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In studies of glass-forming liquids, one of the important questions is to understand to which degree chemically different classes of liquids have the same type of dynamics. In this context, room-temperature ionic liquids are interesting because they exhibit both van der Waals and Coulomb interactions. In this work we study the $\ensuremath{\alpha}$ relaxation and faster relaxation dynamics in the room-temperature ionic liquid 1-butyl-1-methylpyrrolidinium bis(trifluoromethanesulfonyl)imide (Pyr14-TFSI). The paper presents quasielastic neutron and shear mechanical spectroscopy data measured over seven decades in frequency (${10}^{\ensuremath{-}3}\ensuremath{-}{10}^{4}$ Hz). The use of these two methods in combination reveal the $\ensuremath{\alpha}$ relaxation and four separate, faster modes. Two of these faster modes, based on the partial deuterations, can be assigned to the methyl group and the methyl end of the butyl chain of the cation. The neutron data are also used to determine the mean-square displacement (MSD) on the nanosecond timescale. It is shown that the temperature dependence of the MSD can account for the super-Arrhenius behavior of the $\ensuremath{\alpha}$ relaxation as predicted by the shoving model [Dyre, Rev. Mod. Phys. 78, 953 (2006)], similarly to what is seen in simpler glass-forming liquids.

A large class of liquids obey density scaling characterized by an exponent, which quantifies the relative roles of temperature and density for the dynamics. We present experimental evidence that the density-scaling exponent γ is state-point dependent for the glass formers tetramethyl-tetraphenyl-trisiloxane (DC704) and 5-polyphenyl ether (5PPE). A method is proposed that from dynamic and thermodynamic properties at equilibrium estimates the value of γ. The method applies at any state point of the pressure-temperature plane, both in the supercooled and the normal liquid regimes. We find that γ is generally state-point dependent, which is confirmed by reanalyzing data for 20 metallic liquids and two model liquids.

The linear volume relaxation and the nonlinear volume aging of a glass-forming liquid are measured, directly compared, and used to extract the out-of-equilibrium relaxation time. This opens a window to investigate how the relaxation time depends on temperature, structure, and volume in parts of phase space that are not accessed by the equilibrium liquid. It is found that the temperature dependence of relaxation time is non-Arrhenius even in the isostructural case---challenging the Adam-Gibbs entropy model. Based on the presented data and the idea that aging happens through quasiequilibrium states, we suggest a mapping of the out-of-equilibrium states during isobaric aging to the equilibrium phase diagram. This mapping implies the existence of isostructural lines in the equilibrium phase diagram. The relaxation time is found to depend on the bath temperature, density, and a just single structural parameter, referred to as an effective temperature.