arXiv subjects

Didier Sornette

Publications and source records attributed to Didier Sornette.

At least 37 records · Page 2Linked to original sources

arXiv2026

Pregnancy as a dynamical paradox: robustness, control and birth onset

The timing of human labor is among the most critical determinants of neonatal survival, yet the mechanisms that govern the transition from uterine quiescence to coordinated contractions remain elusive. Here we present a dynamical-systems framework that models the pregnant uterus as a spatially extended network of electrically excitable cells regulated by sparse adaptive feedback mimicking hormonal and mechanical influences. This approach reveals how stability during gestation and sensitivity near parturition can be simultaneously maintained through the interplay of control, network structure, and noise. Our analysis shows that spontaneous contractions such as Braxton-Hicks and Alvarez waves are not epiphenomena, but functional components that reduce control effort and preserve responsiveness. Moreover, we identify preterm labor as a boundary-crossing phenomenon arising when control fails to correctly interpret early-warning signals. These results establish a unifying mechanistic theory for labor onset, yield testable predictions, and suggest new therapeutic strategies to mitigate preterm birth risk.

physics.bio-ph↗

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

Social feedback amplifies emotional language in online video live chats

A growing share of human interactions now occurs online, where the expression and perception of emotions are often amplified and distorted. Yet, the interplay between different emotions and the extent to which they are driven by external stimuli or social feedback remains poorly understood. We calibrate a multivariate Hawkes self-exciting point process to model the temporal expression of six basic emotions in YouTube Live chats. This framework captures both temporal and cross-emotional dependencies while allowing us to disentangle the influence of video content (exogenous) from peer interactions (endogenous). We find that emotional expressions are up to four times more strongly driven by peer interaction than by video content. Positivity is more contagious, spreading three times more readily, whereas negativity is more memorable, lingering nearly twice as long. Moreover, we observe asymmetric cross-excitation, with negative emotions frequently triggering positive ones, a pattern consistent with trolling dynamics, but not the reverse. These findings highlight the central role of social interaction in shaping emotional dynamics online and the risks of emotional manipulation as human-chatbot interactions become increasingly realistic.

cs.SI↗

arXiv2025

Case Study of a 75-Year-Old Woman with Parkinson's Disease: Rehabilitation Trajectory with Logic Workout Training

We report the single-case trajectory of a 75-year-old retired occupational female therapist with idiopathic Parkinson's disease, Hoehn and Yahr stage 2 at diagnosis. Following progressive impairment despite standard care, she initiated training with Logic Workout (LW) in July 2025 under supervision. Within weeks, she reported meaningful improvements spanning motor function, posture, pain, fine motor skill, mood, sleep consolidation, and disappearing of fatigue. Although single cases cannot establish generalizable efficacy, systematic and chronological documentation can be valuable for hypothesis generation and feasibility assessment in real-world settings prior to controlled trials. We summarize the baseline condition and treatment history, describe the LW intervention, compile self-reported outcomes, and interpret the findings in light of the underlying Logic Workout hypothesis, before concluding with key caveats and perspectives for future research.

physics.soc-ph↗

arXiv2025

Biotic Control of Earth's Climate: An Ecohydrological Perspective on the Phanerozoic Temperature Record

We propose a unified framework linking silicate weathering feedbacks, ecohydrological optimality and vegetation-climate interactions to explain Earth's Global Average Temperature evolution over the Phanerozoic. The framework integrates two complementary processes: (i) solute-transport-limited weathering, which governs long-term carbon sequestration, and (ii) ecohydrological optimality, which constrains vegetation productivity through the balance between water availability and carbon uptake. Together, these processes establish two emergent climatic thresholds, around 15 °C and 33 °C, that define a stable corridor for the Earth system. Below 15 °C, declining evapotranspiration and rising albedo accelerate cooling; above 33 °C, heat and water stress suppress vegetation and limit further warming. Analysis of ten independent studies (2019-2024) confirms the recurrent appearance of these thresholds in both modern ecosystems and Phanerozoic temperature reconstructions. Major biological innovations, such as the colonization of land by plants, the rise of forests, and the emergence of $C_4$ photosynthesis, have reorganized these feedbacks, repeatedly shifting the planet between quasi-stable climate states. The resulting picture is one in which the biosphere acts as an active regulator of climate, modulating and at times overriding geochemical feedbacks. This framework unifies climate, tectonics, and life into a single ecohydrological system, offering a coherent explanation for the bounded variability of Earth's temperature across 500 million years and insight into its future resilience. This perspective challenges the view of life as a passive climate responder, positioning the biosphere as an active regulator. Understanding these self-stabilizing mechanisms offers critical insight into how Earth might respond, or fail to respond, to ongoing human-driven climate perturbations.

