The central limit theorem does not hold for strongly correlated stochastic variables, as is the case for statistical systems close to criticality. Recently, the calculation of the probability distribution function (PDF) of the magnetization mode has been performed with the functional renormalization group in the case of the three-dimensional Ising model [Balog et al., Phys. Rev. Lett. 129, 210602 (2022)]. It has been shown in that article that there exists an entire family of universal PDFs parameterized by $\zeta ={lim}_{L,{\xi }_{\infty }\to \infty }L/{\xi }_{\infty }$ which is the ratio of the system size $L$ to the bulk correlation length ${\xi }_{\infty }$ with both the thermodynamic limit and the critical limit being taken simultaneously. We show how these PDFs or, equivalently, the rate functions which are their logarithm, can be systematically computed perturbatively in the $\epsilon =4-d$ expansion. We determine the whole family of universal PDFs and show that they are in good qualitative agreement with Monte Carlo data. Finally, we conjecture on how to significantly improve the quantitative agreement between the one-loop and the numerical results.

We study the effects of stochastic resetting on the reallocating geometric Brownian motion (RGBM), an established model for resource redistribution relevant to systems such as population dynamics, evolutionary processes, economic activity, and even cosmology. The RGBM model is inherently nonstationary and non-ergodic, leading to complex resource redistribution dynamics. By introducing stochastic resetting, which periodically returns the system to a predetermined state, we examine how this mechanism modifies RGBM behavior. Our analysis uncovers distinct long-term regimes determined by the interplay between the resetting rate, the strength of resource redistribution, and standard geometric Brownian motion parameters: the drift and the noise amplitude. Notably, we identify a critical resetting rate beyond which the self-averaging time becomes effectively infinite. In this regime, the first two moments are stationary, indicating a stabilized distribution of an initially unstable, mean-repulsive process. We demonstrate that optimal resetting can effectively balance growth and redistribution, reducing inequality in the resource distribution. These findings help us understand better the management of resource dynamics in uncertain environments.

A new derivation of the generalized Langevin equation (GLE) of motion is presented that exactly describes the reduced dynamics of a particle system acted upon by a time-dependent force field with a generalized (velocity-dependent) potential of general form and arbitrarily far from equilibrium. The derivation is carried out using the Mori-Zwanzig formalism with the stationary Zwanzig projection operator, which is defined on the initial phase variables to exactly project the microscopic Hamiltonian equations of motion. The first major difference with the GLE for the systems perturbed by velocity-independent potentials is the presence of several types of memory functions that rely on the various correlations of projected (fluctuating) forces and velocities. The second difference is a nontrivial GLE dynamics for the coarse-grained positional coordinates, which arises due to the differences in the canonical and kinetic momenta. Similarities include: The projected force remains a two-time-scale process with scales due to the interparticle interactions and the time-dependence of the external forces; the memory functions and the projected forces are related via the explicit time-dependent fluctuation-dissipation relation of the second kind; and the dissipative memory terms are linear functionals of the gradients of the Boltzmann entropy of the irrelevant subsystem that agree with Onsager's phenomenological equations. The theory is applied to a particle-based coarse-graining (via clustering of the microscopic particles). The theoretical presentation is illustrated with an example of a system of charged particles coupled to an electromagnetic field. The GLEs and workflow presented here can be readily used as a starting point to rigorously formulate microscopically informed multiscale treatments (e.g., using dissipative particle dynamics) for a variety of phenomena in particle systems perturbed by velocity-dependent fields, such as the external Lorentz, centrifugal, or Coriolis forces and in nonequilibrium.

We study the probability distribution function (PDF) of the order parameter of the three-dimensional $O\left(N\right)$ model at criticality using the functional renormalization group. For this purpose, we generalize the method introduced by Balog et al. [Phys. Rev. Lett. 129, 210602 (2022)] to the $O\left(N\right)$ model. We study the large $N$ limit, as well as the cases $N=2$ and $N=3$ at the level of the local potential approximation (LPA), and compare our results to Monte Carlo simulations. We compute the entire family of universal scaling functions, obtained in the limit where the system size $L$ and the correlation length of the infinite system ${\xi }_{\infty }$ diverge, with the ratio $\zeta =L/{\xi }_{\infty }$ constant. We also generalize our results to the approach of criticality from the low-temperature phase where another infinite family of universal PDF exists. We find that the LPA describes very well the functional form of the family of PDFs, once we correct for a global amplitude of the (logarithm of the) PDF and of $\zeta$.

