Frequently, nonextensive systems are described through $q$-exponential functions, where the $q$ parameter determines how far a system is from equilibrium. In this work, we study systems constrained to $q-1\ll 1$ to describe systems near thermal equilibrium, and derive the probability density function and temperature fluctuations. To this end, we derive the series expansion of the $q$-exponential function, yielding a perturbative series that is a superposition of gamma distributions. On the other hand, the temperature fluctuations are expressed as a superposition of Dirac delta functions and their derivatives, meaning that the bulk of the system remains at a constant temperature, while point-temperature variations emerge, marking the system's departure from thermal equilibrium. The statistics of the temperature fluctuations exhibit a transition from a symmetric to a nonsymmetric distribution as the nonextensive parameter increases. These results provide evidence of the association between the emergence of nonextensivity and the symmetry breaking of temperature fluctuations.

In the wake of the SARS-CoV-2 pandemic, there has been heightened interest from applied mathematicians in infectious disease modeling. Modeling efforts often focus on predicting whether diseases are likely to be eliminated or, instead, (re)emerge, especially as a result of control measures. This tipping point between elimination and infection waves has been successfully anticipated in the literature through the use of early warning signals and such signals often rely on the theory of critical slowing down. Recent developments have shown that these signals (increases in fluctuation variance and return time) can emerge from the system geometry in the case of non-normal dynamics rather than a change in asymptotic stability. We show how such dynamical behavior occurs in the fluctuations from the mean field in general stochastic systems. Using the susceptible-infectious-recovered model as an example application, we analyze how critical-like behavior can be exploited to anticipate infection waves in the absence of an equilibrium bifurcation.

Spin-boson systems have attracted increasing attention as accessible experimental platforms and for their potential applications in designing quantum technologies. One characteristic of these systems is the transition from regular to completely chaotic behavior when certain control parameters are varied. However, the characterization of their mixed phase space has not been thoroughly explored. In this work, we investigate the properties of mixed eigenstates in spin-boson systems, comparing one-photon interactions with two-photon interactions. We propose a generalized definition of the phase-space overlap index to identify genuine mixed eigenstates. Our study highlights the fundamental differences that arise when two-photon processes are considered compared to one-photon processes and provides complementary evidence supporting the validity of the principle of uniform semiclassical condensation of quasiprobability functions in spin-boson systems.

Biological development is governed by internal clocks and feedback processes with characteristic response times. While circadian ($\sim 24$ h) and ultradian ($\sim \mathrm{hours}$) rhythms are well established, the existence and functional relevance of regulatory processes operating on characteristic subcircadian timescales remain largely unexplored. Here we treat a living organism as a driven dynamical system and introduce a temporal spectroscopy approach to probe its intrinsic regulatory timescales. Using Arabidopsis thaliana as a model system, we apply square-wave light-dark forcing with systematically varied periods spanning 5 s to 5400 s, while conserving the total daily photon dose. The organismal response is strongly nonmonotonic in forcing period and reveals three discrete, highly responsive frequency bands centered on seconds (10.5–42 s), minutes (168–336 s), and hours (1350–5400 s). Forcing within these bands induces sharp transitions in morphology and life-history trajectories, including programmable reallocation of growth between root and shoot systems, suppression of lateral root emergence, and frequency-dependent extension of lifespan by up to 60% without loss of final biomass. These responses are not consistent with simple photon integration or stress accumulation, but instead are consistent with a hypothesis of frequency-selective coupling between external forcing and internal regulatory processes. The characteristic frequencies align with known kinetic timescales of ion fluxes, membrane potential dynamics, photoreceptor signaling, metabolic turnover, and circadian gating, suggesting a hierarchical architecture of biological timescales. Our results uncover a temporal structure underlying development and establish frequency as an independent physical control parameter for reprogramming biological systems. More broadly, this work demonstrates that oscillatory environmental forcing can be used as a discovery tool to map the internal timescales governing complex living matter.

Effectively controlling the spatial distribution of filaments and improving their physical properties are crucial for advancing the applications of dielectric barrier discharge. In this work, we report a dielectric barrier discharge device to simultaneously regulate filament distribution and improve their physical properties by covering the dielectric surface with a metal lattice sheet. With increasing applied voltage, this structure gives rise to several stable filamentary patterns, including a three-dimensional pattern composed of normal filaments and trifurcated filaments with three branches extending along the metal grid. It is demonstrated that the extensions originate from the metal sheet by covering a vertex with a dielectric and replacing the metal sheet with a glass plate. The physical properties of two types of filaments are measured by using an intensified charge-coupled device, photomultiplier tubes, and optical emission spectroscopy. The results reveal that charge transport along the metal grid increases the electron density and prolongs the discharge duration. These findings provide a strategy for dielectric barrier discharge control and plasma structure engineering.

