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The correlation function between two Polyakov loops encodes the free-energyshift due to a pair of separated colour conjugated sources in the hot QCDmedium. This is analyzed in terms of a novel K\"all\'en-Lehmann spectralrepresentation for the separating distance, implying an increasing and concavefree-energy at all temperatures. We express the heavy $\bar{Q} Q$ free-energyshift below the phase transition in QCD in terms of colour neutral purelyhadronic states with no explicit reference to quarks and gluons. Good agreementwith lattice data is achieved when considering the avoided crossing mechanismunderlying string breaking and with standard quenched values of the stringtension known from charmonium and bottomonium phenomenology. We also addressthe role of the corresponding entropy shift and its renormalization groupproperties.

Heavy quark-antiquark free energy and thermodynamics of string-hadron avoided crossings