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# Hagedorn temperature

In theoretical physics, the Hagedorn temperature is the maximal allowed temperature of certain systems above which the partition sum diverges.

$\lim_{T\rightarrow T_H^-} Tr[e^{-\beta H}]=\infty$

$\lim_{T\rightarrow T_H^-}E=\lim_{T\rightarrow T_H^-}\frac{Tr[H e^{-\beta H}]}{Tr[e^{-\beta H}]}=\infty$