We investigate conductance fluctuations across the integer quantum Hall transition in graphene from the perspective of multiscale stochastic dynamics. Using a tight-binding description combined with the Landauer-Büttiker formalism, we generate longitudinal and transverse transmission time series by sweeping magnetic flux and Fermi energy in disordered nanoribbons with armchair and zigzag terminations. The interplateau regime exhibits non-Gaussian, intermittent fluctuations whose increments display scale dependence and broad-tailed statistics. Multifractal detrended fluctuation analysis reveals a broad singularity spectrum, indicating the coexistence of multiple scaling exponents. To rationalize these features, we model the increment distributions within an H-theory approach that leads to analytical expressions in terms of Meijer $G$ functions, while excellent agreement with the data is achieved by incorporating discrete statistical mixtures that account for clustered variance dynamics. Our results establish a quantitative connection between the quantum Hall transition in graphene and a cascadelike hierarchy in the conductance fluctuations, and clarify the role of disorder in enabling this multiscale regime.

As a deep learning-based framework, the physics-informed neural network (PINN) has been widely used to solve partial differential equations (PDEs) in various fields. However, due to causality violation and activation function saturation, PINN typically suffers from poor performance in long-time integration tasks. To address these issues, we propose a variant of PINN named sliding-interval PINN (SI-PINN). First, SI-PINN decomposes the temporal domain and employs a sliding-interval strategy to avoid activation function saturation. It also integrates a pretraining scheme to mitigate causality violation in PINN, thereby enabling long-time integration of PDEs. To validate the effectiveness of our SI-PINN, the proposed strategy is evaluated on a set of typical PDEs and compared with existing methods. Numerical results demonstrate that it enables accurate long-time integration across various systems. Moreover, in most cases we examined, it achieves superior accuracy to that of existing methods. The proposed SI-PINN is expected to provide a promising strategy for long-time integration of PDEs.

Active agents are likely to accumulate near confining obstacles due to collective motion. Here we investigate how the nature of the microscopic drive—self-propulsion or velocity alignment—selects distinct accumulation patterns, leading to either delocalized or compact clustered states. We first characterize the dynamical regimes emerging from the interplay of these two driving mechanisms under perfectly reflective or smooth boundary conditions. We then introduce boundary friction and observe a drastic change in the accumulation patterns, with dynamical phases that are absent in the previous case. By connecting emergent macroscopic structures to their underlying interactions, this work provides a practical route to infer the dominant microscopic mechanism ruling boundary-mediated collective behavior, with potential applications ranging from single-cell migration to bioinspired robotics.

Finite-time information erasure is governed by probability transport through configuration space, not only by final logical populations. We show that a two-dimensional Brownian memory can lower fast-erasure cost by reorganizing probability currents through a transverse degree of freedom. Using physics-informed routing control (PIRC), we optimize conservative protocols at fixed erasure time and final-error criterion, and compare them with tilt-only and static minimum-energy-path (MEP) constrained driving. Constrained scans over transverse-gate strength reveal two regimes: MEP and PIRC enter the target-error band where tilt remains infeasible and, when all three protocols have comparable final error, PIRC has lower entropy production than both baselines. The reduction is not obtained by following the static MEP alone, but by suppressing off-channel dissipation and reshaping the transient current field.

In critical lattice models, distance ($r$)-dependent correlation functions contain power laws $r^{-2\mathrm{\Delta }}$ governed by scaling dimensions $\mathrm{\Delta }$ of an underlying continuum field theory. In Monte Carlo simulations and other numerical approaches, the leading dimensions can be extracted by data fitting, which can be difficult when two or more powers contribute significantly. Here a method utilizing covariance between multiple lattice operators is developed where the $r$-dependent eigenvalues of the covariance matrix reflect scaling dimensions of individual field operators. This disentangling of scaling dimensions is demonstrated explicitly for conformal field theories. The computational scheme is first tested on the critical point of the two-dimensional Ising model, where the two primary scaling dimensions and their respective two lowest descendant dimensions are extracted. The three-dimensional Ising model is studied next, revealing the two relevant primaries and their lowest descendants to high precision. For a more challenging case, the tricritical Ising point in two dimensions is studied with the Blume-Capel (diluted Ising) model. Here the scaling dimensions of all three fully symmetric (under lattice point group and spin-inversion transformations) primary operators are successfully isolated along with the leading descendants. The eigenvectors in the space of the two relevant primary operators are also studied and give useful information on the boundary between the ordered and disordered phases in the neighborhood of the tricritical point. Finally, the crossover from regular to tricritical Ising scaling is investigated on several points on the phase boundary of the Blume-Capel model away from its tricritical point. The scaling of the eigenvalues corresponding to tricritical descendant operators are found to be remarkably stable even far from the tricritical point. The covariance method represents a simple extension of standard analysis of correlation functions and can significantly enhance the utility of Monte Carlo simulations and other computational methods in studies of classical and quantum criticality.

