Hagedorn Temperature

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String theory predicts a maximum temperature the strings can have. This is based off the linear relationship between energy and entropy at high energies providing a constant temperature. As the temperature of your string approaches the hagedron temp the energy and the partition function diverges, new strings are created before that temperature is reached.
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No you got the completely wrong Hagedorn temperature. It's far below the number you gave. around 1.5E12 to 2.0E12

DKFX