First-passage time (FPT) is an important quantity characterizing stochastic processes, but its distribution is often difficult to compute. Here we develop an efficient approach to compute the FPT distribution for a general stochastic process modeled by a master equation or a Fokker-Planck equation. The core of this approach is a differential equation for a moment-generating function, which can be solved by expanding this function in some form. As a result, an approximate FPT distribution can be found up to any pregiven accuracy and even the exact FPT distributions can be derived in some special cases. We validate our proposed approach by analyzing several examples and discuss convergence and renormalization issues of the approach. Our approach has broad applications in various disciplines underlying the FPT issues.

We formulate a nonequilibrium gauge theory for active many-body steady states and derive rigorous, data-accessible lower bounds on dissipation. The setting is an overdamped translational sector on an extended one-particle state space, where internal variables may encode orientations, species, or other hidden degrees of freedom. We show that broken detailed balance enters the response to spatial shift generators through a current-induced gauge anomaly, while the generator algebra itself remains unchanged. At the one-body level, this yields a localized hyperforce balance and an exact projection theorem that decomposes the translational entropy production into visible and hidden non-negative parts at arbitrary retained one-particle resolution. The resulting bounds depend only on equal-time one-body densities, currents, and force densities, and therefore avoid time reversal and full trajectory inference. For active Brownian particles, we show that the physically relevant retained variables are position and orientation, not position alone: position-only fields can be entirely blind to irreversibility even in mechanically static steady states. Brownian-dynamics simulations of ideal, homogeneous interacting, and slit-confined active Brownian particles confirm the theoretical predictions. Our results connect gauge response, coarse graining, and measurable irreversibility in active matter.

Multilevel sociality, in which large communities emerge from interconnected subgroups, is a hallmark of primate societies and a central focus of the social brain hypothesis. We investigate whether such organizational forms can, on their own, foster cooperation when defection is individually optimal and the population is initially dominated by defectors. Using the spatial Prisoner's Dilemma on community-structured networks, we derive analytical conditions under which cooperation, once present, spreads contagiously across communities without altering payoffs or invoking external enforcement. The mechanism arises from intercommunity interactions, which facilitate cross-community transmission and buffer against isolated defections. We further show that larger groups within overlapping communities expand the parameter region supporting propagation. The effect extends to Stag Hunt and Snowdrift games, indicating robustness across incentive structures. While our analytical results rely on deterministic unconditional imitation, extensive numerical simulations demonstrate that the spread of cooperation is robust to stochastic perturbations, revealing that behavioral inertia can counterintuitively stabilize cooperation within small community structures. We also evaluate our framework on a real-world coauthorship network, showing that the emergence of contagious cooperation in community-structured networks is not only present in theoretical networks but also in empirical architectures. Our contributions are to establish sufficient conditions for contagious cooperation within the considered class of networks and dynamics, quantify how overlap and group size determine the propagation threshold, and establish community architecture as a principal determinant of cooperative dynamics in social, economic, and biological systems, showing that, in the right network architecture, cooperation can arise and persist without external support.

Physiological systems exhibit deterministic behavior influenced by dynamic stochasticity, where informative random components play a crucial role in complex system interactions. Fully characterizing multivariate random components is challenging when the underlying deterministic dynamics are unknown. We propose a framework for estimating stochastic coupling in unknown deterministic systems influenced by dynamic noise. Building on a multivariate extension of approximate entropy (MApEn), the proposed framework exploits the divergence of this metric in the presence of dynamical noise. After establishing the theoretical basis and validity of the method, which can accommodate arbitrary multivariate noise probability distributions, we show that, in the case of bivariate white Gaussian noise, the framework enables closed-form estimation of the noise covariance matrix without requiring prior knowledge of the underlying deterministic functions. To this end, we introduce an iterative algorithm to estimate the covariance matrix coefficients. The algorithm identifies the parameter values that rescale the differential behavior of multivariate MApEn along a target curve. We validate the framework using both synthetic datasets and real physiological recordings. The analysis reveals important insights into brain-heart interactions, particularly the modulation of stochastic coupling across sleep-stage transitions through low-frequency oscillatory activity. Our results indicate that conscious wakefulness is characterized by stronger stochastic coupling, which progressively decreases during the transition to sleep. This framework opens new avenues for investigating stochastic physiological dynamics and their associated networks, with potential applications across a wide range of scientific disciplines.

First-passage-times are often the most relevant aspect of a complex Markovian network because they signify when information processing has resulted in a definite decision. Previous studies have shown that for kinetic proofreading networks in the limit of large network size the first-passage-time distribution converges either to a δ or to an exponential distribution. Remarkably, these two forms correspond to the two extreme distributions of minimal and maximal entropy for a fixed mean, respectively. Here we build on the connection between first-passage-times and graph theory to show that these two limits are not model-specific, but arise generically in Markovian networks from the distribution of the eigenvalues of the generator matrix. A deterministic peak emerges when infinitely many eigenvalues contribute, while the exponential limit arises from a single dominant eigenvalue. We also show that the exponential limit emerges robustly for reversible networks when the mean first-passage-time from the initial state to the target state becomes much larger than the mean first-passage-time in the reverse direction. In contrast, the deterministic limit is not obtained from a simple reversal of this condition, but follows from a nonvanishing conductance or a mean-residual lifetime of the process which becomes small compared to the mean first-passage-time in the long-time limit. This reveals a fundamental asymmetry between the two regimes. Our theoretical analysis is illustrated and validated by computer simulations of one-step master equations and random networks.

Bayesian spectral deconvolution provides a data-driven framework for mathematical model selection and parameter estimation from spectral data. Although highly versatile, its computational cost grows with the number of model parameters, data points, and candidate models, often rendering practical applications infeasible. We propose a GPU-accelerated approach in which a sequential Monte Carlo sampler (SMCS) is executed in parallel on a GPU to perform Bayesian model selection for the number of spectral peaks and Bayesian estimation of peak-function parameters. Numerical experiments demonstrate that the GPU-parallelized SMCS reaches the free-energy accuracy of an optimized CPU-parallelized replica exchange Monte Carlo (REMC) baseline up to approximately $37\times$ faster—with smaller gains, down to near parity, in the least favorable settings—and is faster than GPU-parallelized REMC in many of the tested cases. The method is validated on artificial data designed to emulate x-ray photoelectron spectroscopy and x-ray diffraction measurements, as well as on real experimental spectra. As measurement techniques such as microscopic spectroscopy and in situ methods continue to drive rapid growth in the volume of spectral data, the proposed approach offers a practical computational foundation for advanced analysis of each individual dataset.

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.