The equilibrium thermodynamic properties of the $\mathrm{SU}(N)$ plasma are studied nonperturbatively in the large-$N$ limit, via high-precision lattice simulations at temperatures from $0.8T_c$ to $3.4T_c$ ($T_c$ being the critical deconfinement temperature). Our results for $\mathrm{SU}(N)$ Yang-Mills theories with $N=3$, $4$, $5$, $6$, and $8$ colors show a very mild dependence on $N$, supporting the idea that the QCD plasma could be described by models based on the large-$N$ limit. We compare our data with various theoretical descriptions, including, in particular, the improved holographic QCD model proposed by Kiritsis and collaborators. We also comment on the relevance of an AdS/CFT description in a phenomenologically interesting temperature range where the system, while still strongly coupled, becomes approximately scale invariant. Finally, we extrapolate our results to the $N\to \infty$ limit.

We present a first-principle computation of the jet quenching parameter, which describes the momentum broadening of a high-energy parton moving through the deconfined state of QCD matter at high temperature. Following an idea originally proposed by Caron-Huot, we explain how one can evaluate the soft contribution to the collision kernel characterizing this real-time phenomenon, analyzing certain gauge-invariant operators in a dimensionally reduced effective theory (electrostatic QCD), which can be studied nonperturbatively via simulations on a Euclidean lattice. Our high-precision numerical computations at two different temperatures indicate that soft contributions to the jet quenching parameter are large. After discussing the systematic uncertainties involved, we present a quantitative estimate for the jet quenching parameter in the temperature range accessible at heavy-ion colliders, and compare it to results from phenomenological models as well as to strong-coupling computations based on the holographic correspondence.