We present a realizable entropic lattice Boltzmann method (RELBM) for scalar transport at high Péclet (Pe) number. The method combines an ADE-tailored entropic relaxation with a nonorthogonality correction to ghost-mode damping and a strictly conservative population-space realizability limiter activated only when required to enforce positivity. Comprehensive benchmarks including deformational mixing, Graetz transport, and Taylor dispersion up to $\mathrm{Pe}=2\times {10}^5$, demonstrating suppression of spurious oscillations and quantitative agreement with theory. Furthermore, pore-scale simulations in a homogeneous geometry up to $\mathrm{Pe}={10}^4$ resolve scalar-dissipation dynamics consistent with intermediate lamellar and late-time Fickian scalings. These results establish the method's robustness and physical fidelity for multiscale advection-diffusion dynamics across diverse systems.

The ability to quantify the similarity of stochastic processes is important in a wide range of areas including communications, simulation, and operational research. Such processes are commonly modeled as Markov Chains and so a natural way to compare their similarity is to compute distances between pairs of Markov Chains. We propose a distance function on the space of stochastic matrices that draws on ideas from information geometry. We first show that the Bhattacharyya angle is an appropriate measure of distance between Markov chain sequences, drawing on examples taken from healthcare processes and deriving bounds on the convergence of the distance and mixing times. We then extend these ideas to derive a distance measure which enables direct comparison of the transition matrices themselves. Our result is a true metric which has a closed form and is efficient to implement for numerical evaluation. In the case of ergodic Markov chains, it is shown that considering either the Bhattacharyya angle on Markov sequences or our stochastic matrix distance leads to the same distance between models.

Nonequilibrium response theory is a fundamental framework for understanding how physical systems respond to perturbations. Recently, a mutual linearity has been discovered for Markov jump processes using linear algebra analysis. This mutual linearity states that two observables are linearly dependent on each other in the long-time limit when the transition rate of a single edge is altered. It has also been extended to nonstationary cases for current observables. In this work, we provide a trajectory-based derivation of mutual linearity utilizing the trajectory-level linear response theory. The trajectory approach allows us to generalize the mutual linearity to nonstationary relaxation dynamics for state observables and counting observables. Our results shed light on the fundamental response properties far from equilibrium and the trajectory-level origin of mutual linearity. Our trajectory-based approach makes it possible to generalize the mutual linearity to a broader class of systems, including diffusion processes and open quantum systems.

We solve the Fokker-Planck equation for a Brownian particle in a tilted cosine potential and derive the intermediate scattering function (ISF), which captures the full spatiotemporal dynamics of the system. The model consists of a single overdamped Brownian particle in one dimension. We derive a generalized ISF comprising two wave vectors to describe correlations in the periodic potential. Exploiting the periodicity via Bloch's theorem, we formulate the problem within a spectral-theoretical framework and numerically compute the corresponding eigenfunctions and eigenvalues, from which we obtain the ISF and the probability density. Using time-dependent perturbation theory, we expand the ISF and derive low-order moments, including the mean-square displacement, time-dependent diffusivity, skewness, and the non-Gaussian parameter. Our analytical results are validated by Brownian-dynamics simulations and analyzed focusing on different regimes of the tilting force. The results are compared to a harmonic approximation and the deterministic limit.

Constant-intensity (CI) waves are plane-wave-like solutions that are known to propagate in non-Hermitian inhomogeneous media with complex external potential (with the real part corresponding to the refractive index and the imaginary part representing a distribution of gain and loss) while keeping their field amplitudes space-time independent at the expense of acquiring a nonlinear phase. In this paper, it is shown that CI waves can exist in certain situations when the medium is Hermitian—in which case the external potential is purely real—provided that higher-order diffraction or dispersion effects are present. To this end, the one-dimensional nonlinear Schrödinger equation with fourth-order (quartic) diffraction is used to construct examples of localized and periodic real external potentials that support CI waves. Interestingly, the class of potentials presented is directly connected to solutions of the modified Korteweg-de Vries equation and the more general Gardner equation, both of which are well-studied integrable partial differential equations. Throughout a combination of linear stability analysis and direct numerical simulations, regions in parameter space are identified for which CI solutions are predicted to be stable.

