Year: 2026
Type: article
Abstract: 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 κ c , 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.
Source: Communications Physics
Authors: Virgile Troude, Didier Sornette
Institution: Southern University of Science and Technology
Language: English
Subfield: Global and Planetary Change
Field: Environmental Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,990
OpenAlex ID: W7171205958
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