We investigate the use of extended phase-space symplectic integration for simulating two different classes of electron dynamics. The first one, with one and a half degrees of freedom, comes from plasma physics and describes the classical dynamics of a charged particle in a strong, constant, and uniform magnetic field perturbed by a turbulent electrostatic potential. The second one, with an infinite number of degrees of freedom, comes from physical chemistry and corresponds to Kohn-Sham time-dependent density-functional theory. For both we lay out the extension procedure and stability condition for numerical integration of the dynamics using high-order symplectic split-operator schemes. We also identify a computationally inexpensive metric that can be used for on-the-fly estimation of the accuracy of simulations. Our work paves the way for broad application of symplectic split-operator integration of classical and quantum Hamiltonian systems with finite and infinite number of degrees of freedom by comparing different modes of implementation of extended phase-space integration.

In transport theory, physical phenomena are well described using the Boltzmann equation, which is efficiently simulated and discretized with the lattice Boltzmann method. The collision step defines the microscopic molecules behavior, and thus the simulated physical phenomena. For complex phenomena, the collision step becomes complex as well. In this paper, we propose a framework to systematically decompose the collision step into individual collision rules. Each collision rule is easier to understand, and thus a faster understanding of the whole is achieved. By inverting the process, i.e., composing multiple collision rules together, one can create collision steps that can better describe the underlying complex phenomena. This framework's applications are manyfold, from both a theoretical and an application standpoint. Shown here is the decomposition of the Robin boundary condition into the Dirichlet and Neumann boundary conditions, extending it to a partial Robin boundary condition and semipermeable reactive membranes.

We analyze thermodynamic models for fluid systems in equilibrium based on a virial expansion of the internal energy in terms of the volume density. We prove that the models, formulated for finite-size systems with $N$ particles, are exactly solvable to any expansion order, as expectation values of physical observables (e.g., volume density) are determined from solutions to nonlinear C-integrable partial differential equations (PDEs) of hydrodynamic type. In the limit $N\to \infty$, phase transitions emerge as classical shock waves in the space of thermodynamic variables. Near critical points, we argue that the volume density exhibits a scaling behavior consistent with the Universality Conjecture in viscous transport PDEs. As an application, we employ our framework to nuclear and quark matter, constructing a global quantum chromodynamics (QCD) phase diagram that reveals critical points for the nuclear liquid-gas transition and the hadron gas–quark-gluon plasma transition. We demonstrate how finite-size effects smear critical signatures, implying their potential impact on the search for the QCD critical point.

Particle transport in binary stochastic mixtures is classically modeled assuming Markovian or exponential mixing statistics but in many applications material memory invalidates the Markov assumption. For non-Markovian mixing characterized by alternating renewal processes, a transport-theoretic framework is presented that provides an exact description of transport in nonscattering random binary media with general nonexponential statistics. Our approach is to Markovianize the problem by augmenting the (material type, particle flux) state space with the age or distance from the last interface. A Chapman-Kolmogorov equation is formulated for the joint probability density of the material type, particle flux, and age and subsequently reduced to a generalized master equation (GME) in differential form. This constitutes the primary result of this work. A state-updating Monte Carlo algorithm consistent with the GME is developed and benchmarked against analytical solutions for multiple chord-length laws. For purely absorbing renewal statistical media, the GME reproduces analytical benchmarks for the equilibrium age distribution, interior mean and variance of material-conditioned fluxes, and boundary transmittance. Simulations further demonstrate that a Markov (exponential) approximation of nonexponential statistics can introduce large errors in transmittance and interior flux profiles. Finally, the reintroduction of memory due to scattering is briefly addressed through heuristic considerations.

