The dynamics of phase transitions are interpreted within Energy-Efficiency Theory (EET). Starting from the three axioms, we treat a phase transition as a critical escape event: when the energy ratio η=E˙resp/E˙mainη=E˙resp/E˙main approaches unity, the existing constraint reorganizes. The relaxation time is derived as τ∼Eb/E˙mainτ∼Eb/E˙main from the constraint maintenance condition. Critical slowing down corresponds to the vanishing of E˙mainE˙main at the critical point. The Kibble-Zurek mechanism is recovered from the competition between the cooling rate and the divergence of ττ; this is presented as a compatibility discussion, not a new prediction. A testable prediction unique to EET is proposed: in materials with hierarchical constraint structures (e.g., layered cuprates), the dynamic critical exponent zz should depend on the number of nested levels LL as z(L)=z∞+kz/Lz(L)=z∞+kz/L, where z∞z∞ is the universal value of the corresponding dynamic universality class. This prediction is motivated by the hypothesis that constraint nesting affects all critical behavior, and it complements the static prediction for νν given in the companion paper 8. Experimental protocols are outlined, and falsification conditions are specified. This paper focuses on qualitative dynamics and one new testable prediction; it is the dynamical companion to the static ontological framework 8.
Hongpu Yang (Mon,) studied this question.