Residual Entropy and Refinement of the Third-Law Expression

TL;DR

This paper proposes a new, quantitative formulation of the third law of thermodynamics using the concept of classes and internal constraints, providing a unified way to understand residual entropy in various materials.

Contribution

It introduces the notion of classes and frozen coordinates to refine the third law, enabling consistent treatment of residual entropy across different material states.

Findings

Provides a quantitative expression for the third law.

Unifies treatment of residual entropy in amorphous and mixed materials.

Clarifies the origin and irreversibility of residual entropy.

Abstract

Although the third law of thermodynamics was established almost a century ago, it is not yet universally considered to be a fundamental law of physics. A major problem is that there are many materials having residual entropy. Amorphous materials and random alloy systems are well-known examples. A conventional view is that amorphous materials are not in thermodynamic equilibrium and must be exempted from the law. The recent development of material sciences has let to a variety of new materials. Some of them have ambiguous structures which do not fit the qualitative description of metastability. The definition of order states also becomes vague. The establishment of an unambiguous statement which does not depend on the material properties is required. This paper provides a quantitative expression for the third law to meet this requirement. The idea is to introduce the notion of class. Every system belongs to a class. Different classes are thermodynamically separated by special internal constraints which are quantified by the frozen coordinate, r. A frozen coordinate is a state variable that is not commonly possessed between two classes. The third law is restated as all materials within a given class have a common origin of entropy. For two systems belonging to different classes, the entropy origins are shifted by the difference in entropy associated with the difference r between the two systems. When the internal constraint is removed, the entropy origin must be reconstructed in order to establish only one thermodynamic equilibrium. This process is irreversible and this irreversibility is observed as the residual entropy. On the basis of this refinement, the residual entropies of amorphous materials as well as the long-standing problem of mixed states can be treated on an equal footing.