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A fluid-dynamic approach to the diffusion of heavy quarks in the quark--gluonplasma (QGP) is presented. Specifically, we analyze the Fokker-Planck equationfor the momentum transport of heavy quarks from a fluid perspective and use amapping to second-order fluid-dynamics to determine conductivities andrelaxation times governing their spatial diffusion. By investigating therelation between the two approaches, we provide new insights concerning thelevel of local thermalization of charm and bottom quarks inside the expandingQGP. Our results indicate that a fluid-dynamic description of diffusion isfeasible for charm quarks at least for the latest stages of the fireballevolution.

A fluid-dynamic approach to heavy-quark diffusion in the quark-gluon plasma