The Gaussian phase approximation (GPA) underlies many standard diffusion magnetic resonance signal models, yet its validity is rarely scrutinized. Here, we assess the validity of the GPA by analytically deriving the excess phase kurtosis ${\kappa }_4/{\kappa }_2^2$, where ${\kappa }_n$ is the $n\text{th}$ cumulant of the accumulated phase distribution due to motion. We consider the signal behavior of the spin echo with constant gradient amplitude $g$ and echo time $T$ in several one-dimensional model systems: (1) a stationary Poisson pore-hopping model with uniform pore spacing $\mathrm{\Delta }x$ and mean interhop time ${\tau }_{\text{hop}}$; (2) a trapped-release model in which spin isochromats are initially immobilized and then released with diffusivity $D$ following an exponentially distributed release time, ${\tau }_{\text{rel}}$; and (3) restricted diffusion in a domain of length $L$. To our knowledge, this is among the first systematic analytical treatments of spin-echo phase kurtosis without assuming Gaussian compartments or infinitesimally short gradient pulses. In the pore-hopping system, ${\kappa }_4/{\kappa }_2^2=(9/5){\tau }_{\text{hop}}/T$, inversely proportional to the mean hop number, $T/{\tau }_{\text{hop}}$. In the trapped-release system, ${\kappa }_4/{\kappa }_2^2$ is positive and decreases roughly log-linearly with $T/\langle {\tau }_{\text{rel}}\rangle$, where $\langle {\tau }_{\text{rel}}\rangle$ is the average release time. For restriction, ${\kappa }_4/{\kappa }_2^2$ vanishes at small and large $L/\sqrt{DT}$, but has complicated intermediate behavior. There is a negative peak at $L/\sqrt{DT}\approx 1.2$ and a positive peak at $L/\sqrt{DT}\approx 4.4$. Monte Carlo simulations are included to validate the analytical findings. Overall, we find that the GPA does not generally hold for these systems under moderate experimental conditions, i.e., $T=10\mathrm{ms}, g\approx 0.2–0.6\mathrm{T}/\mathrm{m}$. These results suggest that signal models reliant on the GPA must be carefully examined, particularly for strong, extended gradients and in media with complex kinetics, morphology, and/or microstructure.

We investigate the subcritical and supercritical behavior of a hard-sphere fluid with attractive interactions described by the Wolf potential, focusing on the role of the interaction range. Coexistence curves are obtained from computer simulations over a wide range of interaction lengths and critical parameters are determined from simultaneous fits of the liquid and vapor branches with the critical exponent $\beta$ treated as a free parameter. As the interaction range decreases, the critical temperature drops rapidly, whereas the critical density displays a nonmonotonic dependence, increasing over most of the range explored before declining mildly at the shortest interaction lengths. The reduced second virial coefficient at criticality, $B_2^{*}\left(T_c\right)$, remains negative over the entire range of interaction lengths and exhibits a nonmonotonic dependence on the inverse-range parameter, suggesting in the short-range regime a finite limiting value distinct from the conventional Noro-Frenkel prediction. In the supercritical region, we analyze parallel critical-isochore (PCI) Widom lines using a previously developed Helmholtz free-energy expression. These lines define a thermodynamic framework that bounds conventional Widom lines associated with extrema of response functions. Their evolution with interaction range reveals a strong asymmetry between the PCI Widom lines branches and characterizes the extension of criticality into the supercritical domain. We additionally examine the Zeno and Boyle ideal lines, which converge in the dilute limit and exhibit a systematic, $\alpha$-dependent curvature away from it.

We study a stochastic model of collective orientation dynamics in which individuals update their orientation through pairwise aligning or antialigning copying interactions. We analyze both annealed dynamics, where interaction types are chosen probabilistically at each update, and quenched dynamics, where individuals are permanently assigned to aligning or antialigning subpopulations. Starting from the microscopic master equation on the circle, we derive a closed mesoscopic description via a Fourier-mode expansion and a systematic large-$N$ expansion, obtaining closed Fokker-Planck equations and effective stochastic differential equations for the polarization. We show that competing alignment and antialignment suppress long-range polar order in the thermodynamic limit in both cases, while finite systems display nontrivial fluctuation-induced structure controlled by the interaction composition. Our results, validated by Gillespie simulations, establish an analytically tractable framework for collective dynamics characterized by competing copying rules and intrinsic noise.