This article presents a new quantum PageRank algorithm on graphs using discrete-time open quantum walks. Google's PageRank is a widely used algorithm for ranking the web pages on the world wide web in classical computation. From a broader perspective, it is also a fundamental measure for quantifying the importance of vertices in a network. Similarly, the new quantum PageRank also serves to quantify the significance of a network's vertices. In this work, we extend the concept of discrete-time open quantum walk on arbitrary directed and undirected graphs by utilizing the Weyl operators as Kraus operators. This new model of quantum walk is useful for building up the quantum PageRank algorithm, discussed in this article. We compare the classical PageRank and the newly defined quantum PageRank for different types of complex networks, such as the scale-free network, Erdős-Rényi random network, Watts-Strogatz network, spatial network, Zachary Karate club network, GNC, GN, GNR networks, Barabási and Albert network, etc. In addition, we study the convergence of the quantum PageRank process and its dependency on the damping factor $\alpha$. We observe that this quantum PageRank procedure is faster than many other proposals reported in the literature.

Human interactions and mobility shape epidemic dynamics by facilitating disease outbreaks and their spatial spread across regions. Traditional models often isolate commuting and random mobility as separate behaviors, focusing either on short, recurrent trips or on random, exploratory movements. Here, we propose a unified formalism that allows a smooth transition between commuting and exploratory behavior based on travel and return probabilities. We derive an analytical expression for the epidemic threshold, revealing a nonmonotonic dependence on recurrence rates: while recurrence tends to lower the threshold by increasing agent concentration in high-contact hubs, it counterintuitively raises the invasion threshold in low-mobility scenarios, suggesting that allowing recurrence may foster local outbreaks while suppressing global epidemics. These results provide a comprehensive understanding of the interplay between human mobility patterns and epidemic spread, with implications for containment strategies in structured populations.

Progress in miniaturized technology allows us to control physical systems at nanoscale with remarkable precision. Experimental advancements have sparked interest in control problems in stochastic thermodynamics, typically concerning a time-dependent potential applied to a nanoparticle to reach a target stationary state in a given time with minimal energy cost. We study this problem for a particle subject to thermal fluctuations in a regime that takes into account the effects of inertia, and, building on the results of a previous work, we provide a numerical method to find optimal controls even for non-Gaussian initial and final conditions, corresponding to nonharmonic confinements. Although we focus on a regime where the driving time is long compared to the characteristic relaxation times of the dynamics, the control protocol and the time-dependent position distribution are qualitatively different from the corresponding overdamped limit: in particular, a symmetry of the boundary conditions, which is preserved in the absence of inertia, turns out to be broken in the underdamped regime. We also show that the momentum mean tends to a constant value along the trajectory, except close to the boundary, while the evolution of the position mean and of the second moments is highly nontrivial. Our results also support that the lower bound on the optimal entropy production computed from the overdamped case is tight in the adiabatic limit.

The theory of large random matrices has proved an invaluable tool for the study of systems with disordered interactions in many quite disparate research areas. Widely applicable results, such as the celebrated elliptic law for dense random matrices, allow one to deduce the statistical properties of the interactions in a complex dynamical system that permit stability. However, such simple and universal results have so far proved difficult to come by in the case of sparse random matrices. Here, we perform an expansion in the inverse connectivity, and thus derive general modified versions of the classic elliptic and semicircle laws, taking into account the sparse correction. This is accomplished using a dynamical approach, which maps the hermitized resolvent of a random matrix onto the response functions of a linear dynamical system. The response functions are then evaluated using a path integral formalism, enabling one to construct Feynman diagrams, which facilitate the perturbative analysis. Additionally, in order to demonstrate the broad utility of the path integral framework, we derive a generic non-Hermitian generalization of the Marchenko-Pastur law, and we also show how one can handle non-negligible higher-order statistics (i.e., non-Gaussian statistics) in dense ensembles.