We study exact quantum resonances in the double kicked top (DKT), a driven spin model that extends the quantum kicked top (QKT) by introducing an additional time-reversal symmetry-breaking kick. By expressing the dynamics in terms of effective parameters $(k_r,k_{\theta })$, we analytically show the exact periodicity of the Floquet operator for integer and half-odd integer spin $j$ at $k_r=j\pi /2$. The analysis is further extended to $k_r=j\pi /4$ for integer spin $j$ and proves the absence of recurrences for half-odd-integer spin $j$. Remarkably, resonances are observed across the time-reversal symmetry (or its breaking) and generalize the QKT resonances. Spectral statistics and entanglement entropy in the pseudoclassical limit reveal qualitatively distinct behavior at the two resonances. Near $k_r=j\pi /2$, the level-spacing ratio distribution evolves from Poisson statistics (PS) to Gaussian orthogonal ensemble (GOE) statistics, indicating a crossover from resonant dynamics to quantum-chaotic behavior through an intermediate regime. No comparable intermediate-statistics regime is observed in the case of $k_r=j\pi /4$. In the time-reversal symmetric case $k_{\theta }=0$, our computations of the rate function associated with fidelity show the dynamical quantum phase transition (DQPT) only for half-odd-integer $j$ values. Our work demonstrates the DKT as a controllable platform where resonance, integrability, and quantum chaos can be tuned for any system size through the parameters $k_r$ and $k_{\theta }$, making the DKT a useful setting for quantum control and information processing applications.

We show that higher-order interactions naturally emerge from time-delayed pairwise coupling in Kuramoto oscillators. By expanding the delayed pairwise coupling to the second order, we derive a delay-free Kuramoto model possessing both pairwise and three-body interactions. Numerical simulations and stability analysis demonstrate that the three-body Kuramoto model and the time-delayed pairwise Kuramoto model exhibit qualitatively consistent synchronization transitions under appropriate conditions. In particular, the bistability arising in the time-delayed Kuramoto model is accounted for by the three-body interactions. Our findings reveal that time delays can be recast effectively as higher-order interactions, providing an insight into how coupling delays shape collective dynamics.

The elliptic cylindrical Kadomtsev-Petviashvili (ecKP) equation is derived from the incompressible Euler equations governing surface gravity waves with nearly elliptic fronts. Using Hirota's bilinear method, this paper systematically investigates ring solitons, lump chains, and lump waves of the ecKP-I equation in physical coordinates. It is shown that ring solitons and ring-type lump chains appear only after a critical time; they originate from a centrally symmetric bulge on the water surface that collapses and subsequently propagates outward. The ring soliton is unstable and, under perturbation, gives rise to lump waves or lump chains. In contrast to the KP-I equation, lump waves in the ecKP-I equation exhibit several distinctive features: a dark lump wave with a larger amplitude propagates more slowly and its speed possesses an upper bound; in the standard two-lump solution, the lump waves initially propagate with equal amplitudes along curved trajectories, their collision involves energy transfer, and after the interaction they move along straight lines; degenerate lump waves do not collide, they travel with varying instantaneous velocities while sharing the same asymptotic amplitudes and velocities as their standard counterparts. These findings reveal fundamental properties of asymptotic solutions to the incompressible Euler equations, deepen our understanding of gravity-capillary waves, and may offer new insight into the formation mechanisms of small-scale shallow-water waves.

This study investigates the dynamical origins and statistical properties of extreme events (EEs) in a diffusively coupled theoretical Brusselator system, extending from pairwise interactions to globally coupled networks. Statistically, the emergence of EEs is characterized by heavy-tailed probability density functions and exponential interevent interval distributions, alongside an analysis of the complementary cumulative distribution function and return periods. To elucidate the underlying generative mechanism, we employ invariant manifold computations and vector field divergence analysis. Our results demonstrate that EEs are triggered by a critical region formed by the geometric alignment of stable and unstable manifolds near a saddle-type invariant set governed by the Shilnikov mechanism. Furthermore, extending the analysis to a globally coupled network reveals that network dimensionality does not affect the prevalence of EEs. Finally, these numerical findings are corroborated by experimental observations from an analog electronic circuit, confirming the robustness of these dynamical phenomena in physical systems.