Oscillators defined on curved spaces provide a natural framework for exploring geometry-induced nonlinear dynamics. The two-dimensional Mathews-Lakshmanan oscillator and Higgs oscillator are prominent examples of geometrically induced nonlinear oscillators. The two-dimensional Higgs oscillator in flat space arises from a conformal (stereographic) projection of the harmonic oscillator on the sphere ${\mathcal{S}}^2$ onto the two-dimensional plane. Its one-dimensional counterpart, defined by a non-Euclidean geometry with curvature parameter, exhibits chaotic dynamics and extreme events (EEs) when subjected to damping and external driving forces [Ahamed et al., Chaos 35, 023119 (2025)]. In this work, we introduce coupling through mass interaction among multiple one-dimensional damped and forced Higgs oscillators, and we investigate the resulting collective nonlinear dynamics within a many-particle framework. More importantly, we establish the connection between the conformal mass $m\left(x\right)$ and the extrema of velocity through a power-law relation, demonstrating how the conformal mass regulates the turning points leading to the emergence of extreme events EEs. Furthermore, to provide additional insight into the underlying mechanism, we quantify the energy synchronization error among the oscillators, thereby revealing how energy synchronization evolves during the onset of EEs.

From gene regulatory networks to mutualistic networks, controlling a small portion of nodes in complex networks can drive such dynamical systems from nonideal states to ideal ones. Currently, there are only methods for handling linear systems and one-dimensional nonlinear systems. However, real-world complex systems are typically nonlinear and multidimensional, such as mutualistic systems involving flowering plants and pollinating insects. In such systems, nodal dynamics are governed by multiple nonlinear differential equations. To address this limitation, we develop a method for controlling a single node to revive networked multidimensional dynamical systems. The uncontrolled nodes are stratified based on their shortest path to the controlled node. In this way, a large-scale dynamical system can ultimately be replaced by a much simpler one. Through analysis of the reduced system, we can predict the degree of control required to revive the system to its ideal state. We apply this method across diverse domains, achieving successful revival in various multidimensional complex dynamical systems.

We formulate a Derjaguin-corrected Kelvin equation for phase transitions in finite open slits. In such pores, capillary condensation is modified by the finite wall length because the condensed phase is bounded by two terminal menisci pinned at the slit ends. Starting from the macroscopic generalized Kelvin equation, we introduce a scaling approximation which replaces the implicit edge-contact-angle condition with a closed analytic expression while preserving the exact limiting behaviors. We then incorporate mesoscopic wetting-layer contributions into the finite-slit free-energy balance. The single-wall contribution naturally separates into a planar Derjaguin term and a residual finite-length correction controlled by the competition between the wall length $H$ and the parallel correlation length ${\xi }_{\parallel }$. The resulting equation reduces to the standard Derjaguin-Kelvin equation for infinitely long slits and to the macroscopic finite-slit Kelvin equation when adsorbed layers are absent. Explicit forms are derived for long-ranged dispersion forces and for short-ranged forces. The theory is tested using classical density functional theory for finite slits with attractive Lennard-Jones walls and hard walls, corresponding respectively to capillary condensation and its drying analog, capillary evaporation. The Derjaguin-corrected theory substantially improves on the purely macroscopic prediction, capturing both the correct infinite-slit limit and the observed dependence on wall length. For the short-ranged hard-wall system, the agreement with DFT remains nearly quantitative even for very narrow slits.

Trail interactions occur when past particle trajectories bias future motion, rendering the system out of thermodynamic equilibrium. While such systems are abundant in nature, their understanding is limited to the single-particle level or phenomenological mean-field theories. Here, we introduce a minimal model of many trail-interacting particles, which extends this paradigm to the fluctuating collective level in arbitrary dimension. Particles diffuse while depositing long-lasting repelling/attracting trails that act as a shared memory field, coupling their dynamics across time and space. Using stochastic density functional theory, we derive fluctuating hydrodynamic equations and analyze analytically and numerically the resulting behaviors. We show that memory, coupled with fluctuations, fundamentally reshapes collective dynamics. In the repulsive case, the particle density displays superdiffusive spreading for $d=1$ and diffusive spreading for $d\ge 2$, characterized by transient clustering and ballistic motion. In the attractive case, the system condensates in finite time into frozen, localized states. Our results establish general principles for trail-interacting systems and reveal how persistent fields generate instabilities and drive self-organization.

