When a glassblower models and manipulates a glass-forming liquid to fabricate a desired piece, he has an intuitive but precise notion on the expected result of his fabrication protocol. This suggests the existence of a deterministic law that associates a unique result to each fabrication protocol. Although glasses have accompanied humanity for thousands of years, no molecular theory exists so far that satisfactorily explains and predicts from first principles the phenomenology of the glass transition (so well-known empirically to the glassblower). Explaining the phenomenology of the glass transition from a molecular perspective, however, is a relevant fundamental and practical challenge: many amorphous solids of everyday importance, including ordinary glasses, but also gels, foams, etc., are found in non-equilibrium states analogous to the glass state.
Starting from the study of the dynamics of colloidal suspensions, within the last ten years our group has developed a theory of the equilibrium dynamics of liquids. This theory, referred to as the Self-consistent Generalized Langevin Equation (SCGLE) theory, allows us to describe the main dynamic properties of the liquid (self- and collective diffusion, mean squared displacement, etc.) from first principles, i.e., in terms of the fundamental interactions between the particles that constitute the liquid. One of its most relevant predictions refers to the determination of the conditions under which the mobility of the particles of a given species might collapse due to the strong interparticle interactions, thus leading to the spatial localization of the particles of that species. This implies the partial or total loss of the ergodicity of the system, and the passage to glassy (or dynamically ``arrested") states, which may thus be fully arrested states or partially non-ergodic states, such as those observed in some amorphous solid electrolytes.
Up to this point, our self-consistent theory may be viewed as an independent version of the well-known mode coupling theory (MCT) of the ideal glass transition. In its most recent development, however, our theory has been extended to describe the irreversible evolution of the system while it remains off thermodynamic equilibrium during its equilibration or its aging process, thus becoming the only first-principles theory which is able to explain quantitatively some of the main features of the dynamic arrest of simple "fragile" glass-forming liquids. You are welcome to take a closer look at what we have understood so far and to what we still would like to understand.