The dynamics of heavy particles propagating through a thermal environment has been a topic of interest in theoretical physics (at least) since the times of Einstein’s theory of Brownian motion. The simultaneous production of heavy quarks and quark-gluon plasma in heavy-ion collisions provides an ideal configuration in which to test and extend our understanding of this process in relativistic settings — and, rather uniquely, in terms of the degrees of freedom of the Standard Model of particle physics. The fact that this process is mediated by the strong force makes it all the more interesting, as it provides insight into the strongly coupled dynamics of deconfined QCD matter.

Over the past two decades, the heavy quark diffusion coefficient — the essential ingredient for the definition of a (Gaussian) stochastic process characterizing the in-medium evolution of heavy quarks — has been studied extensively. However, less attention has been given to the non-Gaussian features of the momentum transfer between heavy quarks and quark-gluon plasma. Recently, we showed that these features are in fact essential in order to reach kinetic equilibrium via a direct calculation in N=4 SYM [2501.06289]. More recently, we were able to derive the corresponding equilibration condition in a theory-independent way [2504.21139], as a consequence of a KMS relation for line operators — specifically, timelike Wilson lines characterized by the heavy quark velocity. I will review these developments and show how they can be used to obtain predictions that can be tested with data from heavy-ion collisions.