Abstract

We will derive bounds on the equilibration times in open and closed systems. For open systems, we will find that thermalization times cannot, typically, be shorter than Planck’s constant divided by the temperature; a more general (and accurate) relation involving the heat capacities will be explained. For closed systems, the inequalities that we will obtain suggest that non-adiabatically driven systems may display long range correlations. We will explain how such long range correlations appear in certain soluble models and review how experimental measurements of equilibrated systems may be used to infer the average properties of eigenstates of many body Hamiltonians. We will then piece these results together to predict the viscosity and relaxation times of supercooled liquids and glasses. These predictions will be compared to the viscosities and dielectric relaxation times of glass formers of all known types. The comparison shows that the viscosities/relaxation times of all known supercooled liquids collapse onto a universal curve over 16 decades. The collapsed form predicted by theory has only one (nearly constant) liquid dependent parameter.