We study caging/trapping in Sokoban-type models, featuring a random walker moving through a disordered medium of obstacles and capable of pushing some obstacles blocking its path. In one-dimension, we allow the walker to push up to an arbitrary $N_{\mathrm{P}}$ number of obstacles. For $N_{\mathrm{P}}\gg 1$, we use large-deviation theory to show that the survival probability to remain uncaged exhibits crossover from an exponential decay with time at intermediate times to a stretched-exponential decay at long times, with an exponent $1/3$ independent of $N_{\mathrm{P}}$. The long-time exponent matches the Balagurov-Vaks-Donsker-Varadhan (BVDV) theory of the classical trapping problem, while the exponential decay is qualitatively distinct from the Rosenstock's intermediate-time theory for classical trapping. Similarly, in two dimensions, numerical simulations reveal that both the Sokoban model and its generalized version exhibit long-time stretched-exponential relaxation with exponent $1/2$, again consistent with the BVDV theory. Finally, in two dimensions, we find that the mean trap size is nonmonotonic in $\rho$: it is small at both low and high densities, but reaches a peak at a characteristic density ${\rho }_{*}$. We estimate ${\rho }_{*}\approx 0.55$ for the Sokoban model and ${\rho }_{*}\approx 0.675$ for the generalized Sokoban model.

We present a semianalytical method based on the backward master equation to find the optimal transition path time (TPT) of self-propelled run-and-tumble particles (RTPs) under stochastic resetting. The particle moves in a one-dimensional transition region $[x_A,x_B]$ with two absorbing boundaries. It resets at rate $\gamma$ to position $x_R$. Upon each resetting event, the particle either reverses its velocity direction with probability $\eta \in [0,1]$ or retains it with probability $1-\eta$. From the backward master equation we derive exact analytical results for the splitting probability, the mean TPT, and the coefficient of variation ($\mathrm{CV}$) of the TPT distribution. A semianalytical solution for the optimal TPT is also obtained. The mean TPT depends nonmonotonically on $\gamma , \alpha$, and $\eta$, reaching a minimum at optimal parameter values. For large transition regions, resetting the particle to its initial position can accelerate escape compared with reset-free dynamics. In the strong-resetting limit for $\eta >0$ when $x_R=x_A$, the probabilistic reversal upon resetting effectively replaces natural tumbling. The asymptotic TPT then becomes independent of the tumbling rate $\alpha$ and reduces to the ballistic traversal time $L/v$. A speed-reliability trade-off emerges: the parameters that minimize the mean TPT do not generally minimize the $\mathrm{CV}$. Efficient search requires balancing a short mean TPT against high predictability.

Random quantum states drawn from the Haar ensemble with a constraint on the energy expectation value $E_{\text{av}}=\langle \psi \left|H\right|\psi \rangle$ display eigenstate condensation: For $E_{\text{av}}$ below a critical value $E_{c-}$ or above $E_{c+}$, they develop macroscopic overlap with the ground state or anti–ground state. We use analytical calculations and state-of-the-art numerical methods to investigate the eigenstate condensation phase transition. We give compact expressions for the critical energies, derive an analytical scaling form for the order parameter in systems with an extensive free energy, show that in those systems the phase transition itself has exponential rather than power-law finite-size scaling, and test these results with large-scale numerical sampling in random matrices and a range of local spin Hamiltonians. In local spin systems the two critical energies approach the middle of the spectrum as $1/V$ with $V$ the number of spins. Our scaling form, however, demonstrates that the condensation phase transitions have exponential, rather than polynomial, finite-size scaling, which justifies treating the high-temperature phase as an extended phase.

We study numerically the enveloping $f$function of the fluctuation term in eigenstate thermalization hypothesis statement. We concentrate on the energy (or entropy) dependence of this function in two-dimensional systems. Our numerical results show that it is, in general, a monotonically increasing function of the entropy. This is in agreement with the general expectation that fluctuations increase with increasing entropy. We observe that the $f$function locally flattens with increasing system size. The flattening rate is directly proportional to the system size. We also observe that the flattening rate is directly proportional to the particle number for systems of same spatial size. This variation of the $f$ function is important for physics at subleading order of the system-size. So, it is relevant for intermediate-size systems (upto a few hundred qubits) which are experimentally accessible. One exception we find is that the $f$function of the order parameter of a thermal phase transition defies the monotonic behavior.

A wide range of real-world systems, ranging from physical and biological systems to social systems, can be described as temporal networks, where link temporality has profound effects on many dynamical processes taking place on networks. Here we study the susceptible-infected-susceptible model on temporal complex networks, where edges are randomly activated or terminated at each time step. We analytically obtain the epidemic threshold for temporal complex networks with arbitrary initial degree distributions. The approximate endemic equilibrium prevalence for temporal complex networks with arbitrary initial degree distributions is derived analytically for the system close to the epidemic threshold and far away from it. In addition, we demonstrate that the system undergoes a continuous transition from the disease-free state to the endemic state. Our results pave the way to understand how the degree distributions will affect a wide variety of binary-state dynamics on temporal complex networks.