physics.geo-ph↗

arXiv2025

Mastering Uncertainty: From Understanding to Prediction

Uncertainty defines our age: it shapes climate, finance, technology, and society, yet remains profoundly misunderstood. We oscillate between the illusion of control and the paralysis of fatalism. This paper reframes uncertainty not as randomness but as ignorance: a product of poor models, institutional blindness, and cognitive bias. Drawing on insights from physics, complex systems, and decades of empirical research, I show that much of what appears unpredictable reveals structure near transitions, where feedbacks, critical thresholds, and early-warning signals emerge. Across domains from financial crises to industrial disasters, uncertainty is amplified less by nature than by human behavior and organizational failure. To master it, prediction must shift from prophecy to diagnosis, identifying precursors of instability rather than forecasting exact outcomes. I propose a framework of dynamic foresight grounded in adaptive leadership, transparent communication, and systemic learning. Mastering uncertainty thus means transforming fear into foresight and building institutions that navigate, rather than deny, the complexity of change.

physics.soc-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

Sensor optimization for urban wind estimation with cluster-based probabilistic framework

We propose a physics-informed machine-learned framework for sensor-based flow estimation for drone trajectories in complex urban terrain. The input is a rich set of flow simulations at many wind conditions. The outputs are velocity and uncertainty estimates for a target domain and subsequent sensor optimization for minimal uncertainty. The framework has three innovations compared to traditional flow estimators. First, the algorithm scales proportionally to the domain complexity, making it suitable for flows that are too complex for any monolithic reduced-order representation. Second, the framework extrapolates beyond the training data, e.g., smaller and larger wind velocities. Last, and perhaps most importantly, the sensor location is a free input, significantly extending the vast majority of the literature. The key enablers are (1) a Reynolds number-based scaling of the flow variables, (2) a physics-based domain decomposition, (3) a cluster-based flow representation for each subdomain, (4) an information entropy correlating the subdomains, and (5) a multi-variate probability function relating sensor input and targeted velocity estimates. This framework is demonstrated using drone flight paths through a three-building cluster as a simple example. We anticipate adaptations and applications for estimating complete cities and incorporating weather input.

cs.LG↗

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↗

arXiv2025

Emergence of Finite-Time Singularities from Accelerated Event Recurrence: Insights into the Mechanism of Catastrophic Failure

We develop a discrete-event modeling framework that captures the progression of geophysical systems toward catastrophic failure through sequences of distinct damage events. By representing system evolution as a succession of temporally accelerating and amplitude-varying events, the framework reveals how finite-time singularities, both logarithmic and power law types, naturally emerge from the interplay between shrinking interevent intervals and growing event magnitudes. This event-based perspective provides an intuitive physical understanding of rupture processes, highlighting how precursory signals such as accelerating strain rate, event frequency, and energy release can be traced back to simple underlying mechanisms. A mean-field formulation further links the observed power law exponents to the evolving stiffness of the system under constant or time-varying stress. Incorporating stochastic fluctuations, the model captures the inherent randomness of natural systems leading to the emergence of stochastic finite-time singular behavior. Altogether, this unified approach offers a simple conceptual and quantitative tool for interpreting the lead-up to failure in a wide range of geophysical settings.

physics.geo-ph↗

arXiv2025

Unifying the Gutenberg-Richter Law with Probabilistic Catalog Completeness

We propose a probabilistic approach to modeling catalog incompleteness through four candidate augmented Gutenberg-Richter (GR) laws, which incorporates incompleteness into the frequency-magnitude distribution (FMD) using two parameters, mc, the transition magnitude, and σc, which defines the transition range from incompleteness to completeness. The four GR models are tested on synthetic and empirical catalogs, using multiple performance evaluation metrics. The GR-AEReLU model, which allows for an asymmetry in the convergence to the pure linear GR law for m > mc relative to the censorship of earthquakes of sizes smaller than mc, is found to consistently outperform, providing more robust estimates of seismological parameters (e.g., b-value) that better reflect realistic physical conditions and observational characteristics. This augmented framework offers three main advantages: (1) unified modeling of incompleteness into the FMD, (2) parameters with clear physical and statistical meaning, and (3) the ability to capture nonlinear and asymmetric detection behaviors. Finally, our analysis reveals systematic regional variations in earthquake b-values that deviate significantly from the assumed universal value of 1.0, challenging a fundamental paradigm in seismology and demonstrating the need for region-specific values that reflect local tectonic conditions in seismic hazard assessments.

physics.geo-ph↗

arXiv2025

Harnessing the "Reactive Falling Effect" for rehabilitation and performance boosting

