The recently developed non-equilibrium self-consistent generalized Langevin equation theory of the dynamics of liquids of non-spherically interacting particles [J. Phys. Chem. B 120, 7975 (2016)] is applied to the description of the irreversible relaxation of a thermally and mechanically quenched dipolar fluid. Specifically, we consider a dipolar hard-sphere liquid quenched (at tw = 0) from full equilibrium conditions towards different ergodic–non-ergodic transitions. Qualitatively different scenarios are predicted by the theory for the time evolution of the system after the quench (tw > 0), that depend on both the kind of transition approached and the specific features of the protocol of preparation. Each of these scenarios is characterized by the kinetics displayed by a set of structural correlations, and also by the development of two characteristic times describing the relaxation of the translational and rotational dynamics, allowing us to highlight the crossover from equilibration to aging in the system and leading to the prediction of different underlying mechanisms and relaxation laws for the dynamics at each of the glass transitions explored.

Providing a physically sound explanation of aging phenomena in non-equilibrium amorphous materialsis a challenging problem in modern statistical thermodynamics. The slow evolution of physical propertiesafter quenches of control parameters is empirically well interpreted via the concept of material time (orinternal clock), based on the Tool-Narayanaswamy-Moynihan (TNM) model. Yet, the fundamental reasonsof its striking success remain unclear. We propose a microscopic rationale behind the material time onthe basis of the linear laws of irreversible thermodynamics and its extension that treats the correspondingkinetic coefficients as state functions of a slowly evolving material state. Our interpretation is based onthe recognition that the same mathematical structure governs both the Tool model and the recently devel-oped non-equilibrium extension of the self-consistent generalized Langevin equation theory (NE-SCGLE),guided by the universal principles of Onsager's theory of irreversible processes. This identification opensthe way for a generalization of the material-time concept to aging systems where several relaxation modeswith very different equilibration processes must be considered, and partially frozen glasses manifest theappearance of partial ergodicity breaking, and hence materials with multiple very distinct inner clocks.

We investigate the structural relaxation of a soft-sphere liquid quenched isochorically (φ = 0.7) and instantaneously to different temperatures Tf above and below the glass transition. For this, we combine extensive Brownian dynamics simulations and theoretical calculations based on the non-equilibrium self-consistent generalized Langevin equation (NE-SCGLE) theory. The response of the liquid to a quench generally consists of a sub-linear increase of the α-relaxation time with system's age. Approaching the ideal glass-transition temperature from above (Tf > Ta ) sub-aging appears as a transient process describing a broad equilibration crossover for quenches to nearly arrested states. This allows us to empirically determine an equilibration timescale t eq(Tf) that becomes increasingly longer as Tf approaches Ta . For quenches inside the glass (Tf less than or equal to Ta) the growth rate of the structural relaxation time becomes progressively larger as Tf decreases and, unlike the equilibration scenario, τα remains evolving within the whole observation time-window. These features are consistently found in theory and simulations with remarkable semi-quantitative agreement, and coincide with those revealed in a previous and complementary study [Phys. Rev. 96, 022608 (2017)] that considered a sequence of quenches with fixed final temperature Tf = 0 but increasing φ towards the hard-sphere dynamical arrest volume fraction φ a HS = 0.582. The NESCGLE analysis, however, unveils various fundamental aspects of the glass transition, involving the abrupt passage from the ordinary equilibration scenario to the persistent aging effects that are characteristic of glass-forming liquids.

Linear response methods allow studying magnetic susceptibility relaxation in isotropic colloidal magnetic fluids. We show a relationship between the susceptibility of macroscopic magnetization at thermal equilibrium and the diffusion constant of a tracer particle. The comparison of the predicted frequency-dependent susceptibility with computer simulations shows their agreement. Besides, at a low concentration of particles, it has the expected Debye behavior. However, the initial susceptibility yields only the qualitative trends of the existing experiments at a low volume fraction of particles and its temperature dependence.