Where is the residual entropy of a glass hiding?

TL;DR

This paper defends the reality of residual entropy in glasses, arguing that the entropy remains finite in kinetically frozen states and that the residual entropy loss conjecture violates thermodynamic principles.

Contribution

It clarifies the misunderstanding about entropy in glasses, emphasizing the importance of ensemble entropy and refuting the residual entropy loss conjecture.

Findings

Residual entropy remains in frozen glasses.

The entropy continuity at the glass transition contradicts the entropy loss conjecture.

Temporal entropy definitions are not meaningful for glasses.

Abstract

We revisit the controversy, discussed recently by Goldstein in this journal[J. Chem. Phys. 128,154510 (2008)], whether the residual entropy is real or fictional. It is shown that the residual entropy loss conjecture (ELC) at the glass transition, which results in a discontinuous entropy violates many fundamental principles of classical thermodynamics, and also contradicts some experimental facts. Assuming, as is common in the field, that glasses are in internal equilibrium, we show that the continuity of enthalpy and volume at the glass transition require the continuity of the Gibbs free energy and the entropy, which contradicts ELC. It is then argued that ELC is founded on an incorrect understanding of what it means for a glass to be kinetically trapped in a basin and of the concept of probability and entropy. Once this misunderstanding is corrected in our approach by the proper identification of entropy as the ensemble entropy, which is in accordance with the principle of reproducibility (see Sect. II), it follows immediately that the residual entropy does not disappear in a kinetically frozen glassy state and all the violations of thermodynamics disappear. We show that the temporal definition of entropy over finite times does not make sense for glasses as it is not unique. There is no loss of ergodicity and causality, contrary to some recent claims.