Instabilities are a common occurrence in plasma discharges where they play an important role in system behavior and performance. While such instabilities are typically in the kHz and MHz range, this work reports a low frequency ($\sim 100\mathrm{Hz}$) instability observed in supersonic inductively coupled plasmas. Using a novel swirl gas injection, two concentric, counter-propagating vortices are produced that segment the flow field. While discharge properties only vary moderately within the outer vortex, intense plasma-gas heating leads to pressure fluctuations that drive a large-amplitude instability within the inner vortex. By adjusting the injection conditions, the instability can be damped or amplified.

Photochromic materials enable dynamic optical modulation through reversible transitions between distinct absorption states, with broad potential for smart windows, adaptive optics, and reconfigurable photonic devices. Micron-scale photochromic hybrid films present a particularly attractive platform for these applications, combining straightforward preparation with substantial optical modulation and scalability for high-volume fabrication. However, rational design of such films remains fundamentally constrained by the absence of well-defined optical constants. Unlike homogeneous thin films, micron-scale hybrid photochromic materials comprise active particles dispersed nonuniformly within polymer matrices. Conventional first-principles electromagnetic simulations face substantial computational costs and discrepancies between simulated and experimental particle distributions. Here, we introduce a data-driven framework that extracts effective optical constants directly from minimal experimental transmittance measurements. Our dual-state effective model approximates the complex inhomogeneous photochromic layer as a compressed homogeneous medium characterized by pseudorefractive indices and pseudoextinction coefficients for both pristine and UV-irradiated states. Through systematic optimization against experimental data from tungsten oxide–polyvinylpyrrolidone hybrid films, we determine wavelength-dependent pseudooptical constants and compression ratios that enable accurate prediction of optical modulation within the tested thickness range. Our methodology establishes a framework for engineering hybrid photochromic systems and demonstrates how data-driven modeling can overcome limitations in characterizing complex nanostructured materials.

We introduce a generalized version of the Biswas-Chatterjee-Sen (BChS) model [S. Biswas et al., Physica A 391, 3257 (2012)] with group interactions of size $q$, extending the original pairwise interaction dynamics. Within a mean-field framework, we derive an exact expression for the critical noise $p_c\left(q\right)$, showing that it increases monotonically with $q$ and approaches $1/2$ in the large $q$-limit, consistent with a Gaussian approximation. Despite this shift in the phase boundary, the critical behavior remains unchanged across all $q$: the order parameter scales as ${(p_c\left(q\right)-p)}^{1/2}$ and the relaxation timescale diverges as $|p-p_c{\left(q\right)|}^{-1}$, identical to the original BChS model [S. Biswas et al., Physica A 391, 3257 (2012)]. Finite-size scaling of the Binder cumulant, order parameter, and its fluctuations confirm that the system belongs to the mean-field Ising universality class for all $q$. Our results demonstrate that higher-order interactions modify the location of the transition without altering its universality class.

The critical behavior of the Baxter-Wu model belongs to the universality class of the four-state Potts model. While the introduction of annealed vacancies does not alter the criticality of the four-state Potts model, the dilute Baxter-Wu model has remained the subject of several competing scenarios. Here we investigate the phase diagram of the spin-1 Baxter-Wu model in the presence of a crystal field using transfer-matrix calculations and large-scale Monte Carlo simulations. Our results reveal a systematic evolution of the effective critical behavior with increasing crystal field, accompanied by increasingly strong finite-size corrections near the crossover to the first-order regime. Along the line of continuous transitions, the central charge remains close to $c=1$, while the scaling dimensions systematically deviate from the spin-$1/2$ limit as the crystal field increases, consistent with either continuously varying effective critical exponents or a slow crossover between competing critical behaviors. The first-order regime is independently characterized through multicanonical simulations, which confirm the expected finite-size scaling and interfacial behavior. Taken together, our results provide a unified picture of the dilute spin-1 Baxter-Wu model, substantially narrowing the range of possible scenarios for the crossover between continuous and first-order phase transitions.

When a gas of particles interacts with much a larger reservoir the density dynamics on large scales is typically governed by diffusion. We study this paradigmatic problem for weakly coupled integrable systems and show that this picture gets altered when transport is investigated on top of long-lived nonthermal states. Remarkably, for states noninvariant under parity we find the Burgers equation arising in the hydrodynamic limit. We explicitly compute the diffusion constant and nonlinear advective coefficient of the Burgers equation using a variant of the Chapman-Enskog theory. We find an excellent agreement between our theory and numerical simulations of a simplified model of stochastic two-body collisions. Our conclusions are based only on Galilean invariance, existence of a small system-bath coupling parameter, and a small momentum exchange between the system and the bath particles during two-body scattering.

