On Thermodynamics of Glasses

Abstract

The purpose of this paper is to give a clear meaning to thermodynamics of glasses and to provide a simple illustration. The paper does not offer any new contribution to the microscopic understanding of the glass transition phenomena. The analysis leading to the formulation of thermodynamics proceeds as follows. Let M-level and N-level be two levels of description that are found (by making a comparison of predictions with results of observations) to be well suited for describing the time evolution of glasses. Let the N-level be the more macroscopic one (less detailed) of them. Thermodynamics on the N-level is a geometry in the state space used on the N-level. The geometry arises from an analysis of the time evolution on the M-level, in particular then, from the analysis of the approach of the time evolution on the M-level to the time evolution on the N-level. In the special case when the N-level is chosen to be the level of description used in equilibrium thermodynamics, then this view of thermodynamics becomes just one of the well known formulations of equilibrium thermodynamics. In the context of the analysis of glasses the level of equilibrium thermodynamics is not admissible since glasses do not reach equilibrium states. Two illustrations are worked out. In the first one, the N-level is chosen to be the level of description introduced in the hole theory of liquids, in the second one, the N-level is the level of description used frequently in rheology of polymeric fluids.