We investigate how the nature, rather than just the strength, of coupling controls synchronization between self-sustained oscillators. By parametrizing the coupling between two van der Pol oscillators as $J{e}^{i\theta }$ at fixed overall strength $J$, we continuously tune from purely coherent ($\theta =0$) to purely dissipative ($\theta =\pi /2$) coupling. We find that dissipative coupling yields a substantially wider frequency-locking window than coherent coupling in both the weakly and strongly nonlinear regimes. In the weakly nonlinear regime, hybrid coherent-dissipative coupling unlocks an unbalanced synchronization (U-sync) regime with strongly asymmetric amplitudes, extending the locking window far beyond the conventional balanced-synchronization (B-sync) boundary. A systematic bifurcation analysis, supported by Matcont numerical continuation, identifies the synchronization boundaries as saddle-node bifurcations in the strongly nonlinear regime for all coupling angles, and as saddle-node (for purely dissipative coupling) or Hopf (otherwise) bifurcations in the weakly nonlinear regime. We confirm the predicted synchronization enhancement and both the B-sync and U-sync regimes experimentally using coupled self-sustained LC resonators with tunable coherent-dissipative coupling. Our results establish the coupling angle as a practical tuning knob for synchronization engineering and suggest design principles, based on the dissipative-to-coherent ratio of each pairwise link, for controlling synchronization robustness and amplitude distributions in oscillator networks.

We numerically studied active Brownian particles with attractive interactions. Contrary to our intuition, the attractive force between particles disrupts the formation of a single cluster observed in motility-induced phase separation, giving rise to a multicluster state. This transition is driven by a decrease in effective motility caused by the persistent cohesion between particles. We also found that the self-propulsion directions spontaneously align within each cluster in the multicluster state, despite the absence of explicit alignment interactions. This study revealed the intricate role of attractive interactions in the aggregation of motile systems.

When a granular material composed of elongated grains is sheared in a split-bottom shear cell, a pressure difference develops within the material. This pressure difference depends on the interparticle friction, which affects shear localization and particle alignment. At high friction, alignment is confined to a narrow shear band, leading to localized increases in packing density and pressure. At low friction, the particles align over a wider region, leading to a nearly uniform packing density and pressure throughout the material. In contrast, assemblies of spherical particles exhibit a uniform packing density and pressure, independent of the friction coefficient. Elongated grains behave similarly to the Weissenberg effect in non-Newtonian fluids, where the normal stress differences are associated with pressure variations, in contrast to the nearly uniform pressure field observed for spherical particles.

Microcanonical inflection-point analysis (MIPA) identifies third-order transitions from derivatives of the microcanonical entropy, yet this classification has lacked a direct canonical counterpart accessible from measurable fluctuations without reconstructing the density of states. Here we establish such a fluctuation-based canonical framework for MIPA-type third-order transitions using a cumulant-ratio diagnostic. Its signed extrema identify the corresponding canonical signatures and, in the single-saddle regime, are asymptotically linked to microcanonical classification. Because the diagnostic depends only on energy cumulants, it avoids explicit density-of-states reconstruction and is accessible from measurable fluctuations. Physically, it is a canonical fluctuation-asymmetry observable whose extrema mark high- and low-energy tail reorganizations of the canonical energy distribution. Benchmarks on Ising, Potts, and nonreciprocal Ising models support the framework.

Lee-Yang theory offers a unifying framework for understanding classical phase transitions and dynamical quantum phase transitions through the analysis of partition functions and Loschmidt echoes. Recently, this framework was extended to characterize quantum phase transitions of quantum Ising models by introducing the concepts of non-Hermitian parity-symmetry breaking and fidelity zeros. Here, we generalize the theory by studying a broad class of quantum models, including the XY, the XXZ, the XYZ, and the ${\mathbb{Z}}_p$ clock models in one dimension, subject to a complex magnetic field. For the XY, XXZ, and XYZ models, we find that the complex field breaks parity symmetry and induces oscillations of the ground state between the two parity sectors, giving rise to fidelity zeros within the ordered phases. For the ${\mathbb{Z}}_3$ clock model, the complex field splits the real part of the ground-state energy between the neutral sector $(q=0)$ and the charged sectors $(q=1,2)$, while preserving the degeneracy within the charged sector. Fidelity zeros arise only after projecting out one of the charged sectors. For the ${\mathbb{Z}}_4$ and ${\mathbb{Z}}_5$ clock models, the ground states are instead projected to oscillate between the neutral sector ($q=0$) and the charged sectors $q=2$ and $q=1$, respectively, giving rise to fidelity zeros. Finite-size scaling of these zeros yields critical exponents in full agreement with analytical predictions, demonstrating that this approach is applicable not only to the Ising model with ${\mathbb{Z}}_2$ symmetry, but also to more general Heisenberg-type models and systems with higher discrete symmetries.

We investigate the fragment-size distribution produced by a hierarchical generalization of Gilbert's two-dimensional random tessellation. The study is motivated by experimental data on fragmentation processes, obtained by Kooij and coworkers [S. Kooij et al., Nat. Commun. 12, 2521 (2021)], where the reasons for which experimental data can exhibit a scale-free behavior resulting in power distributions (for unstressed materials) or exponential distribution with a characteristic length scale (for stressed material) are analyzed in great detail. We study two tessellation models, Dichotomous Gilbert (DG) and Hierarchical Gilbert (HG), which implement different hierarchical splitting rules. Both models generate fragment-area distributions well described by a truncated power-law function, namely a power multiplied by a stretched exponential function or generalized Gamma function. The Gilbert's classic tessellation model gives rise, on the contrary, to a simple exponential distribution. To further characterize the underling complexity, we perform a multifractal analysis of the fragment areas. The results demonstrate that Gilbert's hierarchical fragmentation reveals a multifractal scaling.

Inspired by the phenomenologies of an open totally asymmetric simple exclusion process (TASEP) with Langmuir kinetics (Lk) and finite resources that dynamically control the entry and exit rates of the TASEP lane, we study the stationary densities and phase transitions in a TASEP with Lk connected to both ends of a particle reservoir. The resulting phase diagrams in the plane of the control parameters are significantly different from those in an open TASEP with Lk. In particular, some of the phases admissible in the open TASEP with Lk model are no longer possible. Intriguingly, our model is closely related to a TASEP coupled with Lk on a ring with a point defect, but admits more phases than the latter. Phenomenological implications of our results are discussed.

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.