Macroscopic active matter systems, such as bristle bots, provide a compelling platform for investigating nonequilibrium dynamics at highly visible scales. To fully leverage their accessibility, accurate mathematical models are needed to corroborate experiments. In this work, we study the motion of a free chiral hexbug (Nano-Newton Series) via video tracking and compare the results to theoretical predictions from overdamped Langevin equations for active Brownian circle swimmers (ABCs). We find good agreement between the hexbug's dynamics and ABC model predictions, particularly for the mean-squared displacement and the intermediate scattering function (ISF). Deviations between the hexbug data and the ABC model arise primarily in the short-time behavior of the real-space propagator, where translational noise is most evident. Our results generally support the use of models based on overdamped Langevin equations as a robust framework for describing hexbug motion when the influence of translational noise is negligible. Moreover, they demonstrate the sensitivity of ISF- and propagator-based analyses in characterizing active systems. Our approach opens new avenues toward refining coarse-grained models and advancing the theoretical understanding of macroscopic active systems.

The thermodynamic properties of time-delayed dynamics remain largely unexplored, especially for systems that exhibit asymptotically nonstationary behavior. Here, we investigate heat dissipation in two classes of marginally stable linear time-delayed Langevin dynamics: (i) diffusive criticality, which asymptotically manifests as scaled Brownian diffusion, and (ii) oscillatory criticality, which shows oscillation with diffusive amplitude. By analytical derivations, we find fundamentally different thermodynamic signatures: the average heat dissipation rate asymptotically approaches a constant for diffusive criticality but diverges linearly with oscillations for oscillatory criticality, despite both showing linearly growing variance over time. We discuss in detail how the heat dissipation rate behaves differently as the dynamics asymptotically approaches these two criticality classes from the stable regime. We also numerically study the probability distributions of heat dissipation rates for both types of critical dynamics. Our results demonstrate that nonstationary time-delayed dynamics with similar time-dependence of variance can yield qualitatively distinct heat dissipation behaviors, depending on the underlying dynamical details. This work provides a concrete foundation for future investigations into thermodynamic properties of general nonlinear time-delayed systems.

We study the Ising model under a time-varying, but spatially homogeneous, Gaussian random magnetic field. In the Monte Carlo simulations, we go beyond the standard analysis of the order parameter by measuring the magnetization probability distribution as a function of temperature and field strength, and by computing the time required for the system to escape from a completely ordered state of the magnetization. We identify three distinct phases: a broad-paramagnetic phase, a broad-ferromagnetic phase, and a bona fide ferromagnetic phase. These broad phases display wide magnetization distributions that tend toward limiting forms that remain finite in both height and width in the thermodynamic limit. The transition between the broad-paramagnetic and broad-ferromagnetic phases is noise-induced and, for small field amplitudes, occurs at the critical temperature of the field-free Ising model. The transition from the broad-ferromagnetic to the ferromagnetic phase occurs at lower temperatures and is discontinuous, yet it does not fall into the conventional first-order class. Instead, it is characterized by a diverging escape time from an ordered magnetization state.

Extreme events are the ones for which the magnitude of the event is much larger than its typical values. They have been extensively investigated on classical dynamical and stochastic processes on networks. In this work, in analogy with well-studied extreme events of random walks, the extreme events of quantum walks on regular lattices, a scale-free network, and Erdős-Rényi network are studied. Due to unitary quantum evolution, the quantum walk dynamics usually differs from that of the classical random walks, and hence we expect extreme event properties to be different in classical and quantum settings. In contrast to this expectation, we report that extreme events of phase coherent quantum walks are qualitatively similar to that of classical random walks. We show that this counterintuitive behavior originates from the dominance of nodal fluctuations over internode correlations in disordered network structures. In particular, the occurrence probability for extreme events on scale-free and Erdős-Rényi networks displays a decaying power law with the degree of nodes. That is, the extreme event probability is larger for small degree nodes compared to the hubs on the network, in qualitative agreement with corresponding classical random walk results. Further, it is shown that extreme event probability scales with the threshold used to define extreme events.

