The transition from subdiffusion to normal diffusion is ubiquitous in complex systems, with experimentally observed transition times spanning several orders of magnitude. However, a scaling law governing the transition time remains unclear. To address this issue, we introduce an analytically tractable model that exhibits a unified subdiffusive-to-diffusive transition, in which tracer particles diffuse in a heterogeneous landscape under Ornstein-Uhlenbeck driving. From this model, we find a scaling law for the transition time, $t_{\text{T}}\simeq f(\alpha ,K_0,L)D_{\text{e}}{(D,\tau )}^{\frac{1}{\alpha -1}}$. Here, the prefactor $f$ depends on the intrinsic system parameters (the subdiffusion exponent $\alpha$, diffusion coefficient $K_0$, and characteristic length $L$), while $D_{\text{e}}$ denotes an effective driving strength determined by the driving correlation strength $D$ and correlation time $\tau$. Experimental data from diverse complex systems support this scaling law, providing a predictive framework for subdiffusive-to-diffusive transition times across a wide range of scales.

We present a hydrodynamic theory of anisotropic and inversion-asymmetric moving active permeable fluid membranes. These are described by an anisotropic Kardar-Parisi-Zhang equation. Depending upon the anisotropy parameters, the membrane is either effectively isotropic and algebraically rough with translational short, but orientational long-range order, or unstable, suggestive of membrane crumpling.

In this work, we investigate the autonomous charging process of a quantum battery coupled to a structured reservoir composed of two qubits, each locally coupled to its own bosonic thermal bath. Moreover, the reservoir interacts with a charger–battery architecture through three configurations: (I) direct coupling between reservoir qubits and battery; (II) collective coupling among the reservoir qubits, charger, and battery; and (III) a collective coupling between the reservoir qubits and charger together with a local charger–battery interaction. However, by using incoherent and coherent initial states, we analyze the stored energy, ergotropy, and charging power of the battery, and derive upper and lower bounds on the extractable work in terms of the free energy of coherence and the correlations exchanged between subsystems. Our results show that global and local coherences, as well as total correlations, act as quantum resources that enhance autonomous charging. Additionally, we demonstrate that the free energy stored in the quantum battery splits into contributions from coherence and correlations, providing numerical evidence that supports the derived ergotropy bounds. Importantly, this work highlights how structured reservoirs enable autonomous and resource-enhanced quantum battery operation.

The Kuramoto model provides a paradigmatic framework for studying the synchronization of interacting oscillators, and has been generalized to arbitrary dimensions to describe swarms, flocks, and multidimensional opinion dynamics. Yet, existing formulations neglect inertia, a key mechanism known to enhance information propagation and collective responsiveness. Here, we introduce and analyze an inertial Kuramoto model in arbitrary dimensions. We show that inertia fundamentally alters the nature of the synchronization transition, inducing a crossover from continuous to discontinuous behavior, with the onset of hysteresis depending explicitly on both inertia and dimensionality parity. Our analytical theory is supported by extensive numerical simulations. These results establish inertia as a crucial ingredient of high-dimensional collective dynamics and reveal a universal structure in synchronization phenomena.

Viscous fingering instabilities reduce the efficiency of immiscible displacement processes in radial Hele-Shaw flows. Time-dependent injection protocols provide a practical means of mitigating these instabilities, and previous studies have shown that linearly increasing injection rates can strongly suppress finger growth when both the total injected volume and the total injection time are fixed. Here we reformulate this optimization problem by prescribing a fixed radial distance and terminating the injection when the most advanced finger reaches it, a condition inspired by breakthrough in displacement processes. We then introduce a linear-plateau injection protocol, in which the injection rate increases linearly up to a switching time $t_m$ and subsequently remains constant at a maximum value $Q_{max}$, reflecting the finite capacity of pumping systems. Using linear stability analysis and fully nonlinear boundary-integral simulations, we show that this linear-plateau protocol stabilizes the interface and increases the swept area, even though the interface evolves for a longer time than in a reference protocol with constant injection $Q_{max}$ throughout the process. Finally, we introduce a profitlike function that balances the gain in swept area against the cost associated with longer injection times. This formulation is motivated by potential applications of the proposed control strategy to displacement processes in porous media, such as enhanced oil recovery and ${\mathrm{CO}}_2$ injection for geological storage. Optimization of this function identifies the switching time that provides the best trade-off between displacement efficiency and injection duration. These results establish a Hele-Shaw framework for optimizing injection protocols under a swept-area–injection-time trade-off while accounting for a maximum allowable injection rate.

