arXiv subjects

Virgile Troude

Publications and source records attributed to Virgile Troude.

7 recordsLinked to original sources

arXiv2026

Eigenvector Geometry as a New Route to Criticality in Random Multiplicative Systems

Heavy-tailed fluctuations and power law distributions pervade physics, biology, and the social sciences, with numerous mechanisms proposed for their emergence. Kesten processes, which are multiplicative stochastic recursions with additive noise or reinjection, provide a canonical explanation, where power law tails arise from transient supercritical excursions as eigenvalues intermittently cross the stability boundary. Here we uncover a distinct and more general mechanism in multidimensional systems: non-normal eigenvector amplification. In random non-normal matrices, the non-orthogonality of eigenvectors, quantified at each time step by the condition number $κ_t$ in Kesten-like processes, induces transient growth that increases the effective Lyapunov exponent $γ\to γ+ \mathbb{E}\left[\ln κ_t \right]$ and lowers the tail exponent $α\simeq -2γ/ σ_κ^2$, where $\mathbb{E}\left[\ln κ_t \right]$ and $σ_κ^2$ are respectively the mean and variance of $\ln κ_t$. As the system dimension $N$ grows, $κ$ typically increases proportionally, making non-normal amplification the dominant source of scale-free behavior. We illustrate this mechanism in polymer stretching in turbulent flows, where intermittent extensions arise from eigenvector amplification of velocity gradients.

nlin.CD↗

arXiv2025

Life as Non-Normal Chemical Accelerator

Life is commonly described as a self-organized, far-from-equilibrium process that maintains internal order by consuming free energy and exporting entropy. This thermodynamic view underlies diverse theoretical frameworks -- from autopoiesis and relational biology to autocatalytic sets and hypercycles -- yet dissipation is typically treated as a necessary consequence of living organization rather than as a property shaped by its internal dynamics. Here, through explicit calculations of biotic chemical reactions and empirical documentation, we show that living systems universally function as non-normal chemical accelerators. Their elevated entropy production emerges from the asymmetric and hierarchical architecture of their biochemical networks. We introduce a general conceptual and mathematical framework in which biological structuration is understood as a dynamical property. Characterized by asymmetric couplings and transient amplification despite asymptotic stability, non-normal dynamics are shown to naturally generate kinetic acceleration, enhanced energy throughput, and phase-transition-like reorganizations without classical bifurcations. In this view, biological organization is not merely compatible with dissipation but actively structured to amplify free-energy flux and entropy export. We support this perspective with empirical and theoretical evidence that biochemical networks generically give rise to intrinsically non-normal operators through non-reciprocal interactions and hierarchical design. This framework yields testable predictions for dissipation rates, robustness, and evolutionary design principles, and suggests a kinetic principle of evolution in which living systems preferentially construct increasingly non-normal reaction architectures, driving sustained amplification of chemical fluxes and entropy flow.

physics.bio-ph↗

arXiv2025

Non-Normal Eigenvector Amplification in Multi-Dimensional Kesten Processes

Heavy-tailed fluctuations and power law statistics pervade physics, finance, and economics, yet their origin is often ascribed to systems poised near criticality. Here we show that such behavior can emerge far from instability through a universal mechanism of non-normal eigenvector amplification in multidimensional Kesten processes $x_{t+1}=A_t x_t+η_t$, where $A_t$ are random interaction matrices and $η_t$ represents external inputs, capturing the evolving interdependence among $N$ coupled components. Even when each random multiplicative matrix is spectrally stable, non-orthogonal eigenvectors generate transient growth that renormalizes the Lyapunov exponent and lowers the tail exponent, producing stationary power laws without eigenvalues crossing the stability boundary. We derive explicit relations linking the Lyapunov exponent and the tail index to the statistics of the condition number, $γ\!\sim\!γ_0+\lnκ$ and $α\!\sim\!-2γ/σ_κ^2$, confirmed by numerical simulations. This framework offers a unifying geometric perspective that help interpret diverse phenomena, including polymer stretching in turbulence, magnetic field amplification in dynamos, volatility clustering and wealth inequality in financial systems. Non-normal interactions provide a collective route to scale-free behavior in globally stable systems, defining a new universality class where multiplicative feedback and transient amplification generate critical-like statistics without spectral criticality.