The importance of Fisher information is increasing in nonequilibrium thermodynamics, as it has played a fundamental role in trade-off relations such as thermodynamic uncertainty relations and speed limits. In this work, we investigate temporal Fisher information, which measures the temporal information content encoded in probability distributions, for both classical and quantum systems. We establish that temporal Fisher information is bounded from above by physical costs, such as entropy production in classical Langevin and Markov processes, and the quantum entropy production and the expectation of the effective interaction Hamiltonian in open quantum systems. Conversely, temporal Fisher information is bounded from below by statistical distances (e.g., the Bhattacharyya arccos distance), leading to classical and quantum speed limits that constrain the minimal time required for state transformations. We perform numerical simulations on two quantum dot models to validate the obtained bounds. Our work provides a unified perspective on speed limits from the point of view of temporal Fisher information in both classical and quantum dynamics.

In this paper, we have presented the three-dimensional dynamics in the velocity space of a Brownian particle coupled to a non-Markovian thermal bath in the presence of a magnetic field (MF), as well as external deterministic and stochastic force fields. The directions of the MF and the deterministic force are taken to be arbitrary. Furthermore, there are no restrictions on the nature of correlation or the strength of the components of the Gaussian thermal and external noises. We solve the coupled Langevin equations of motion and demonstrate that, in the steady state, a nontrivial symmetry breaking emerges in the motion, manifested in the components of the average velocity resulting from the combined effects of the MF and the deterministic force. The average velocity in this state may be independent of the nature of the thermal bath. We further identify that, in the absence of the external stochastic force (ESF), the relevant variances do not depend on the magnetic field for Markovian dynamics (MD). However, for the corresponding non-Markovian dynamics (NMD), these quantities do depend on the MF, serving as a generic signature of non-Markovianity. Although the equations of motion are coupled, the equal-time cross-correlations vanish for MD in the absence of ESF, whereas they may become nonzero for NMD provided the magnetic field has at least two nonzero components. This can be regarded as another generic signature of non-Markovian dynamics. The consequences of these signatures are discussed in terms of the information entropy, the nonequilibrium kinetic temperature, and the entropic temperature. Writing a Fokker-Planck-like equation (FPLE) in the velocity space for a Brownian particle coupled to a Markovian thermal bath in the presence of nonwhite Gaussian external noise remains an open problem. It is noteworthy that we formulate the FPLE corresponding to the coupled Langevin equations of motion, which appears to be an even more complex and open issue. Using this equation, we compare the relaxation processes in Markovian and non-Markovian dynamics in terms of the total entropy production, the entropy production of irreversible thermodynamics, and their respective bounds.

We perform a numerical study of random walks (RWs) on 3D lattices with random and periodic distributions of blocked sites, analyze the dependence of effective diffusion coefficients $D_E$ on the effective porosity $\epsilon$, and show applications to diffusive solute transport in some porous materials. In the low-porosity regime of randomly disordered lattices (typically $0.03\lesssim \epsilon \lesssim 0.2$), where the total porosity exceeds $\epsilon$ by more than $1\%$, reliable estimates of $D_E/D_0$ are obtained by assuming that the mean square displacement is a sum of normal and anomalous contributions ($D_0$ is the free diffusion value). An extended form of the Archie's law, $D_E/D_0\approx A{\epsilon }^m$, is obtained with an uncommonly large exponent $m\approx 5$ and $A>1$, in agreement with the universal value $m=4.9\pm 0.3$ predicted by scaling arguments. The fit of diffusion data in a silty clay loam soil gives $m\approx 4.8$ and $A>1$, confirming the absence of long-range correlations in that pore system. This approach advances over previous studies that related $D_E/D_0$ to the total porosity and required an estimation of percolation thresholds. In periodic lattices with narrow planar gaps and the same low-porosity range, fits with $m\approx 1$ and $A<1$ are explained by the long-range correlations of the (nontortuous) pore systems. Similar values of $m$ and $A$ are obtained in ion diffusion and conductivity data in bentonite and granite samples, which may be a consequence of fractures that cross their pore systems. In the high-porosity regimes of the same lattices and of deposits produced by a growth model ($\epsilon \ge 0.8$), random walk values of $D_E/D_0$ are significantly smaller than the values of the diffusion equation [obtained in effective medium approximations (EMA) of Bruggeman or Maxwell]. This occurs because RWs do not reach the diffusion limit in lengths near the lattice constant, which is the order of magnitude of the widths of blocked domains; however, those EMA are recovered for RWs on lattices with obstacle sizes much larger than the lattice constant. This analysis suggests deviations from the EMA whenever RW models are used to model Knudsen diffusion. Finally, from intermediate to high porosities of randomly disordered lattices ($\epsilon \gtrsim 0.3$), fits of the original Archie's law $D_E/D_0={\epsilon }^m$ give $2<m<3$, which is the range obtained in several materials and suggests that their pore organization may be random at long distances.