Using fully kinetic three-dimensional particle-in-cell (EPOCH) simulations, we investigate resonant planar nanoantenna configurations supporting localized surface plasmon resonances in hydrogen-rich media under irradiation by 795 nm femtosecond laser pulses with intensities of ${10}^{17}–{10}^{19} \mathrm{W}/\mathrm{c}{\mathrm{m}}^2$. The study compares higher-order resonant dipoles with coupled planar nanoantenna configurations, including double-dipole and double-Yagi structures. We show that extended resonant nanoantennas support higher-order longitudinal modes with multiple field hot spots, markedly longer plasmon lifetimes, and enhanced absorptivity compared with fundamental λ/2 dipoles. Close-pair 3/2 λ double dipoles sustain resonance for almost the entire pulse duration, yielding proton energies of approximately 0.28 MeV. Among the planar configurations investigated, double-Yagi nanoantennas provide the strongest near-field localization and the highest proton energies, exceeding 0.5 MeV. Coupled nanoantenna configurations sustain plasmon resonances for a substantially larger fraction of the laser pulse, even under strong irradiation, increasing proton energies by approximately two to three orders of magnitude compared with undoped media. At laser intensities above approximately ${10}^{18} \mathrm{W}/\mathrm{c}{\mathrm{m}}^2$, rapid electron depletion suppresses the plasmon resonance and limits further ion-energy gain, highlighting the importance of plasmon longevity. These results identify coupled planar resonant nanoantenna configurations, particularly double-Yagi structures, as efficient platforms for enhanced nonthermal laser energy coupling and localized proton acceleration in dense media, with potential relevance for future fusion-oriented target concepts.

The problem of reconstructing a quantum channel from a sample of classical data is considered. When the total fidelity can be represented as a ratio of two quadratic forms (e.g., in the case of mapping a mixed state to a pure state, projective operators, unitary learning, and others), semidefinite programming (sdp) can be applied to solve the fidelity optimization problem with respect to the Choi matrix. A remarkable feature of sdp is that the optimization is convex, which allows the problem to be efficiently solved by a variety of numerical algorithms. We have tested several commercially available sdp solvers, all of which allowed for the reconstruction of quantum channels of different forms. A notable feature is that the Kraus rank of the obtained quantum channel typically comprises less than a few percent of its maximal possible value. This suggests that a relatively small Kraus rank quantum channel is typically sufficient to describe experimentally observed classical data. The theory was also applied to the problem of reconstructing projective operators from data. Finally, we discuss a classical computational model based on quantum channel transformation, performed and calculated on a classical computer, possibly hardware-optimized.

The emergence of heavy-tailed statistics in complex systems is conventionally attributed to nonlocal stochastic jumps or non-Markovian memory. Here, we present a one-dimensional random walk where power-law behaviors arise instead from a strictly local, discrete-time Markovian mechanism. The step length is governed by a deterministic function of the walker's position, establishing a positive feedback loop that induces strong effective correlations along the trajectories. Through analytical derivations in the continuum limit and extensive numerical simulations, we show that this rule yields a robust, non-Gaussian stationary state. The exact analytical solution is obtained in the closed form of a symmetric, Lorentz-like distribution ${\rho }_{\text{st}}\left(x\right)\propto {\left(\right|x|/l+r\mathrm{\Delta }x)}^{-2}$, confirming asymptotic power-law tails that decay as ${\left|x\right|}^{-2}$ over six decades. Furthermore, by employing the Onsager-Machlup path-integral formalism, we demonstrate that effective velocity and acceleration acquire physical meaning along the shortest fluctuation trajectories. Crucially, we find that a nonzero initial acceleration acts as the fundamental mechanism driving the walker away from the origin, ensuring both the emergence of scale-free statistics and the normalizability of the stationary distribution. This minimal pathway provides a microscopic foundation for the widespread $-2$ power law observed across multidisciplinary complex systems.

Remote synchronization (RS)—the emergence of phase coherence among nonadjacent peripheral nodes while remaining desynchronized from the mediating hub—is a fundamental mechanism for long-range coordination in complex networks. So far all studies have been focusing on only a single RS plateau generated by tuning intrinsic parameters such as coupling strength or time delay. Here we report an unobserved phenomenon: the coexistence of two distinct forms of RS in externally forced star networks. Using coupled Stuart-Landau oscillators, we show that a weak external forcing can induce an abrupt, explosive transition in which the leaf nodes synchronize at an intrinsic, network-selected frequency, yielding an explosive RS state (RS1) that is independent of the forcing frequency. As the forcing amplitude increases, the leaves undergo a second transition and become entrained by the external drive, producing a driven RS state (RS2). This double-RS structure occupies a well-defined region in the forcing-parameter space and depends sensitively on the spatial location of the stimulus. We further develop a simple theoretical framework that links explosive RS1 to a forcing-induced renormalization of the effective coupling and explains RS2 as a hub-assisted entrained RS regime. These results reveal two qualitatively different mechanisms of RS and suggest a mechanistic framework by which external stimuli can sculpt coherent interactions between distant brain areas.