cond-mat.stat-mech↗

arXiv2025

Phase Transitions Without Instability: A Universal Mechanism from Non-Normal Dynamics

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.

cond-mat.stat-mech↗

arXiv2025

Illusions of Criticality: Crises Without Tipping Points

Abrupt shifts in ecosystems, brains, markets, and climate are often diagnosed as signs of approaching a tipping point, i.e. a critical bifurcation where stability is lost. Here we reveal a broader and more deceptive mechanism: pseudo-bifurcations. In stochastic non-normal systems, asymmetric interactions produce transient episodes of apparent instability despite long-term stability. We show analytically, numerically, and with empirical evidence from brain dynamics during epileptic seizures that pseudo-bifurcations reproduce the full set of early-warning signals usually taken as proof of proximity to tipping points, including critical slowing down, increased variance, and dimensional collapse. Crucially, these false alarms can occur well before any true bifurcation, systematically biasing crisis diagnosis. This discovery reframes how abrupt transitions are interpreted across disciplines: what has long been attributed to ``criticality'' may instead reflect the hidden geometry of non-normal dynamics. By uncovering this illusion of criticality, we call for a fundamental reassessment of how crises are identified, predicted, and managed in natural, social, and technological systems.

nlin.CD↗

arXiv2025

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

We identify a new universality class of phase transitions that emerges in non-normal systems, extending the classical framework beyond eigenvalue instabilities. Unlike 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, acting as an emergent temperature. Once the non-normality index $κ$ exceeds a critical threshold $κ_c$--the balance between restoring curvature and non-normal shear--stable equilibria lose practical relevance: fluctuations are amplified enough to induce escapes even though spectral stability is preserved. This mechanism defines 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. In biology, we demonstrate that DNA methylation, a cornerstone of epigenetic regulation, operates in this regime: by extending a bistable CpG dyad model to include non-normality, we reconcile long-term epigenetic memory with rapid stochastic switching observed on minute timescales. More broadly, the same mechanism underlies abrupt tipping in climate, ecological collapse, financial crises, and engineered network failures. By showing that phase transitions can arise from non-normal amplification rather than spectral instabilities, our work provides a predictive framework for sudden transitions across disciplines.

cond-mat.stat-mech↗

arXiv2025

Unifying Framework for Amplification Mechanisms: Criticality, Resonance and Non-Normality

We bring together three key amplification mechanisms in linear dynamical systems: spectral criticality, resonance, and non-normality. We present a unified linear framework that both distinguishes and quantitatively links these effects through two fundamental parameters: (i) the spectral distance to a conventional bifurcation or to a resonance and (ii) a non-normal index $K$ (or condition number $κ$) that measures the obliqueness of the eigenvectors. Closed-form expressions for the system's response in the form of the variance $v_\infty$ of the observable responding to both Gaussian noise and periodic forcing reveal a general amplification law $v_\infty = v_0 \left( 1 + \mathcal{G}(K) \right)$ with non-normal gain $\mathcal{G}(K) \propto K^2$ represented in universal phase diagrams. By reanalyzing a model of remote earthquake triggering based on breaking of Hamiltonian symmetry, we illustrate how our two-parameter framework significantly expands both the range of conditions under which amplification can occur and the magnitude of the resulting response, revealing a broad pseudo-critical regime associated with large $κ$ that previous single-parameter approaches overlooked. Similarly, in the Non-Hermitian extensions of quantum optics provided by Forward Four-Wave Mixing (FFWM) experiments, we show the presence of a counterintuitive gain-from-loss effect that directly manifests non-normal amplification in a propagating-wave setting. This predicts the possibility to engineer transient optical energy amplification without the need for true lasing or exact $\mathcal{PT}$-symmetry breaking. Our framework applies to many other physical, natural and social systems and offers new diagnostic tools to distinguish true critical behavior from transient amplification driven by non-normality.

nlin.CD↗