than the inverse temperature ($rT\ll1$) the dominant scale is set by distance and the QCD running coupling will be controlled by the distance. In this limit the thermal modification of the strong interaction will become negligible and the finite temperature free energy will be given by the zero temperature heavy quark potential (solid line). With increasing quark anti-quark separation, however, thermal effects will dominate the behavior of the finite temperature free energies ($rT\gg1$). Qualitative and quantitative differences between quark anti-quark free energy and internal energy will appear and clarify the important role of the entropy contribution still present in free energies. The quark anti-quark internal energy will provide a different look on the inter-quark interaction and thermal modifications of the finite temperature quark anti-quark potential. Further details of these modifications on the quark anti-quark free and internal energies will be discussed.

This paper is organized as follows: We start in section \[sect0\] with a discussion of the zero temperature heavy quark potential and the coupling. Both will be calculated from $2$-flavor lattice QCD simulations. We analyze in section \[secfreee\] the thermal modifications on the quark anti-quark free energies and discuss quarkonium binding. Section \[seccon\] contains our summary and conclusions. A 