High-dimensional chaotic dynamics can emerge in a large random recurrent neural network when the synaptic gain crosses a threshold. Recent works showed that the kinetic energy of neural activity links the chaotic dynamics and the supporting unstable fixed points (equilibria) in the phase space. Here, we investigate the kinetic-energy-centric properties of random recurrent neural networks by combining dynamical mean-field theory with extensive numerical simulations. We find that the average kinetic energy shifts continuously from zero to a positive value at the known critical value of coupling variance (synaptic gain) and exhibits a cubic scaling behavior near the critical point from above. This scaling behavior is supported by numerical simulations and provides a quantitative characterization of how fast the dynamics change during the onset of chaos as well as how far the chaotic dynamics are away from the unstable fixed points. The steady-state activity distribution is further calculated by the theory and compared with simulations on finite-size systems from the kinetic-energy optimization perspective as well. The activity distribution is also analyzed in a geometric angle, revealing that although the original chaotic dynamics and the gradient dynamics of the kinetic energy are arranged in a shell-like structure, they are well separated in the polar direction. The trajectory length on the chaotic manifold can be derived from the stationary kinetic energy, and the associated stationary behavior is analyzed as well.

Modern critical infrastructure networks optimize for maximum efficiency under stationary conditions, yet increasingly face nonstationary physical environments. We demonstrate through large-scale Monte Carlo simulation (1.55 million cascade events across five network scales) that efficiency-driven optimization drives supply networks toward a complex, two-stage phase transition. By coupling a spatially correlated stress model with topological simulation on Barabási-Albert scale-free networks, we identify two distinct critical thresholds: a continuous onset near ${\eta }_{\mathrm{onset}}\approx 0.79$ marking the emergence of significant cascades, and a catastrophic threshold ${\eta }_{\mathrm{sys}}\approx 0.97$ marking the discontinuous onset of systemic “dragon king” events. Between these thresholds lies a “deceptive safety zone” where operators observe frequent but contained failures, potentially normalizing risk while remaining unaware of proximity to total collapse. Finite-size scaling across $N\in \{{10}^3,2.5\times {10}^3,5\times {10}^3,{10}^4,2.5\times {10}^4\}$ shows the catastrophic threshold is essentially size independent (varying by $\approx 0.004$ across a $25\times$ range in $N$) while the onset converges as $N^{-1/2}$ to ${\eta }_{\mathrm{onset}}\left(\infty \right)=0.786\pm 0.002$, characteristic of a continuous transition. Pilot simulations on Watts-Strogatz and Erdős-Rényi topologies demonstrate that the dual-threshold gap persists universally, with threshold positions scaling monotonically with degree heterogeneity. We validate the framework against five historical infrastructure failures, demonstrating that recoverable events align with the robust regime while catastrophic collapses cluster near ${\eta }_{\mathrm{sys}}$. Model comparison ($\mathrm{\Delta }\mathrm{AIC}=7057$) decisively favors a bimodal dragon king distribution over a unimodal alternative at high efficiency.

Large chemical networks appear in various branches of chemistry and biology, in particular, cellular metabolism and prebiotic chemistry. Detailed simulations of such networks are difficult, or even impossible for lack of kinetic data. Various strategies have been developed to produce synthetic random networks mimicking the large scale organizational properties of experimental chemical networks. These random networks are however mathematical artifacts, which fail to reflect the general reactivity structure of chemistry. We present here a class of random models of prebiotic (uncatalyzed) chemistry, based on context-independent rules, which is coherent with the general compositional logic of metabolism. The general organization of the random networks fits within the small-world paradigm. We get a phase diagram of the models through an approximate mapping to a solvable tree growth model. Our predictions go beyond a purely abstract connectivity analysis of the reaction graph by studying the diversity of chemical mechanisms, and singling out evolutionary patterns, such as autocatalysis and multistationarity, paving the road to possible open-ended evolution.

