Apparent entropy, residual entropy, causality, metastability, constraints, and the glass transition

A thermodynamic framework for the investigation of ‘residual entropy’ and related phenomena is developed, expanding and clarifying the work of Kivelson and Reiss and the important work of several other investigators. The main difficulties encountered in the development of such a framework are the need to deal with constrained equilibrium as well as to include irreversible processes in the overall study. These challenges are met by using the device of auxiliary constraints and the equivalent equilibrated states that they produce. The importance of a thermodynamic framework is tied to the fact that evolving molecular theories of residual entropy, which also impact the glass transition, no matter how sophisticated, invariably contain approximations whose effects are hard to assess. Thus a thermodynamic framework provides a vehicle within which the internal consistency of a theory can be tested. Phenomena that are treated in such a framework, along with others, are those mentioned in the title of this paper. The concept of residual entropy, its reality or unreality, is often considered to be an unimportant issue. The findings of this paper, besides emphasizing the unreality of residual entropy, show that the question of its existence is a significant one. Among other things, the fundamental principle of causality is involved and we should not be so cavalier as to dispense with it. Among other rigorous analysis we present an argument involving an ideal binary solution whose behavior as the limiting behavior of a real solution provides access, in principle, to experiment. The argument does make the generally accepted assumption that, at equilibrium at 0 K, pure crystals of the binary system’s components have zero entropy. It strongly suggests that residual entropy, in general, is an impression that stems from the inclusion of an irreversible step in an experimental thermodynamic cycle.