We theoretically investigate how information flows when two particles interact with each other. Understanding the physical mechanisms of directional information flow is crucial for advancing information thermodynamics and stochastic computing. However, the fundamental connection between mechanical motion and causal information transfer remains elusive. To focus only on essential effects of physical dynamics, we examine two interacting Brownian particles confined in a one-dimensional potential. By simulating their Langevin dynamics, we quantify the causal information exchange using transfer entropy. We demonstrate that a mass asymmetry inherently breaks the symmetry of information flow, inducing a net directional transfer from the heavier to the lighter particle. Physically, the heavier particle, possessing larger inertia and higher active information storage, retains the memory of its trajectory longer against thermal fluctuations, thereby acting as a source of information. We analytically clarify that this net transfer is governed by a competition between the difference in memory capacity and the predictability of the particle trajectories. Furthermore, we reveal that the net information flow scales logarithmically with the mass ratio. These findings provide essential insights into the physical significance of transfer entropy and the nature of information flow in general physical systems.

Power spectral densities are often interpreted through ensemble averages and long-time asymptotics. In many experiments, however, only a single finite record is available, so spectral estimators remain broadly distributed, and the usual independence assumptions across frequencies need not hold. Here we develop an exact finite-$T$ multispectral theory for an overdamped Brownian particle in a harmonic trap. For a collection of frequencies $\left\{{\omega }_i\right\}$, we obtain an exact characterization of the joint law of the finite-time estimators $\left\{S({\omega }_i,T)\right\}$, together with a covariance-explicit Gaussian representation for the associated Fourier projections. This representation makes the observation-window-induced interfrequency correlations explicit and shows how they vanish as $T\to \infty$, thereby recovering the asymptotic Whittle picture. We then use this structure to formulate a hierarchy of spectral likelihoods for inference from a single trajectory, ranging from the factorized Whittle approximation to blockwise covariance-aware approximations in frequency space. Monte Carlo simulations validate the finite-time theory and quantify the effect of neglected cross-frequency correlations on single-trajectory estimates of the trap parameters. Our results provide a controlled finite-time benchmark for spectral inference beyond the asymptotic regime.

We investigate the angular momentum and kinetic energy of a classical charged Brownian particle in a static magnetic field within the framework of the generalized Langevin equation with Ornstein–Uhlenbeck noise. The mean kinetic energy retains its equilibrium value for all times after the external field is switched on. An analytical expression for the mean time-dependent angular momentum is derived and supported by high-precision numerical calculations. We show that, in the long-time limit, the mean angular momentum approaches a finite nonzero value. While this result might appear to contradict the Bohr–van Leeuwen theorem, we demonstrate that the system considered here does not correspond to a canonical equilibrium ensemble due to the absence of spatial confinement. In particular, although the velocity distribution thermalizes, the position of the particle remains unbounded, and the partition function over position space is not normalizable. The obtained nonzero angular momentum should therefore be interpreted as a property of a nonequilibrium asymptotic dynamical regime within the Langevin description rather than as a violation of equilibrium statistical mechanics. The present results provide a transparent analytical reference for stochastic dynamics of charged particles in magnetic fields and highlight the role of unbounded motion and noncommuting limits in such systems.

We investigate non-Markovian stochastic processes with long-range temporal memory described by a generalized Langevin (Mori-Zwanzig) equation with a power-law memory kernel. Special attention is paid to the critical regime where the system parameters lie on the boundary separating stable and unstable dynamics, leading to diffusionlike behavior with memory. We derive analytical expressions for the asymptotic behavior of the process and show that, under appropriate conditions on the memory kernel, the system exhibits superdiffusive scaling. In particular, we establish an explicit relation between the exponent of the power-law memory kernel and the growth rate of the variance. Analytical predictions are supported by numerical simulations, confirming the emergence of superdiffusive regimes in systems with long-range memory.