We are looking for different phases in hidden Markov models (HMMs). By analyzing the stationary solution of the master equation, we discover different situations with localized or delocalized distributions for the stationary distributions of the master equation. We hypothesize that these phases are related to the relaxation dynamics of the HMM ensemble. We have derived precise phase transition points. We test whether the behavior of the HMMs and their associated numerical algorithms change near the transition points. We find that the accuracy of the Viterbi and Baum-Welch algorithms sometimes is worse near the phase transition, which contradicts the edge of chaos hypothesis.

We investigate equilibration dynamics in a lattice-gas model with spatially restricted coupling to a particle reservoir. Using kinetic Monte Carlo simulations, we isolate the role of reservoir-access geometry by comparing spatially uniform exchange with exchange confined to a limited access region while keeping the thermodynamics and diffusion kinetics fixed. Under uniform access, equilibration is diffusion controlled, and relaxation times increase monotonically with diffusion barrier. In contrast, restricted access introduces an additional kinetic bottleneck without altering the final equilibrium state. The resulting slowdown is nonmonotonic: it is most pronounced at intermediate diffusion barriers, where reservoir access and internal diffusion compete, and weakens when intrinsic diffusion becomes the dominant limitation. Under these conditions, equilibration also becomes observable dependent. Coarse observables such as total coverage can suggest stationarity on a different timescale from internal configurational observables such as the fractional occupation $f_O\left(t\right)$. Sensitivity tests of the stationarity criterion and finite-size checks confirm that the restricted-access delay is not an artifact of the numerical equilibration definition or lattice size. These results show that reservoir accessibility can act as an independent kinetic control parameter, generating delayed and observable-dependent relaxation even when equilibrium thermodynamics remain unchanged.

Alternating (temporally period-2) stripes, clusters, and labyrinths have been observed in chemical and biochemical reactions, in Min-protein dynamics in E. coli and in vitro systems, and in calcium alternans in cardiac myocytes. However, the mechanisms underlying the formation of these spatiotemporal patterns and the transitions among them remain incompletely understood. In this article, we use an amplitude-equation (AE) approach to perform theoretical analysis and numerical simulations to elucidate the mechanisms of the alternating pattern formation and selection, and we then use reaction-diffusion models to validate the predictions of the AE model. It was shown previously that in chemical reactions and cardiac myocytes, a global feedback loop plays a key role in the formation of alternating clusters. Based on previous AE models developed to describe cardiac alternans dynamics, we first develop an AE model that incorporates either a spatially uniform global feedback (UGF) loop or a spatially nonuniform global feedback (NUGF) loop. The NUGF is represented by a spatially Gaussian-weighted function. We then use the AE model to conduct nonlinear stability analysis to reveal the mechanisms underlying the emergence of alternating patterns under different feedback conditions. Under positive UGF, no patterns can form. When the UGF is negative, the stable patterns are only multiple stripes and circular clusters. For stripe patterns, they may be spatially periodic or random as long as they satisfy the requirements for pattern selection. For circular clusters, a medium can support one or multiple circular alternating clusters of the same radius depending on the size of the medium. Under NUGF, in addition to stripe and circular-cluster patterns, lateral instability arises when the width of the Gaussian function falls within an intermediate range, leading to transitions from stripes or circular clusters to labyrinths. Other initial-condition-dependent patterns are also observed under NUGF. Under UGF, the width of the stripe can be periodic or random, but under NUGF, the patterns become less random in space as the feedback strength increases. Finally, we incorporate the UGF and NUGF loops into several reaction-diffusion models, including the Belousov-Zhabotinsky reaction model, the carbon monoxide oxidation model, and the periodically paced FitzHugh-Nagumo model. These models successfully reproduce the alternating pattern dynamics predicted by the AE model, validating the theoretical predictions.