We present Logic Workout, a novel training method based on radical dynamic instability combining rolling, deformation and spring instability on small fitballs. By exploiting the "reactive falling effect", it re-engages innate balance mechanisms and forces real-time motor corrections, leading to better joint control, coordination, and movement precision. Preliminary results from a cohort of 18 participants show complete resolution of chronic pain, enhanced functional mobility, and surprising improvements in strength and performance -- challenging the belief that instability training impairs power output. We hypothesise that, by harnessing maximal instability, Logic Workout activates deep neuromuscular pathways and improve rehabilitation outcomes, training efficiency, and athletic performance.

physics.soc-ph↗

arXiv2025

Endo-exo classification of episodic rock creep in deep mines: Implications for forecasting catastrophic failure

Rock masses in deep underground environments under high in-situ stress often exhibit episodic creep behavior, driven by complex interactions between external perturbation and internal reorganization. The causes of these creep episodes and their link to potential catastrophic failure remain poorly understood. Here, we present a novel 'endo-exo' framework for analyzing episodic rock creep in deep underground mines, capturing the interplay between exogenous triggers (e.g., blasting and excavation) and endogenous processes (e.g., damage and healing within rock masses). The underlying physical mechanism involves cascades of locally triggered rock block movements due to fracturing and sliding. We identify four fundamental types of episodic dynamics, classified by the origin of disturbance (endogenous or exogenous) and the level of criticality (subcritical or critical). All four types exhibit power law relaxations with distinct exponents: 1+θ(exogenous subcritical), 1-θ(exogenous critical), 1-2θ(endogenous critical) and 0 (endogenous subcritical), all governed by a single parameter 0 < θ< 1. Our theoretical predictions are examined using the comprehensive dataset of a platinum mine in South Africa, where stopes display episodic closure behavior during successive mining operations. All creep episodes recorded can be accounted for in our classification with θ\approx 0.35\pm0.1, providing strong validation of our theory. This θvalue is interpreted in terms of a first-passage process driven by anomalous stress diffusion, represented by fractional Brownian motion or Lévy-type processes. Finally, we offer new insights into endo-exo interactions and the system's transition from episodic creep to catastrophic failure, with important implications for forecasting large-scale panel collapses.

physics.geo-ph↗

arXiv2025

Endo-exo framework for a unifying classification of episodic landslide movements

Landslides exhibit intermittent gravity-driven downslope movements developing over days to years before a possible major collapse, commonly boosted by external events like precipitations and earthquakes. The reasons behind these episodic movements and how they relate to the final instability remain poorly understood. Here, we develop a novel "endo-exo" theory to quantitatively diagnose landslide dynamics, capturing the interplay between exogenous stressors such as rainfall and endogenous damage/healing processes. We predict four distinct types of episodic landslide dynamics (endogenous/exogenous-subcritical/critical), characterized by power law relaxations with different exponents, all related to a single parameter \vartheta. These predictions are tested on the dataset of the Preonzo landslide, which exhibited multi-year episodic movements prior to a catastrophic collapse. All its sporadic activities can be accounted for within this classification with \vartheta \approx 0.45\pm0.1, providing strong support for our parsimonious theory. We find that the final collapse of this landslide is clearly preceded over 1-2 months by an increased frequency of medium/large velocities, signaling the transition into a catastrophic regime with amplifying positive feedbacks. Our research suggests that landslides may not permanently operate at a critical state, which has major implications for forecasting catastrophic failure events.

physics.geo-ph↗

arXiv2025

Log-Periodic Precursors to Volcanic Eruptions: Evidence from 34 Events

Forecasting volcanic eruptions remains a formidable challenge due to the inherent complexity and variability of volcanic processes. A key source of uncertainty arises from the sporadic nature of volcanic unrest, which is often characterised by intermittent phases of quiescent deceleration and sudden acceleration, rather than a consistent, predictable progression towards eruption. This seemingly erratic pattern complicates volcano forecasting as it challenges conventional time-to-failure models that often assume a simple smooth power law acceleration. We propose a log-periodic power law singularity model, which effectively captures the intermittent and non-monotonic rupture dynamics characteristic of reawakening volcanoes at the site scale. Mathematically, generalising the power law exponent by extending it from real to complex numbers, this model captures the partial break of continuous scale invariance to discrete scale invariance that is inherent to the intermittent dynamics of damage and rupture processes in heterogeneous crustal systems. By performing parametric and nonparametric tests on a large dataset of 34 historical eruptions worldwide, we present empirical evidence and theoretical arguments demonstrating the statistical significance of log-periodic oscillations decorating power law finite-time singularities during pre-eruptive volcanic unrest. Log-periodicity in volcanoes may originate from various mechanisms, including diffusion-dominated magma flow, magma-driven propagation of subparallel dykes, interaction between stress drop and stress corrosion, and/or interplay of inertia, damage, and healing within volcanic systems. Our results have important implications for volcano forecasting, because understanding and characterising log-periodicity could turn the intermittency of volcanic activity from a challenge into a valuable asset for improving predictions.

physics.geo-ph↗