We study two-banded, non-Hermitian random matrices inspired by sparse neural networks with a circular, one-dimensional topology. We focus on two paradigmatic models, a Su-Schrieffer-Heeger (SSH) chain and a ladder model, which have both non-Hermitian directional bias and random sign disorder in the hoppings. The random sign disorder, which follows Dale's law, leads to localization of the eigenstates, while the directional bias drives a delocalization transition in these states. The competition between disorder and directional bias results in rich eigenspectra with loops of extended states in the complex plane surrounded by regions of localized ones, and the eigenvalues are all confined to an annular region. Furthermore, the distinct band structures of the SSH chain and ladder model lead to different delocalization phenomena. Even in the absence of disorder, tuning the directional bias can lead to an eigenvalue degeneracy, which is an exceptional point for the SSH chain but a diabolic point for the ladder. In the presence of the disorder, these special eigenvalue degeneracies are preserved and also highlight key stages in the delocalization process. For both models, increasing the directional bias initially delocalizes states starting from within the bands. For the SSH chain, for large enough directional bias, the delocalized states open up a hole in the spectrum in the complex plane, similar to prior results for single band systems. But for the ladder model, as the directional bias is increased, the states delocalize in two stages, leading to two separate loops of extended states with localized states in between. The precise contours on which the extended states reside can be predicted from the Lyapunov exponents associated with products of random transfer matrices, in agreement with direct numerical diagonalization. Although we focus on periodic boundaries, results are discussed for open boundaries as well.

We study the response of Chua's circuit driven by a chaotic signal of variable timescale. We observe that when the frequency of the driving signal is significantly lower than that of the response and the driving strength is above a threshold, Chua's circuit exhibits multiple stable attractors. The features of the attractors change as the driving strength $\varepsilon$ increases; for instance, the attractors are double-scroll at low $\varepsilon$ and are single-scroll when $\varepsilon$ is high. We also investigate generalized synchronization (GS) between the drive and the response systems by employing the auxiliary system approach. When the drive is much slower than the response, we observe different scenarios of remote synchronization (RS) between response and auxiliary units. In addition to complete synchrony between response and auxiliary systems indicating GS between drive and response, we notice that the response and auxiliary units can be lag-synchronized and can also have correlated trajectories indicating novel forms of RS. The slow drive can induce multistability between these RS states, which disappears as the frequency of the driving signal increases and becomes equivalent to that of the response of Chua's circuit.

We investigate the coarsening kinetics in a long-range variant of the persistent voter model in space dimensions $d=1$ and 2. In this model, agents can hold two confidence levels, normal and zealot. Normal agents imitate another opinion chosen at a distance $r$ with probability $P\left(r\right)\propto r^{-\alpha }$, with $\alpha >d$. On the contrary, while in the zealot state, agents keep their own opinion. Normal (zealot) agents can become zealots (normal) if their opinion is equal (different) to that of the chosen neighbor. Through numerical simulations, we show that, for any values of $\alpha$, the model belongs to the same universality class as the long-range Ising model quenched to a small (nonzero) temperature, similarly to what was already known for the nearest-neighbor case. For the one-dimensional case, we further develop an analytical treatment, which reproduces the $\alpha$-dependence of the correlation length and the functional form of the correlation function. These results not only confirm that the introduction of opinion inertia mitigates the strong interfacial noise present in the voter model, thus reinstating the basic kinetic mechanism of the Ising model, but also expand the applicability of this correspondence.

We analyze a multi-phase-field model for an epithelial monolayer with pairwise adhesions between neighboring cells following an Ornstein-Uhlenbeck process, representing the stochastic turnover of junctional molecular motors. These fluctuations in junctional adhesion result in rearrangements in the tissue, fluidizing it and producing diffusive cell motion. Similar junctional fluctuations have proven a very useful tool in the vertex model literature, and we hope they will be equally helpful to the multi-phase-field model approach. Moreover, we observe that the cells' effective diffusion coefficient depends nonmonotonically on the persistence time of the fluctuations, confirming results previously observed in the vertex model.

Previous studies dealing with Floquet stability analysis of non-zero-mean time-modulated Rayleigh-Bénard convection have shown the existence of only harmonic and subharmonic instability modes. Here, we emphasize the existence of quasiperiodic instabilities that have not yet been reported in the literature. This is achieved through both a Floquet-based analysis of the basic state and direct numerical simulations of the linearized stability equations. Particular attention is devoted to highlighting the existence of kinks in the numerically computed marginal stability curves that render difficult the detection of the stability exchange between quasiperiodic instabilities and their harmonic and subharmonic counterparts. Depending on the Prandtl number of the working fluid, such instability exchanges set in via either bicritical states or the migration of complex-conjugate pairs Floquet multipliers which can be combined to produce subharmonic responses.

