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Display information for equation id:math.2497.38 on revision:2497

* Page found: Thermodynamische Stabilität (eq math.2497.38)

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Thermodynamische Stabilität Eq: math.2497.38

Hash: ba0751a9c4870be0bb5b38a0159a0c07

TeX (original user input):

\begin{align}

& \Gamma \left( \alpha  \right)=\ln \left\langle {{e}^{\alpha b}} \right\rangle =\ln tr\left( \rho {{e}^{\alpha b}} \right) \\

& {{e}^{\alpha b}}={{\rho }^{-\alpha }} \\

& \Rightarrow \Gamma \left( \alpha  \right)=\ln \left\langle {{e}^{\alpha b}} \right\rangle =\ln tr\left( {{\rho }^{1-\alpha }} \right)=!=\sum\limits_{n=0}^{\infty }{{}}\frac{{{\alpha }^{n}}}{n!}{{C}_{n}} \\

\end{align}

TeX (checked):

{\begin{aligned}&\Gamma \left(\alpha \right)=\ln \left\langle {{e}^{\alpha b}}\right\rangle =\ln tr\left(\rho {{e}^{\alpha b}}\right)\\&{{e}^{\alpha b}}={{\rho }^{-\alpha }}\\&\Rightarrow \Gamma \left(\alpha \right)=\ln \left\langle {{e}^{\alpha b}}\right\rangle =\ln tr\left({{\rho }^{1-\alpha }}\right)=!=\sum \limits _{n=0}^{\infty }{}{\frac {{\alpha }^{n}}{n!}}{{C}_{n}}\\\end{aligned}}

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\begin{aligned} Γ (α) = \ln ⟨ e^{α b} ⟩ = \ln t r (ρ e^{α b}) \\ e^{α b} = ρ^{- α} \\ \Rightarrow Γ (α) = \ln ⟨ e^{α b} ⟩ = \ln t r (ρ^{1 - α}) =! = \sum_{n = 0}^{\infty} \frac{α^{n}}{n!} C_{n} \end{aligned}

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Identifiers

$Γ$

$α$

$e$

$α$

$b$

$t$

$r$

$ρ$

$e$

$α$

$b$

$e$

$α$

$b$

$ρ$

$α$

$Γ$

$α$

$e$

$α$

$b$

$t$

$r$

$ρ$

$α$

$n$

$α$

$n$

$n$

$C_{n}$

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