We numerically revisit the transfer-matrix formulation of directed polymers in random media and show that a common finite-dimensional framework organizes the canonical one-point fluctuation laws in $(1+1)$ dimensions. For a fixed realization of the bulk disorder, full-space partition functions are obtained from the same time-ordered product $W\left(t\right)$ through endpoint contractions or a Brownian-weighted initial vector, while the half-space construction modifies only the transfer rule at the absorbing boundary. These choices yield distributions consistent with the standard KPZ subclasses: Tracy-Widom GUE for point-to-point geometry, Tracy-Widom GOE for point-to-line geometry, Tracy-Widom GSE for half-space point-to-point geometry, and Baik-Rains for the stationary line-to-point construction. In all four cases, the free-energy fluctuations grow as $t^{1/3}$, and the low-order cumulants approach the corresponding universal benchmarks. The matrix-product formulation also provides access to intrinsic spectral observables. For the leading eigenvalue ${\lambda }_1\left(t\right)$, the fluctuations of $ln{\lambda }_1\left(t\right)$ exhibit an intermediate $t^{1/3}$ regime, while the standardized distribution remains distinct from the canonical benchmark laws over the studied time range.

First-passage theory usually emphasizes when absorption occurs. Here, we instead treat where absorption occurs—the first-hitting location (FHL)—as a primary boundary observable of drift–diffusion processes. We formulate its law as the exit measure induced by the diffusion generator and recover its density from the normal derivative of an elliptic Green function. This yields exact half-space kernels in arbitrary ambient dimension $d$ for constant drift, with the two- and three-dimensional cases validated by Monte Carlo simulations. In the zero-drift limit, the kernels reduce to scale-free Cauchy-type laws with algebraic tails; drift introduces exponential screening and the characteristic length ${\ell }_u={\sigma }^2/\parallel \mathit{v}\parallel$, where $\sigma$ is the noise strength and $\mathit{v}$ is the constant drift vector, thereby localizing the boundary footprint. An entropy-based effective width provides a finite diagnostic of this crossover. To test the geometric reach of the planar theory, we also analyze drift-free exterior hitting of a circle. Its exact Poisson kernel recovers the planar Cauchy law as a local near-boundary limit, admits an exact Cauchy–Poisson composition through an intermediate line, and yields a finite-time supporting-line bound. These results organize geometry, drift, and pathwise constraints within a unified description of first-hitting location laws.

Synchronization of self-sustained oscillators under fixed frequency and amplitude forcing is well understood, but how time-varying forcing mangles phase locking has been much less explored. Theory predicts that slow deterministic modulation of the drive amplitude or frequency can lead to a peculiar synchronization regime characterized by intermittent locking of the oscillation phase beyond the Arnold-tongue boundaries associated with fixed harmonic forcing. We test these predictions in a controllable aeroacoustic self oscillator, i.e., a whistle, that exhibits a robust limit cycle and is subject to external acoustic forcing with programmable frequency and amplitude modulation. Under both slowly varying frequency and amplitude of the forcing, three regimes are observed: (i) strict synchronization, (ii) intermittent synchronization, characterized by alternating phase-locking and brief phase-slip episodes, and (iii) no synchronization, with regular phase slips. Particularly in the strict synchronization regime, the phase of the oscillator will follow an arbitrary, slowly varying drive phase and under amplitude modulation its amplitude fluctuations are strongly suppressed.

Swarmalators are active agents that move in position space and exhibit internal degrees of freedom. Due to interactions of their positions and phases of oscillation, they show on the one hand swarming, similar to the effect of flocking of birds. In addition, they exhibit synchronization behavior, analogous to what has been observed in fireflies. Previous works studied scenarios in which the phases are forced externally. Here, we consider a pseudoforce that acts on the positions of the swarmalators. Due to the resulting attraction toward the center of position space, transitions from the splintered and active phase-wave state to the static asynchronized state are induced. To quantify the crystal order of swarmalators, we introduce an order parameter that is based on the Fourier transform of their positions.

The templex is a topological object bridging homologies and templates for chaotic dynamics. This article places the templex within category theory, introducing a directed path algebra, an edge operator on directed paths, and an equivalence relation for directed cycles that is distinct from directed homologies. The resulting functorial invariants are of two kinds: Abelian-group invariants, namely the homology groups, and semigroup invariants, namely the generatex semigroups. These invariants are separable through forgetful functors and constitute a robust framework for identifying tipping points, disambiguating physical mechanisms, and benchmarking data-driven models against observations or simulations. The formulation sets forth a nonmetric criterion for chaos from finite-time data and reveals that the concatenable nature of topological modes of variability is a direct consequence of the semigroup structure of the directed path algebra. Two applications are presented: an experimental speech signal and a climatic numerical simulation.

