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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2510.07938 |
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| _version_ | 1866915541712633856 |
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| author | Troude, Virgile Sornette, Didier |
| author_facet | Troude, Virgile Sornette, Didier |
| contents | We identify a new universality class of phase transitions that arises in non-normal systems, challenging the classical view that transitions require eigenvalue instabilities. In traditional bifurcation theory, critical phenomena emerge when spectral stability is lost; here, we show that transitions can occur even when all equilibria are spectrally stable. The key mechanism is the transient amplification induced by non-orthogonal eigenvectors: noise-driven dynamics are enhanced not by lowering energy barriers, but by increasing the effective shear of the flow, which renormalizes fluctuations 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, providing a fundamentally new route to critical phenomena. Its implications are broad: in biology, DNA methylation dynamics reconcile long-term epigenetic memory with rapid stochastic switching; in climate, ecology, finance, and engineered networks, abrupt tipping points can arise from the same mechanism. By demonstrating that phase transitions can emerge from non-normal amplification rather than eigenvalue instabilities, we introduce a predictive, compact framework for sudden transitions in complex systems, establishing non-normality as a defining principle of a new universality class of phase transitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07938 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Phase Transitions Without Instability: A Universal Mechanism from Non-Normal Dynamics Troude, Virgile Sornette, Didier Statistical Mechanics We identify a new universality class of phase transitions that arises in non-normal systems, challenging the classical view that transitions require eigenvalue instabilities. In traditional bifurcation theory, critical phenomena emerge when spectral stability is lost; here, we show that transitions can occur even when all equilibria are spectrally stable. The key mechanism is the transient amplification induced by non-orthogonal eigenvectors: noise-driven dynamics are enhanced not by lowering energy barriers, but by increasing the effective shear of the flow, which renormalizes fluctuations 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, providing a fundamentally new route to critical phenomena. Its implications are broad: in biology, DNA methylation dynamics reconcile long-term epigenetic memory with rapid stochastic switching; in climate, ecology, finance, and engineered networks, abrupt tipping points can arise from the same mechanism. By demonstrating that phase transitions can emerge from non-normal amplification rather than eigenvalue instabilities, we introduce a predictive, compact framework for sudden transitions in complex systems, establishing non-normality as a defining principle of a new universality class of phase transitions. |
| title | Phase Transitions Without Instability: A Universal Mechanism from Non-Normal Dynamics |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2510.07938 |