Active wave-particle entities (WPEs) emerge as self-propelled oil droplets on the free surface of a vibrating oil bath. The particle (droplet) periodically imprints decaying waves on the liquid surface which in turn guide the particle motion, resulting in a two-way coupling between the particle and its self-generated waves. Such WPEs have been shown to exhibit hydrodynamic analogs of various quantum features. In this work, we theoretically and numerically explore a dynamical analog of tunneling by considering a simple setup of a one-dimensional WPE incident on an isolated Gaussian potential barrier. Our idealized model takes the form of a perturbed Lorenz system, which we use to explore the dynamics and statistics of barrier crossing as a function of initial conditions and system parameters. Our work highlights that velocity fluctuations of the WPE at high memories that are rooted in nonequilibrium features of the Lorenz system, such as spiraling motion toward equilibrium points and transient chaos, give rise to (i) sensitivity and unpredictability in barrier crossing, (ii) smooth variations in transmission probability as a function of system parameters, and (iii) wave-like features in the transmitted and reflected probability density profiles.

Thermophoresis is a force exerted on particles in nonisothermal flows, acting opposite to the thermal gradient and potentially dominant in rarefied conditions. This force is not well understood in the transition regime, where the mean-free path of gas molecules, $\lambda$, is comparable to the particle radius, $r$. The rarefaction is quantified by the particle Knudsen number, $\text{Kn}=\lambda /r$. To determine the thermophoretic force in the transition regime, we conducted experiments by measuring the settling velocities of spherical melamine particles in argon or helium under rarefied conditions, where a thermal gradient was applied. The ratio of the thermal conductivities of the particle to the gas $\mathrm{\Lambda }$ is 21 for argon and 2.4 for helium with respect to the melamine particles. Drag force measurements resulted in momentum accommodation coefficients of $0.9\pm 0.1$ and $1.0\pm 0.1$ for argon and helium, respectively. Subsequently, the thermophoretic forces were measured in the range $0.07\lesssim \text{Kn}\lesssim 60$ for argon and $0.05\lesssim \text{Kn}\lesssim 35$ for helium. The experimental data were compared with several theoretical predictions of the thermophoretic force covering the transition regime. An important conclusion is that the energy accommodation coefficient, ${\alpha }_e$, cannot be neglected when predicting the thermophoretic force, as it is found that the approximation of ${\alpha }_e\approx 1$ is seldom accurate.

Compact spin-polarized positron accelerators play a major role in promoting significant positron application research, which typically require high acceleration gradients and polarization degrees, both of which, however, are still greatly challenging. Here, we put forward a spin-polarized positron acceleration method, which employs an ultrarelativistic high-density electron beam passing through any hole of multilayer microhole array films to excite strong electrostatic and transition radiation fields. Positrons in the polarized electron-positron pair plasma, filled in the front of the multilayer films, can be captured, accelerated, and focused by the electrostatic and transition radiation fields, while maintaining high polarization degrees of above $90\%$ and high acceleration gradients of about $\mathrm{TeV}\text{/}\mathrm{m}$. A multilayer design allows for capturing more positrons and achieving cascade acceleration. Our method offers promising solutions to the issues of accelerator miniaturization, positron injection, and polarization preservation, and also can be used to accelerate other charged particles.

The migration of active particles in slowly moving, crowded, and heterogeneous media is fundamental to various biological processes and technological applications. In this study, we numerically investigate the dynamics of a single active particle in a multicomponent medium composed of mixtures of rigid and flexible rings. We observe a nonmonotonic dependence of diffusivity on the relative fraction of rigid to flexible rings, leading to the identification of an optimal composition for enhanced diffusion. This long-time nonmonotonic diffusion, resulting from the different responses of the active particle to rigid and flexible rings, is coupled with transient short-time trapping. The probability distribution of trapping durations is well described by the herein-proposed extended entropic-trap model. We further theoretically establish a universal relationship between particle activity and the optimal rigid-to-flexible ring ratio for diffusion, which aligns closely with our numerical results.

