Phase transitions without instability from non-normal dynamics
摘要
It is often assumed that a system must become unstable in order to undergo a transition. This assumption reflects a deeper bias: state changes are usually interpreted as consequences of bifurcations or spectral instabilities. Here we identify a universality class of phase transitions in non-normal systems and show that transitions can occur even when all equilibria remain spectrally stable. The key mechanism is transient amplification by non-orthogonal eigenvectors: fluctuations are enhanced not by lowering energy barriers, but by increasing the effective shear of the flow, which renormalizes them and acts as an emergent temperature. Once the non-normality index κ exceeds a critical threshold κc, stable equilibria lose practical relevance, enabling escapes and abrupt transitions despite preserved spectral stability. This pseudo-criticality generalizes Kramers’ escape beyond potential barriers and offers a fundamentally different route to critical phenomena. Its implications are broad: DNA methylation reconciles long-term epigenetic memory with rapid switching, and abrupt tipping points in climate, ecology, finance, and engineered networks may arise from the same mechanism.