Thermal stability originates the vanishing of the specific heats at the absolute zero

TL;DR

The paper explores how the vanishing of heat capacities at absolute zero relates to thermal stability, showing it aligns with established thermodynamic principles rather than being a new law.

Contribution

It clarifies the connection between specific heat vanishing and thermal stability, emphasizing that this phenomenon confirms existing thermodynamic frameworks.

Findings

Heat capacities vanish at T=0 for stable states.

Weakly vanishing heat capacities indicate critical conditions at T=0.

Vanishing specific heat is a thermodynamic consistency, not a new law.

Abstract

The relationship between the vanishing of the heat capacities as $T\to0^+$ and the thermal stability is examined. The heat capacities vanish as fast as or faster than $T$ as $T\to0^+$ for states at the phase space boundary ($T=0$) to sustain the standard thermal stability criterion $U_{ss}>0$. Conversely, weakly vanishing heat capacities, which signify a loss of curvature in $U(S)$ at $T=0$, are the signature of a critical condition precisely at $T=0$, as exemplified in marginal Fermi liquids. Therefore, the vanishing of the specific heat should be viewed not as a new law but as a confirmatory result of the existing framework of thermodynamics.