Nonlinear Quantum Intelligence Framework for Coevolutionary Scaling and Multifractality across Far-from-Equilibrium Earth System Dynamics and Multi-Hazards

Scaling dynamics, intermittency, and multifractality in complex natural systems remain a central challenge across physics, geoscience, and hazard science. Earth system dynamics exhibit strongly non-equilibrium behaviour, long-range codependences, irreversible energy and information flows, and multiscale spatiotemporal coevolution, including dynamically adaptive interactions across spatial, temporal, and organizational domains.

The present contribution introduces and explores our latest advances in information physical intelligence for addressing these challenges, further building from our recent developments in non-ergodic nonlinear open quantum systems, where systems non-recurrently exchange energy, matter and information with structural-functional coevolutionary environments. In this setting, entropy production, information backflow, coherence, and decoherence are anchored on cross-scaling organizing principles spanning from microphysical foundations to emergent macrophysical behaviour, dynamically traceable and solvable through our novel nonlinear quantum developments.

Our new nonlinear quantum intelligence framework is then equipped with our latest non-ergodic information physical categorical algebraic infrastructure and associated mathematical physics apparatus, underlying the natural emergence of coevolutionary cyber-physical cognitive systems. These are then tested in controlled synthetic and free-range natural experiments, in order to provide operational insights on their ability to autonomously unfold and shape structural-functional emergence of complex system dynamics including scaling mechanisms in nonlinear non-ergodic multiscale stochastic-dynamical systems exhibiting scale-dependent entropy production rates, anomalous dissipation, and multidirectional cascades, on an inherent information physical thermodynamic process for far-from-equilibrium coevolutionary multifractal scaling.

One of the advances herein brings out a novel coevolutionary far-from-equilibrium thermodynamic renormalization of non-ergodic open quantum dynamics, where delocalization and aggregation across scales induces effective non-Markovianity, memory kernels, and scale-dependent effective energetics. These features are then shown to map naturally onto formal multifractal signatures observed in turbulence, precipitation fields, seismicity, geomagnetic activity, and climate variability.

Within this framework, coevolutionary multifractality emerges as a signature of competing irreversible processes operating across coevolving subsystems, rather than as a purely statistical or kinematic geometric construct. The corresponding generalization of information-theoretic quantities, including quantum relative entropy, Fisher information, and entropy production fluctuations, provide structural descriptors of scaling regimes and phase-transition-like behaviour in Earth system dynamics.

From theory to operation, we demonstrate how these information physical foundations and developments enable cross-domain integration in multiscale, multidomain Earth system modeling and more broadly across our System-of-Systems for Multi-Hazard Risk Intelligence Networks (SoS4MHRIN) platform. In doing so, we unveil and elicit coevolutionary scaling mechanisms linking traditional quantum information to meso and macroscale complexity, and harness elusive predictability pertaining to far-from-equilibrium non-ergodic non-recurrent emergence, intermittence and persistence of structural-functional changes, critical transitions and extreme events, along with their interactions and impacts.

This is particularly relevant for compound, cascading, coevolutionary and synergistic multi-hazards, where earthquakes, volcanic eruptions, extreme weather, floods, wildfires, and landslides interact across scales and domains. Far-from-equilibrium entropy production and information physical flows act as early warning indicators and organizing variables for multi-hazard interactions and tipping dynamics.

By synergistically articulating non-ergodic information physics, nonlinear open quantum thermodynamics, scaling theory, and Earth system science, this work provides a physically grounded, scale-aware framework for better understanding and operating on complexity, predictability, and resilience in the Earth system under ongoing structural-functional multiscale coevolution.