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Display information for equation id:math.2284.27 on revision:2284

* Page found: Beispiel des Großkanonischen Ensenbles (eq math.2284.27)

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TeX (original user input): 

\begin{align}
  & ={{\operatorname{Tr}}_{1}}\left( {{\rho }_{1}}\ln \left( {{\rho }_{1}} \right) \right)\underbrace{{{\operatorname{Tr}}_{2}}\left( \rho  \right)}_{1}+{{\operatorname{Tr}}_{2}}\left( {{\rho }_{2}}\ln \left( {{\rho }_{2}} \right) \right)\underbrace{\operatorname{Tr}\left( {{\rho }_{1}} \right)}_{1} \\
 & \Rightarrow S={{S}_{1}}+{{S}_{2}} 
\end{align}

TeX (checked): 

{\begin{aligned}&={{\operatorname {Tr} }_{1}}\left({{\rho }_{1}}\ln \left({{\rho }_{1}}\right)\right)\underbrace {{{\operatorname {Tr} }_{2}}\left(\rho \right)} _{1}+{{\operatorname {Tr} }_{2}}\left({{\rho }_{2}}\ln \left({{\rho }_{2}}\right)\right)\underbrace {\operatorname {Tr} \left({{\rho }_{1}}\right)} _{1}\\&\Rightarrow S={{S}_{1}}+{{S}_{2}}\end{aligned}}

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MathML (2.48 KB / 434 B) :

=Tr1(ρ1ln⁡(ρ1))Tr2(ρ)⏟1+Tr2(ρ2ln⁡(ρ2))Tr⁡(ρ1)⏟1⇒S=S1+S2
<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"><mo stretchy="false">=</mo><msub><mo data-mjx-texclass="OP" mathvariant="normal">Tr</mo><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>ρ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mi>ln</mi><mo>&#x2061;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>ρ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><munder><mrow data-mjx-texclass="OP"><munder><mrow data-mjx-texclass="ORD"><msub><mo data-mjx-texclass="OP" mathvariant="normal">Tr</mo><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ρ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow><mo>⏟</mo></munder></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></munder><mo stretchy="false">+</mo><msub><mo data-mjx-texclass="OP" mathvariant="normal">Tr</mo><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>ρ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mi>ln</mi><mo>&#x2061;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>ρ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><munder><mrow data-mjx-texclass="OP"><munder><mrow data-mjx-texclass="ORD"><mo data-mjx-texclass="OP" mathvariant="normal">Tr</mo><mo>&#x2061;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>ρ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow><mo>⏟</mo></munder></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></munder></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">⇒</mo><mi>S</mi><mo stretchy="false">=</mo><msub><mi>S</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">+</mo><msub><mi>S</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mtd></mtr></mtable></mstyle></mrow></math>

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

Identifiers

  • ρ1
  • ρ1
  • ρ1
  • ρ2
  • ρ2
  • ρ11
  • S
  • S1
  • S2

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