Physical learning systems require a means to store information about the past. In the brain, information is thought to be stored in synaptic connections between neurons whose weights change in response to pre- and postsynaptic action potentials, or spikes, according to specific plasticity rules. To date, most models of synaptic plasticity are derived from in vitro studies in which spike times are under precise experimental control, but whether these models generalize to in vivo regimes of high spike time variability is not known. To shed light on this problem theoretically, here I estimate the mutual information between Poisson spike trains in a network of neurons and the synaptic weight updates they trigger via different plasticity rules. Although most synaptic plasticity models propose correlation- or coincidence-based rules based on the measurement of pre- and postsynaptic spike times, I show that such rules do not always maximize information storage. In the biologically important, energy-efficient operating regime of low firing rates and sparse plasticity, rules that simply count pre- and/or postsynaptic spikes in fact store more information per synapse than spike-timing-dependent rules that measure coincidence events. In such regimes, spikes are more common than coincidences hence better able to transmit information into synaptic weights. It may in turn be advantageous to encode information to be stored as spike counts, or time averages, rather than correlations. The theory suggests a normative account for recently discovered noncanonical hippocampal plasticity rules in vivo and predicts that spike-timing-dependent rules will be preferentially active in neural circuits operating at higher firing rates.

Reaction-diffusion processes play an important role in a variety of physical, chemical, and biological systems. Conventionally, the kinetics of these processes are described by the law of mass action. However, there are various cases where these equations are insufficient. A fundamental challenge lies in accurately accounting for the microscopic correlations that inevitably arise in bimolecular reactions. While approaches to describe microscopic correlations in many specific cases exist, no general theory for multistage reactions has been established. In this article, we apply the quantum field theory approach to derive kinetic equations for general multistage reactive systems termed complete modified encounter theory (CMET). CMET can be formulated as a set of coupled partial differential equations that can be easily integrated numerically, thereby serving as a versatile tool for investigating reaction-diffusion processes. Across multiple case studies, we demonstrated that CMET reproduces the kinetics predicted by many other theories within their respective scopes of applicability.

We study the effects of spatially inhomogeneous diffusion on the nonequilibrium phase transition in the unidimensional contact process. The directed-percolation critical point in the contact process is known to be stable against the addition of a spatially uniform diffusion term. Correspondingly, we find quenched randomness in the diffusion rates to be irrelevant by power counting in the field theory of the contact process. However, large-scale Monte Carlo simulations demonstrate that such diffusion disorder destabilizes the clean directed percolation critical point. Instead, the transition belongs to the same infinite-randomness universality class as the contact process with disorder in the infection or healing rates. To explain these results, we develop an effective model with an infinite diffusion rate; it shows that diffusion disorder generates an effective disorder in the healing rates. The same mechanism also appears in the field-theoretic description: Whereas diffusion disorder is irrelevant by power-counting, it generates standard random-mass disorder under renormalization. We discuss the validity of this mechanism at higher dimensions and for other absorbing state transitions and nonequilibrium phase transitions in general.

Feedback between game strategies and environmental states is common in human–natural systems. Existing studies have reported several interesting dynamical behaviors by studying the impact of environmental state on strategy selection. In this paper we construct a characterization of environmental states, assuming that environmental states are determined by local and global environmental states. Based on this we construct a spatial multiagent coevolutionary model to describe the strategy evolution of populations and analyze the model's dynamics by means of Monte Carlo simulations and mean-field approximation. We find that spatial structure can enhance the system stability, preventing the emergence of complex dynamical behaviors such as chaos. Furthermore, we incorporate a diffusion mechanism into the model. Results show that resource diffusion accelerates strategy switching by weakening differences in local environmental states. Numerical results further indicate that spatial structure significantly affects the system stability: the system self-organizes into stable spatial structures analogous to Turing patterns, thus enhancing the system stability. This study investigates the mechanisms by which environmental states and spatial structures influence system stability, offering new insights into understanding the coevolutionary dynamics in real-world systems.

Complex networked systems are prevalent in biology, engineering, and the social sciences, yet their high-dimensional, nonlinear dynamics pose major challenges for analysis and prediction. A mathematically rigorous route to simplification is to represent system behavior on a low-dimensional, smooth invariant manifold known as a spectral submanifold (SSM). Here we present a comprehensive SSM reduction framework and its globalized extension (gSSM) for dimensionality reduction in large-scale nonlinear networks. Our approach yields accurate global and node-level predictions across synthetic and real networks, including highly heterogeneous topologies and systems with higher-order interactions. Crucially, SSM is a robust tipping-point predictor: even at low truncation order [e.g., $O\left(2\right)$] it reliably identifies the onset of sustained activity, while higher orders and gSSM capture postonset amplitudes and saturation. Consistently, the reduction collapses the full network dynamics to a one-dimensional system, offering clarity and efficiency. Across all the realizations, SSM and gSSM consistently outperform classical spectral and mean-field methods in modeling critical transitions at both microscopic and macroscopic scales, establishing SSM-based reduction as a robust, interpretable tool for nonlinear networked systems with broad applicability to epidemiology, ecology, and engineered networks.