"Inner clocks" of glass-forming liquids.

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