This paper studies how small departures from local equilibrium in the quark–gluon plasma (QGP) affect two common probes: heavy quarks and thermal dileptons. The authors compute, for the first time, the effect of viscous corrections up to second order in gradients using a Chapman–Enskog–like expansion of the Boltzmann transport equation. They compare these results with the more familiar Grad’s 14‑moment approximation and follow the evolving medium using second‑order causal viscous hydrodynamics.

Chapman–Enskog is a method that builds the non‑equilibrium particle distribution as a series in the size of space‑time gradients (roughly how quickly the medium changes compared with particle mean free paths). The calculation is done in the relaxation‑time approximation (RTA), where particles relax to equilibrium on a time scale τR that the paper treats as independent of particle momentum. Grad’s 14‑moment approach, by contrast, expands the distribution in powers of particle momentum. The authors insert these modified distributions into kinetic formulas for heavy‑quark transport (drag and diffusion, treated with a Fokker–Planck picture) and for thermal dilepton emission, and they evolve the medium with a one‑dimensional boost‑invariant (Bjorken) expansion.

Their main findings are concrete. For heavy quarks, the Chapman–Enskog (CE) second‑order corrections strongly reduce the drag force, introduce a non‑trivial momentum dependence in transverse momentum diffusion, and produce only a smaller change in longitudinal momentum diffusion. For thermal dileptons, the CE second‑order terms boost the contribution from early times in the QGP evolution; that enhancement then falls during the expansion and approaches the first‑order CE result. The authors also note that the CE corrections stay better behaved (less pathological) than those from Grad’s approximation in the cases they study.