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Does the quark-gluon plasma become weakly coupled at infinite temperature (due to asymptotic freedom), or does it maintain some non-perturbative behavior?

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QGP develops perturbative properties early, when so called invariant measure $(Eps-3P)/T^4$ decreased enough - maybe above $T=0.4\ GeV$. Nobody looked seriously beyond $T=1\ GeV$ since we do not expect to find anything but very slow logarithmic approach to ideal gas properties, and experimental reach ends before that value of $T$.

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