>R</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mstyle></mrow></math>
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