Natural and behavioral sciences increasingly model measurement time series as random multiplicative cascades—nonlinear processes that divide, branch, or aggregate structures across generations, creating multiplicative interactions that break ergodicity. Multifractal formalisms provide a framework for studying cascades, where multifractal spectrum width, $\mathrm{\Delta }\alpha$, fluctuates with the number of estimable power-law relationships. However, multifractality without surrogate comparison can be ambiguous, as the original measurement series' multifractal spectrum width, $\mathrm{\Delta }{\alpha }_{\text{original}}$, is sensitive to series length, ergodicity-breaking linear correlations (e.g., fractional Gaussian noise, fGn), or additive dynamics. To address these challenges, we constructed random cascades varying in length, noise type (additive white Gaussian noise, awGn, or fGn), mixtures of awGn and fGn across generations (progressively more awGn, progressively more fGn, or random mixing of awGn and fGn across generations), and noise operations (addition versus multiplication). We found that “multifractal nonlinearity,” $t_{\text{MF}}$ (a $t$-statistic comparing $\mathrm{\Delta }{\alpha }_{\text{original}}$ to surrogate spectra width, $\mathrm{\Delta }{\alpha }_{\text{surrogates}}$), reliably identifies random multiplicative cascades regardless of series length or noise type—$t_{\text{MF}}$ is more sensitive to interactivity and number of generations than series length. Unlike random additive cascades, random multiplicative cascades exhibit stronger ergodicity breaking due to their heavy histogram tails and show progressively greater ergodicity breaking with more correlated noise (e.g., fGn as opposed to awGn) and additional generations—independent of series length. Consequently, $t_{\text{MF}}$ robustly identifies multiplicative cascade processes, quantifies the depth of cross-scale interactivity, and pinpoints sources of ergodicity breaking while remaining independent of ergodicity-breaking and series length. These properties highlight the potential of $t_{\text{MF}}$ as a powerful metric for advancing our understanding of the mechanisms and origins of cascading processes in natural and behavioral sciences. The simulations further suggest its utility in extending findings from group-level analyses to the level of individuals.

Community modularity structure is widely observed across various brain scales, reflecting a balance between information processing efficiency and neural wiring metabolic efficiency. Revealing the relationship between community structure and brain function facilitates our further understanding of the brain. Here, we construct an adaptive neural network (ANN) consisting of leaky integrate-and-fire neurons with adaptivity governed by spike-time-dependent plasticity rules. The ANN demonstrates diverse dynamic collective behaviors, including traveling waves dominated by initial states, phase-cluster formations, and chimeralike states. In addition to functional clustering, ANN spontaneously organizes into community structures characterized by densely interconnected modules with sparse interconnections. Neurons within modules synchronize, while those across modules remain asynchronous, forming phase-cluster states. By encoding neural rhythms, the ANN segments into asynchronous and synchronous structural modules, leading to chimeralike states. These findings provide further evidence supporting the perspective that function emerges from structure and that structure is influenced by function in complex dynamic processes.

We present a numerical analysis of local community assembly through weak migration from a regional species pool. At equilibrium, the local community consists of a subset (“clique”) of species from the regional community. Our analysis, based on numerical integration of the generalized Lotka-Volterra equations, reveals that the interaction networks of these cliques exhibit nontrivial architectures. Specifically, we demonstrate a pronounced nested structure of the clique interaction matrix in the case of symmetric interactions and a hyperuniform structure seen in asymmetric communities. For a local community to be stable, its composition must meet two requirements: first, it must be feasible on its own, such that internal competition does not lead to species extinction. Second, it must be resistant against invasion by species from the regional community. We show that the nestedness property, although it slightly compromises feasibility, is essential to ensure noninvadability and, thus, characterizes communities with symmetric interactions. In the case of asymmetric interactions, achieving a nested structure is challenging; therefore, the local community at any given moment is hyperuniform, ensuring feasibility but making it invasion-prone. As a result, the dynamics of systems with strong asymmetric interactions is unstable.

In hot dense plasma, the interaction between charged particles leads to the ionization potential depression (IPD), which further affects the physical properties of plasma, such as opacity and equation of state. The experiment of IPD of solid-density Al plasma has indicated that present theoretical models cannot give reasonable descriptions of the IPD in hot dense plasma. So, reasonable theoretical methods are needed to describe the effects of hot dense environments on IPD, and the process of generating hot dense plasmas through the interaction between ultrashort laser pulse and solid-density matter also needs to be carefully considered. In the manuscript, two kinds of temperatures for ions and electrons are considered when we compute the ionization potential depression in hot dense plasma. And, the influences of the hot dense environments are included in the electronic structure calculations by using the modified flexible atomic code (FAC), which has included the screening of free electrons and the correlation of ions by correlation functions obtained from the hyper-netted chain (HNC) approximation. A self-consistent-field method is used to calculate the electronic structures. Based on the calculations, the IPD is obtained through the two-step model. Considering the interaction of the femtosecond laser on the solid-density Al plasma of Ciricosta's experiment, we use the two-temperature model to calculate the IPD in nonlocal thermodynamic equilibrium, and the theoretical results are in good agreement with the experimental results. In addition, we also calculated the electron collision ionization cross section and compared it with the results from other models.