It was recently conjectured and verified for the transverse-field Ising model [Phys. Rev. B 113, 165102 (2026)] that, after a sudden quench within the same equilibrium phase, the initial ground state has its largest overlap with the final ground state. We show that this phase-based criterion is generally false, even in translationally invariant free-fermion systems. For Hamiltonians that factorize into independent $2\times 2$ momentum sectors, we derive the exact necessary-and-sufficient condition for ground-state overlap dominance: the initial and final sector Bloch vectors must have positive dot product for every momentum. This result proves the conjecture in classes where same-phase quenches enforce this geometric condition, but gives explicit same-phase counterexamples in Kitaev chains, where excited final eigenstates can dominate the overlap distribution. We further show that the same obstruction controls real-time Fisher-zero crossings, allowing dynamical quantum phase transitions without crossing an equilibrium phase boundary.

We study the role of randomness in the scrambling of quantum information within integrable free-fermionic systems. Considering quadratic Hamiltonians with varying degrees of randomness, we analyze entanglement-based measures to characterize the scrambling structure. We show that the memory effect in the entanglement of disjoint subsystems of Gaussian states vanishes when the local couplings are random, indicating information delocalization. The tripartite mutual information exhibits negative saturation values similar to those in chaotic systems, albeit with a smaller magnitude, revealing weaker scrambling under integrable quadratic dynamics. Despite integrability, spectral analyses reveal that local random models display a spectral-form-factor ramp and a partial crossover in the single-particle level-spacing ratio from Poisson-like to Wigner–Dyson-like behavior within a certain range of random couplings. These results demonstrate that randomness can act as a minimal ingredient for inducing information scrambling in integrable quadratic fermionic models.

We study a two-dimensional, off-lattice particle model introduced to describe absorbing phase transitions in driven non-Brownian suspensions. We numerically explore the $(\varphi ,\epsilon )$ phase diagram, where $\varphi$ is the packing fraction and $\epsilon$ controls the amplitude of particle jumps. We use a binary mixture to suppress crystallization, which allows us to disentangle the model's distinct phase transitions between amorphous states. At large $\varphi$, we find that the approach to the absorbing transition is preceded by a nonequilibrium glass transition to a nondiffusive amorphous state. This dynamic arrest makes the location of the critical absorbing transition protocol-dependent. The $\epsilon \to 0$ end point of the transition line defines a jamming transition whose location is shown to vary continuously with the preparation protocol, and cannot serve as a unique definition of random close packing. Near jamming, we observe a complex landscape and marginal stability, reminiscent of Gardner phases found in thermal glasses. The critical exponents characterizing packings at the jamming transition numerically agree with alternative approaches based on energy minimization, and with analytic predictions from mean-field replica theory. We analyze hyperuniformity of large-scale density fluctuations in fluid and glass phases, where it emerges with qualitatively distinct signatures, and show that random-organization dynamics does not determine the hyperuniformity observed in jammed packings, which is found to be nonuniversal. Our results show that random organization models share deep physical similarities with thermal soft-particle systems undergoing glass and jamming transitions, with little impact of the nonequilibrium nature of the microscopic dynamics on emerging physical properties.

Many complex systems are described by Langevin-type equations in which the noise exhibits long-range correlations and couples to the system in a state-dependent, multiplicative manner, leading to heterogeneous non-Markovian diffusion. Here, we investigate the problem of diffusion driven by fractional Gaussian noise with a general multiplicative coefficient from a path-integral perspective. Using a stationary-phase approximation, we derive a Gaussian propagator expressed in terms of the Lamperti transform of the process. In the additive limit, our results recover the path-integral representation of fractional Brownian motion based on its Riemann-Liouville formulation and establish its equivalence with the Langevin construction. We further analyze the effect of subordinating the process to a killing rate within the Feynman-Kac framework and develop a general procedure to derive kinetic equations in terms of effective local Hamiltonians. We show that the interplay between multiplicative diffusion and confinement induces an effective drift term, leading to probability accumulation in regions of low noise amplitude.