detailed discussion of the quark anti-quark internal energy and entropy will be given separately [@pap2].

The zero temperature heavy quark potential and coupling {#sect0}
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Heavy quark potential at $T=0$
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For the determination of the heavy quark potential at zero temperature, $V(r)$, we have used the measurements of large smeared Wilson loops given in [@Karsch:2000kv] for the same simulation parameters ($N_f$=2 and $ma=0.1$) and action. To eliminate the divergent self-energy contributions we matched these data for all $\beta$-values (different $\beta$-values correspond to different values of the lattice spacing $a$) at large distances to the bosonic string potential, $$\begin{aligned}
V(r) &=& - \frac{\pi}{12}\frac{1}{r} + \sigma r \nonumber\\
&\equiv&-\frac{4}{3}\frac{\alpha_{\text{str}}}{r}+\sigma r\;,
\label{string-cornell}\end{aligned}$$ where we already have separated the Casimir factor so that $\alpha_{\text{str}}\equiv\pi/16$. In this normalization any divergent contributions to the lattice potential are eliminated uniquely. In Fig. \[peik\] we show our results together with the heavy quark potential from the string picture (dashed line). One can see that the data are well described by Eq. (\[string-cornell\]) at large distances, [*i.e.*]{} $r\sqrt{\sigma}\;\gsim\;0.8$, corresponding to $r\;\gsim\;0.4$ fm. At these distances we see no major difference between the 2-flavor QCD potential obtained from Wilson loops and the quenched QCD potential which can be well 