Due to the deterministic nature of chaotic systems, fluctuations in their trajectories arise solely from the choice of initial conditions. Some of these dynamical fluctuations may lead to extremely unlikely scenarios. Understanding the impact of such rare events and the trajectories that give rise to them is of significant interest across disciplines. Yet, identifying the initial conditions responsible for those events is a challenging task due to the inherent sensitivity to small perturbations of chaotic dynamics. In a recent paper [Gutiérrez et al., Phys. Rev. Lett. 131, 227201 (2023)], this challenge was addressed by finding the effective dynamics that make rare events typical for one-dimensional chaotic maps. Here we extend such large-deviation framework to $d$-dimensional chaotic maps. Specifically, for any such map, we propose a method to find an effective topologically conjugate map which reproduces the rare-event statistics in the long-time limit. We demonstrate the applicability of this result using several observables of paradigmatic examples of two-dimensional chaos, namely, the two-dimensional tent map and Arnold's cat map.

Behavioral feedback plays a crucial role in shaping epidemic dynamics. In this work, a contagion framework that combines higher-order interactions with a dynamic activity-feedback mechanism is developed and analyzed. An evolution equation describing the temporal dynamics of the activity rate is formulated under the assumption that group behavior is regulated by the current prevalence. Two different bistable states are identified, and the conditions for their appearance and disappearance are clarified. To assess the generality of these findings, we numerically simulated the framework on networks with different levels of hyperedge overlap. Numerical simulations further show that hyperedge overlap modulates the bistable window in a feedback-dependent manner and, under strong behavioral feedback, low-overlap networks can trigger a rapid decline in activity rate, thereby suppressing sustained outbreaks. These results provide a qualitative perspective for understanding behavioral-response patterns reported during the COVID-19 pandemic.

Entrainment is an important collective behavior in complex networks, where the output period of the coupled neuronal oscillator matches the external input period and maintains a stable phase relationship. The typical feature of entrainment is the regions in the input period and input amplitude parameter space, known as the Arnold tongue. In this article, we introduced a higher-order Kuramoto model and found that the transition process of the coupled neuronal oscillators from the unentrainment state to the entrainment state is a discontinuous first-order phase transition process accompanied by the hysteresis phenomenon. Interestingly, this discontinuous first-order phase transition process results in the appearance of two Arnold tongue structures in the parameter space. Our results provide more insights into the emergence of the explosive entrainment and have been confirmed by the theoretical analysis.

Disordered materials occur naturally and also provide a broader design space than ordered or crystalline structures. We investigate a two-dimensional disordered network metamaterial constructed from a Delaunay triangulation of an underlying point cloud. Small perturbations in the point cloud induce discrete topological changes. One such change we identify is a Delaunay flip, in which two neighboring Delaunay triangles that form a convex quadrilateral structure with their common edge being one of the two quadrilateral diagonals exchange this diagonal for the other diagonal. These topological changes can cause substantial jumps in the effective resistance measured diagonally across the network, when the change is located near the source or the sink node. The jumps are explained analytically by showing that the change in effective resistance from edge removal or addition depends on the voltage drop across that edge. However, Delaunay flips have less impact on global resistance measurements and in larger networks. These local topological changes are relevant for finite-sized samples and experimentally measurable properties such as electrical transport. Global characterizations of the network disorder or topology lack the location-specificity of our observed effects on network transport, and thus may be inadequate for predicting certain experimentally measurable transport properties in disordered network metamaterials, highlighting the importance of localized regions in material design.

A scale-by-scale analysis of energy flux in the turbulent cascade can be performed using the spatially filtered magnetohydrodynamic (MHD) equations, while the gradient tensor invariants are widely used to characterize the structure of velocity and magnetic fields. Physical mechanisms responsible for energy flux require specific field configurations whose strength is quantified by these tensor invariants. We explore this requirement, showing that the tensor invariants act as proxies for mechanistic energy fluxes under quantifiable conditions. As a special case, the purely hydrodynamic contributions to energy flux can be expressed exactly in terms of the invariants of the velocity gradient tensor. We also show that the invariants bound the available energy flux for distinct physical mechanisms, formalizing the idea that each transfer mechanism requires field configurations with gradients of sufficient strength to support a given energy flux. Results are illustrated using three-dimensional simulations of freely decaying MHD turbulence. These findings advance our understanding of MHD turbulence by revealing key relationships between field topology and energy transfer across scales due to distinct physical mechanisms. They further provide a tool for probing the turbulent cascade using multispacecraft data where local tensor invariants are directly accessible.