Nonreciprocal interactions in many-body systems lead to time-dependent states, commonly observed in biological, chemical, and ecological systems. The stability of these states in the thermodynamic limit and the critical behavior of the phase transition from static to time-dependent states are not yet fully understood. To address these questions, we study a minimalistic system endowed with nonreciprocal interactions: an Ising model with two spin species having opposing goals. The mean-field equation predicts three stable phases: disorder, static order, and a time-dependent swap phase. Large-scale numerical simulations support the following: (i) in two dimensions, the swap phase is destabilized by defects; (ii) in three dimensions, the swap phase is stable and has the properties of a time crystal; (iii) the transition from disorder to swap in three dimensions is characterized by the critical exponents of the 3D $\mathit{XY}$ model and corresponds to the breaking of a continuous symmetry, time translation invariance; (iv) when the two species have fully antisymmetric couplings, the static-order phase is unstable in any finite dimension due to droplet growth; and (v) in the general case of asymmetric couplings, static order can be restored by a droplet-capture mechanism preventing the droplets from growing indefinitely. We provide details on the full phase diagram, which includes first- and second-order-like phase transitions, and study how the system coarsens into swap and static-order states.

In some models of nonequilibrium phase transitions, fluctuations of the analyzed currents have been observed to diverge with system size. To assess whether this behavior is universal across phase transitions, we examined heat current fluctuations in the Curie-Weiss model, a paradigmatic model of the paramagnetic-ferromagnetic phase transition, coupled to two thermal baths. This model exhibits phase transitions driven by both the temperature and the magnetic field. We find that at the temperature-driven phase transition, the heat current noise consists of two contributions: the equilibrium part, which vanishes with system size, and the nonequilibrium part, which diverges with system size. For small temperature differences, this leads to nonmonotonic scaling of fluctuations with system size. In contrast, at the magnetic-field-driven phase transition, heat current fluctuations do not diverge when observed precisely at the phase transition point. Instead, out of equilibrium, the noise is enhanced at the magnetic field values away but close to the phase transition point, due to stochastic switching between two current values. The maximum value of noise increases exponentially with system size, while the position of this maximum shifts towards the phase transition point. Finally, on the methodological side, the paper demonstrates that current fluctuations in large systems can be effectively characterized by combining a path-integral approach for macroscopic fluctuations together with an effective two-state model describing subextensive transitions between the two macroscopic states involved in the phase transition.

The dynamics of diffusion in complex networks are widely studied to understand how entities, such as information, diseases, or behaviors, spread in an interconnected environment. Complex networks often present community structure, and tools to analyze diffusion processes on networks with communities are needed. In this paper, we develop theoretical tools using multitype branching processes to model and analyze diffusion processes, following a simple contagion mechanism, across a broad class of networks with community structure. We show how, by using limited information about the network—the degree distribution within and between communities—we can calculate standard statistical characteristics of propagation dynamics, such as the extinction probability, hazard function, and cascade size distribution. These properties can be estimated not only for the entire network but also for each community separately. Furthermore, we estimate the probability of spread crossing from one community to another where it is not currently spreading. We demonstrate the accuracy of our framework by applying it to two specific examples: the stochastic block model and a log-normal network with community structure. We show how the initial seeding location affects the observed cascade size distribution on a heavy-tailed network and that our framework accurately captures this effect.

The interaction of intense laser pulses with matter leads to various applications since it enables the transformation of the state of matter owing to a localized energy deposition. The advances in this field rely in particular on the understanding of physical processes at play and the ability to evaluate such a laser energy deposition. The latter can be achieved by developing modeling and associated numerical codes, which have to be efficient to possibly address complex geometries and perform parametric studies. Within this framework, we have developed an efficient numerical tool to describe the interaction of a nanosecond laser pulse with a dielectric material. This description includes the laser propagation, which is consistently coupled to the laser-induced electron dynamics, from which the laser energy deposition is evaluated. The laser propagation and electron dynamics are described by solving the Helmholtz coupled to rate equations. A high-order finite volume scheme is introduced to solve the Helmholtz equation. The physical system dynamics is resolved through a modified Dormand-Prince algorithm, with an adaptive time step designed to efficiently account for the possible rapid change in the optical response of the target when the critical plasma density is reached. The ability of the proposed numerical scheme to efficiently tackle the laser-matter interaction problem is demonstrated. In particular, it is shown that the computational time of our approach can be shorter by one order of magnitude than the one obtained with the usual fourth-order Runge-Kutta method.