Swarmalators, a prototypical model that integrates temporal rhythms with spatial swarming, have been widely used to explore the collective dynamics observed in active-matter systems. Although numerical simulations have revealed a variety of collective states, a general theoretical framework for the stability and bifurcations of the states remains unavailable. Here, by the model of one-dimensional ring-structured swarmalators with general distributions of natural frequencies and velocities, we conduct a systematic theoretical analysis of the stability and bifurcations of four representative collective states observed in simulations: the desynchronization state, the phase-wave state, the synchronization state, and the mixed state. We show that the macroscopic dynamics are governed by a low-dimensional invariant manifold, namely the generalized Ott-Antonsen manifold, and further establish that the same manifold underlies the collective dynamics of high-dimensional agent models, thereby unifying these seemingly different descriptions within a common reduction framework. Building on this connection, we derive stability conditions and bifurcation boundaries for the collective states and construct a bifurcation diagram in the two-parameter coupling plane, with theoretical predictions validated by large-scale numerical simulations. Our results clarify the dynamical origins of state selection in swarmalator systems and provide a theoretical foundation for analyzing nonequilibrium phase transitions in active-matter systems with coupled internal rhythms and spatial motions.

Extracellular vesicles (EVs) hold great promise in drug delivery, disease diagnosis, and treatment; however, the inability to control EVs biogenesis critically limits their therapeutic and diagnostic potential. Although regulatory mechanisms for biochemical cues have been extensively studied, the principles governing how diverse mechanical cues from the extracellular microenvironment orchestrate EV secretion are poorly understood, hindering the development of scalable production strategies. Here, we resolve this by introducing a theoretical model that identifies membrane reservoir depletion as a universal biophysical switch for EV release. We discover that EV secretion is directly activated by the depletion of the membrane reservoir and the consequent rise in membrane tension. This tension-mediated mechanism provides a unifying framework that reconciles disparate experimental observations under various biophysical perturbations, including cell spreading, osmotic shock, contractile perturbation, and substrate stiffening. Furthermore, we identify the membrane reservoir size as a key intrinsic parameter setting the threshold for mechanical activation of EV secretion, offering a rationale for engineering high-yield producer cell lines. Our work thus establishes a unifying mechanochemical framework for EV secretion, explaining disparate experimental observations and providing a quantitative design principle for optimizing EV production.

Recent work [Phys. Rev. Lett. 134, 241901 (2025); Phys. Rev. D 112, 054506 (2025); Phys. Rev. D 112, 014514 (2025)] has shown that the (block) Lanczos algorithm can be used to extract approximate energy spectra and matrix elements from (matrices of) correlation functions in quantum field theory, and identified exact coincidences between Lanczos analysis methods and others [Eur. Phys. J. A 61, 26 (2025); Phys. Rev. D 112, 074506 (2025)]. In this work, we note another coincidence: the Lanczos algorithm is equivalent to the well-known Rayleigh-Ritz method applied to Krylov subspaces. Rayleigh-Ritz provides optimal eigenvalue approximations within Hermitian subspaces, including those arising in the decompositions of non-Hermitian operators describing noisy data. We explore the relation between Lanczos and Prony's method, their block generalizations, generalized pencil of functions (GPOF), and methods based on the generalized eigenvalue problem (GEVP), and find they all fall into a larger “Prony-Ritz equivalence class,” identified as all methods which solve a finite-dimensional spectrum exactly given sufficient correlation function (matrix) data. This equivalence allows simpler and more numerically stable implementations of (block) Lanczos analyses.