We present a model of a crawler consisting of several suction units distributed along a straight line and connected by springs. The suction units are rudimentary proprioceptors-actuators, which sense binary states of compression versus elongation of the springs and can either adhere or remain idle. Muscular contraction is not controlled by the crawler but follows an endogenous, stereotyped wave. The crawler is tasked to learn patterns of adhesion that generate thrust in response to the wave of contraction. Using tabular $Q$-learning we demonstrate that crawling can be learned by trial and error and we ask what are the benefits and limitations of distributed versus centralized learning architectures. We find that by centralizing proprioceptive feedback and control, the crawler leverages long-range correlations in the dynamics and ride the endogenous wave smoothly. The ensuing benefits are measured in terms of both speed and robustness to failure, although they come at increased computational cost. At the opposite extreme, purely distributed feedback and control only leverages local information and yield a jerkier and slower crawling, although computationally cheap. Intermediate levels of centralization can negotiate fast and robust crawling while avoiding excessive computational burden, demonstrating the computational benefits of a hierarchical organization of crawling. Our model unveils the trade-offs among crawling speed, robustness to failure, computational cost, and information exchange that may shape biological solutions for crawling and could inspire the design of robotic crawlers.

Epiboly, during which a tissue closes around the surface of the egg, pervades animal development. This epithelial gap closure involves cell intercalations at the edge of the gap, but the interplay between these plastic cell rearrangements and the elasticity of the tissue is not understood. Here, inspired by serosa closure in the beetle Tribolium, we study this interplay in a minimal continuum model of the closure of a circular gap bounded by a contractile actomyosin cable. We reveal how two different closure mechanisms emerge at the tissue scale from the energy barrier $E_{\text{b}}$ to and the energy $\mathrm{\Delta }E$ released by intercalation: If $E_{\text{b}}\gg \mathrm{\Delta }E$, cells intercalate into the gap to close it. For a fluidized tissue in which $E_{\text{b}}\ll \mathrm{\Delta }E$, however, cells deintercalate from the boundary into the bulk of the tissue, consistently with Tribolium serosa closure. We also discover an emergent mechanical role of the inhomogeneities of the actomyosin cable observed in Tribolium. Our work thus explains the mechanical basis for Tribolium serosa closure and processes of epiboly and wound healing more generally.

The energy landscape for soft sphere packings exists in a high-dimensional space and plays host to an astronomical number of local minima in a hierarchical and ultrametric arrangement. Each point in the landscape is a configuration that can be mapped to its inherent state, defined as the local minima that the configuration will flow to under perfectly overdamped continuous dynamics. Typically, discrete in time dynamics are used to computationally find local minima, but it is not known whether these algorithms are capable of reliably finding inherent states. Here, we use steepest descent dynamics to find the distribution of the largest time step, ${\delta }_{\text{best}}$, which finds the inherent state. We find that ${\delta }_{\text{best}}$ is Weibull distributed. Additionally, for systems of $N$ particles, ${\delta }_{\text{best}}$ falls rapidly with increasing $N$, with a functional form somewhere in between an exponential and inverse power law, and is weakly dependent on $d$ and $\phi$, where $d$ is the packing dimension and $\phi$ is the packing fraction. We argue that this rapid fall is due to saddle points in the energy landscape. Our results suggest that it is impossible, in practice, to reliably find inherent states for systems of about 64 particles or more.

Driven single-file motion, in which particles move unidirectionally along one-dimensional channels, sets the paradigm for a wide variety of one-dimensional directed movements, ranging from intracellular transport and urban traffic to ant trails and controlled robot swarms. Motivated by the phenomenologies of these systems in closed geometries, regulated by number conservation and bottlenecks, we explore the domain walls (DWs) or shocks in a conceptual one-dimensional cellular automaton with a fixed particle number and a bottleneck. For high entry and exit rates of the cellular automaton, and with sufficiently large particle numbers, the DWs formed are independent of the associated rate parameters, revealing a hitherto unknown universality in their shapes, which are, however, enclosed by nonuniversal boundary layers. In contrast, the DWs do depend upon these parameters, if small, and hence have nonuniversal shapes, but without boundary layers. Nonuniversal delocalized DWs can be formed by additional tuning of the control parameters. Our predictions on the DWs are testable in model experiments.

