Heavy Quark Entropy shift: From the Hadron Resonance Gas to Power Corrections

A heavy quark placed in the medium modifies its specific heat. Using a renormalization group argument we show a low energy theorem in terms of the defect in the trace of the energy-momentum tensor which allows the unambiguous determination of the corresponding entropy shift after imposing the third principle of thermodynamics for degenerate states. We show how recent lattice QCD data can be understood in the confined phase in terms of a single-heavy hadronic spectrum and above the phase transition through power corrections which are analyzed by means of a dimension 2 gluon condensate of the dimensionally reduced theory.