Non-Normal Phase Transitions: A New Universality in Complex Systems

We identify a new universality class of phase transitions that arises in non-normal systems, expanding the classical framework beyond eigenvalue instabilities. In contrast to traditional critical phenomena, where transitions occur when eigenvalues cross zero, we show that the geometry of eigenvectors alone can trigger qualitative changes in dynamics. Within a large-deviation framework, transient amplification intrinsic to non-normal operators renormalizes the effective noise amplitude, which can be interpreted as an emergent temperature. Once the non-normality index $\kappa$ exceeds a critical threshold $\kappa_c$ representing the critical balance between restoring potential curvature and non-normal shear, stable equilibria lose practical relevance: fluctuations are amplified strongly enough to induce escapes, even though spectral stability is preserved. This mechanism represents a fundamentally new route to criticality---pseudo-criticality---that generalizes Kramers' escape beyond potential barriers, and can dominate noise-driven transitions in natural and engineered systems. The implications are broad. In biology, we demonstrate that DNA methylation, a cornerstone of epigenetic regulation, naturally operates in this regime: by extending a bistable model of CpG dyads to include non-normality, we reconcile long-term epigenetic memory with rapid stochastic switching observed on minute timescales. More generally, the same mechanism applies to abrupt tipping points in climate dynamics, ecological collapses, financial crises, and failures of engineered networks. By establishing that phase transitions need not be spectrally induced, but can emerge from non-normal amplification, our work introduces a predictive and compact analytical framework for quantifying sudden transitions across disciplines. Non-normality thus defines a new universality class of phase transitions in out-of-equilibrium complex systems, reshaping our understanding of how noise and structure interact to produce abrupt change.