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

Abstract

The relationship between the vanishing of the heat capacitiesas T → 0+ and the thermal stability is examined. The heat capacities vanish as fast as or faster than T as T → 0+ for states at the phase space boundary (T = 0) to sustain the standard thermal stability criterion Uss > 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 heat capacities should be viewed not as a new law but as a confirmatory result of the existing framework of thermodynamics.