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Display information for equation id:math.2282.36 on revision:2282

* Page found: Beispiel des Großkanonischen Ensenbles (eq math.2282.36)

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Hash: 272f6768b58249f636854fb29f890b63

TeX (original user input):

\begin{align}
  & {{\left( \frac{\partial {{S}_{1}}}{\partial {{E}_{1}}} \right)}_{{{V}_{1}},{{{\bar{N}}}_{1}}}}={{\left( \frac{\partial {{S}_{2}}}{\partial {{E}_{2}}} \right)}_{{{V}_{2}},{{{\bar{N}}}_{2}}}} \\
 & {{\left( \frac{\partial {{S}_{1}}}{\partial {{{\bar{N}}}_{1}}} \right)}_{{{V}_{1}},{{E}_{1}}}}={{\left( \frac{\partial {{S}_{2}}}{\partial {{{\bar{N}}}_{2}}} \right)}_{{{V}_{2}},{{E}_{2}}}} \\
 & {{\left( \frac{\partial {{S}_{1}}}{\partial {{V}_{1}}} \right)}_{{{E}_{1}},{{{\bar{N}}}_{1}}}}={{\left( \frac{\partial {{S}_{2}}}{\partial {{V}_{2}}} \right)}_{{{E}_{2}},{{{\bar{N}}}_{2}}}} 
\end{align}

TeX (checked):

{\begin{aligned}&{{\left({\frac {\partial {{S}_{1}}}{\partial {{E}_{1}}}}\right)}_{{{V}_{1}},{{\bar {N}}_{1}}}}={{\left({\frac {\partial {{S}_{2}}}{\partial {{E}_{2}}}}\right)}_{{{V}_{2}},{{\bar {N}}_{2}}}}\\&{{\left({\frac {\partial {{S}_{1}}}{\partial {{\bar {N}}_{1}}}}\right)}_{{{V}_{1}},{{E}_{1}}}}={{\left({\frac {\partial {{S}_{2}}}{\partial {{\bar {N}}_{2}}}}\right)}_{{{V}_{2}},{{E}_{2}}}}\\&{{\left({\frac {\partial {{S}_{1}}}{\partial {{V}_{1}}}}\right)}_{{{E}_{1}},{{\bar {N}}_{1}}}}={{\left({\frac {\partial {{S}_{2}}}{\partial {{V}_{2}}}}\right)}_{{{E}_{2}},{{\bar {N}}_{2}}}}\end{aligned}}

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(S1E1)V1,N¯1=(S2E2)V2,N¯2(S1N¯1)V1,E1=(S2N¯2)V2,E2(S1V1)E1,N¯1=(S2V2)E2,N¯2
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data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>N</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></mrow></msub><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>&#x2202;</mi><msub><mi>S</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>V</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>N</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></mrow></msub></mtd></mtr><mtr><mtd></mtd><mtd><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>&#x2202;</mi><msub><mi>S</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>N</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>V</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></mrow></msub><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>&#x2202;</mi><msub><mi>S</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>N</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>V</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>,</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></mrow></msub></mtd></mtr><mtr><mtd></mtd><mtd><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>&#x2202;</mi><msub><mi>S</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msub><mi>V</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>N</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></mrow></msub><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>&#x2202;</mi><msub><mi>S</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msub><mi>V</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>N</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></mrow></msub></mtd></mtr></mtable></mrow></mstyle></mrow></math>

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Calculated based on the variables occurring on the entire Beispiel des Großkanonischen Ensenbles page

Identifiers

  • S1
  • E1
  • V1
  • N¯1
  • S2
  • E2
  • V2
  • N¯2
  • S1
  • N¯1
  • V1
  • E1
  • S2
  • N¯2
  • V2
  • E2
  • S1
  • V1
  • E1
  • N¯1
  • S2
  • V2
  • E2
  • N¯2

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