Wall roughness plays a central role in determining turbulent friction in pipe flows, yet most predictive frameworks continue to characterize the wall by a single effective roughness scale. Classical datasets—notably Nikuradse's sand-grain experiments and the rough-pipe measurements of Colebrook and White—demonstrate that this description is incomplete: surfaces with comparable nominal roughness heights can exhibit markedly different friction curves, including branch splitting and multiregime behavior. Reexamining the Colebrook-White experiments, we identify clear evidence of multiscale additivity, whereby the contribution of a smaller roughness scale enters once it becomes dynamically accessible and increases approximately linearly with its areal coverage. Motivated by this observation, we develop a multiscale extension of the Gioia-Chakraborty momentum-transfer framework in which roughness elements at distinct geometric scales contribute additive increments to the total friction. In the model, each scale becomes dynamically active when its height exceeds a Reynolds-number-dependent viscous cutoff proportional to the Kolmogorov length, while its contribution is weighted by a scale-dependent coefficient representing the geometric prominence of that roughness scale. This construction generalizes the original scale-selection mechanism by allowing multiple roughness scales to participate concurrently in outer-layer momentum transfer. The resulting framework provides a unified and continuous description connecting the classical roughness-dominated Nikuradse-Strickler regime, Colebrook-White-type trends at intermediate roughness, and smooth-wall behavior. For the applications considered here, however, the model coefficients are not uniquely determined from surface properties and are selected in a data-guided manner; establishing a quantitative mapping from measured surface topography to these coefficients remains an open problem.

When a horizontal plate vibrates strongly enough, it causes small particles such as sand grains to continually bounce on it and, over time, to diffuse across its surface. This phenomenon is the cause of the well-known Chladni figure, which is drawn by a higher density of grains gathering along the nodal lines of a resonating elastic plate. Using a heterogeneous, nonresonating plate, we investigate experimentally this type of diffusion. We find that, for the most part, it is comparable to classical molecular diffusion. We can define a temperature for the bouncing grains, and the system then obeys the fluctuation-dissipation theorem. We also recover Maxwell-Boltzmann statistics at equilibrium, when temperature is uniform. However, when temperature varies across the vibrating plate, the microscopic details of the grains' dynamics affect their macroscopic behavior: Fick's law, for instance, no longer applies. Instead, our experiments support a new transport relation that was recently proposed to represent diffusion in Chladni's experiment. Finally, we propose an expression for the heat flux associated to the nonequilibrium steady state predicted by this new relation and test it against observations.

Thermodynamic uncertainty relations (TURs) bound current precision by entropy production, but transport of noncommuting (non-Abelian) charges lacks a single joint classical record of all current components. We derive an operational, process-level matrix TUR for this setting from the entropy production $\mathrm{\Sigma }=D({\rho }_{SE}^{\prime }\parallel {\rho }_S^{\prime }\otimes {\rho }_E)$. Isolating the bath divergence $D_{\mathrm{bath}}=D({\rho }_E^{\prime }\parallel {\rho }_E)$, we prove a fully nonlinear, saturable lower bound valid for arbitrary current vectors $\mathrm{\Delta }q$: $D_{\mathrm{bath}}\ge B(\mathrm{\Delta }q,V,V^{\prime })$, where the bound depends only on the transported-charge signal $\mathrm{\Delta }q$ and on the pre- and postcollision covariance matrices $V$ and $V^{\prime }$ reconstructed from separate probe measurement settings. In the small-fluctuation regime $D_{\mathrm{bath}}\ge \frac{1}{2}\mathrm{\Delta }{q}^{\mathsf{T}}{V}^{-1}\mathrm{\Delta }q+{O(\parallel \mathrm{\Delta }q\parallel }^4)$, while beyond linear response the full integral bound remains valid. Numerical strong-coupling qubit collisions illustrate the bound and its near-saturation using only local measurements on the bath probe.

Processes controlled by stochastic synthesis and degradation (SSD) are widespread in biology but their reaction kinetics are not well understood. Using methods borrowed from the theory of resetting processes, we determine the first-passage properties of a collection of independent particles that are synthesized and degraded at constant rates, and follow an arbitrary diffusive motion. At equal synthesis and degradation rates, the mean reaction time with a target site can be minimized as in stochastic resetting, and a $CV$ criterion is derived. When the degradation rate is held fixed and the synthesis costs are taken into account, an optimal synthesis rate is obtained. In bounded domains, despite particle degradation, SSD improves the mean search time compared to a single nondegrading particle if the synthesis rate exceeds a critical value which obeys a universal relation. We illustrate these findings with Brownian diffusion on the infinite line and in an interval.