The vanishing of heat capacity as thermodynamic third law implies existence of singular systems

TL;DR

This paper proves that the third law of thermodynamics implies the existence of singular systems, supported by counterexamples that challenge the traditional understanding of heat capacity approaching zero at absolute zero.

Contribution

It establishes a theorem linking the vanishing of heat capacity to the existence of singular systems, clarifying the implications of the third law of thermodynamics.

Findings

Theorem connecting heat capacity vanishing to singular systems

Two counterexamples illustrating the theorem

Implications for thermodynamic system classification

Abstract

A corollary of the third law of thermodynamics is that the heat capacities of a system approach zero as the temperature approaches absolute zero Kevin. Many have attempted to take the corollary as the third law, but two counterexamples has been constructed explicitly. We present a theorem that the vanishing of heat capacity as the third law implies an existence of singular systems, and two known counterexamples are illustrations of the theorem.