Singular zero-temperature system

TL;DR

This paper explores the possibility of singular zero-temperature systems that defy the traditional assumptions of thermodynamics near absolute zero, revisiting models to identify their classification.

Contribution

It challenges the conventional view by introducing the concept of singular zero-temperature systems and classifies existing models within this new framework.

Findings

Some models are identified as singular zero-temperature systems.

The traditional assumptions about heat capacities near absolute zero are not universally valid.

The concept broadens the understanding of thermodynamic systems at low temperatures.

Abstract

It has long been taken for granted that there is only one type of thermodynamic system near absolute zero temperature: the ordinary one compatible with all statements of the third law, with a fundamental yet tacit assumption that all heat capacities in the system vanish as absolute temperature approaches zero. However, in the strict sense, the statements are not mutually equivalent. Once the tacit assumption is released, the inequivalence must remain, and we may have some systems that are only compatible with one or two statements but not all, defining a singular zero-temperature system which can never be excluded from physical feasibility. We revisit some previously proposed theoretical models and identify that they belong to the singular system.