The response of a complex system to a slow varying external force often displays a jump discontinuity in the order parameter near the critical point. However, this discontinuity is not usually a single jump but rather breaks into smaller jumps which makes it difficult to locate the critical point on approaching its vicinity based only on simulations, in the absence of exact results. Our work is a small effort in understanding these breaks in jump through the hysteretic response of a classical Ising spin system to an external field, $h$, in the context of a nonequilibrium zero-temperature random field Ising model on dilute systems. We consider a Bethe lattice with coordination number, $z=4$, and dilute a fraction $(1-c)$ of the sites. Therefore, the lattice now consists of sites with varying $z=4,3,2,1$ and possibly few isolated sites $(z=0)$, depending on the concentration $c$. We obtain the exact solution of the magnetization curve, $m\left(h\right)$ vs $h$, for the entire lattice as well as for each sublattice of different $z$ coordinated sites, $m_4\left(h\right),m_3\left(h\right),m_2\left(h\right),m_1\left(h\right),m_0\left(h\right)$. The discontinuity in total magnetization is the result of the superposition of the jumps of different $z$ coordinated sites and observed at the same value of external field, $h_{\mathrm{crit}}$. The dominant contribution to the jump comes from those sites with higher concentration and larger $z$. However, the triggering sites responsible for large jumps are mostly $z\ge 3$. We test this on cubic lattices as well, where exact results are not available. We hope our analysis will help in understanding fluctuations around a jump in numerical simulations as well as experiments.

We investigate the dynamics of the three-state majority-vote model on a simple cubic lattice. In the model, each site adopts the majority opinion of its neighbors with probability $1-q$, and a different opinion with probability $q$ (the noise parameter). We monitor the magnetization, the magnetic susceptibility, and the fourth-order Binder cumulant using Monte Carlo simulations. The magnetization shows a rapid change near the critical noise parameter $q_c$, consistent with the behavior expected at a weak first-order phase transition. The critical exponent ratio $\gamma /\nu =2.91\left(12\right)$, close to three, is obtained from the peaks in the magnetic susceptibility. Scaling analysis of the susceptibility confirms $\gamma /\nu =2.91$ and yields the correlation-length exponent $\nu \approx 1/3$ corresponding to the weak first-order phase transition. Additional evidence for the weak first-order transition is provided by the Binder cumulant, which develops a pronounced negative dip near $q_c$ for large system size. These results demonstrate that the three-state majority-vote model on a simple cubic lattice undergoes a weak first-order phase transition.

We consider the three-spin Ising model to study the effect of a three-spin interacting term on bipartite entanglement between adjacent spins. The three-dominated disordered region has tripartite entanglement causing a vanishingly small concurrence, while it acquires a maximum value around the critical points. Considering the above model as an environment, we construct a generalized central spin model where two central spins, initially in an unentangled pure state, are coupled locally to two distinct sites of the environmental spin chain. We study the generation of mixed-state entanglement between the central spins when the transverse field of the environment is kept fixed, and suddenly quenched, referring to equilibrium and nonequilibrium dynamics of the central spins, respectively. For the critical environment in the equilibrium, the concurrence shows a dip-revival structure governed by quasiparticle movement. In the nonequilibrium study, we find an initial growth of concurrence followed by a two-stage fall for the interphase quench, which is governed by dynamic decoherence channels. The central spins are maximally entangled for a quench in the vicinity of a multicritical point, which arises due to three-spin interaction only. The concurrence becomes long-lived for an intraphase quench, and this sustainability depends on the strength of the three-spin interaction. Therefore, the three-spin interaction indeed helps in generating bipartite entanglement in the central spins.

We propose an index-space renormalization group (RG) approach to compare and collapse eigenvalue densities across system sizes in structured random matrix ensembles with rank-ordered power-law variance profiles. The approach is to fix a natural spectral scale by letting the model normalization run with size, turning raw spectra into comparable, collapsed density curves. We illustrate this construction on generalizations of two classic random matrix ensembles—Wigner and Wishart—equipped with rank-ordered power-law variance profiles. We use random matrix theory methods to derive self-consistent fixed-point equations for the resolvent to compute their eigenvalue densities. We define an RG scheme based on index-space decimation and compute the Beta function controlling the RG flow as a function of the variance profile power-law exponent. The running normalization leads to spectral collapse which we confirm in simulations and solutions of the fixed-point equations. We expect that the scale-fixing principle underlying our RG construction extends to other structured ensembles, provided an appropriate renormalization map can be defined.

The fractional Kuramoto-Sivashinsky equation (F-KSE) describes a class of spatiotemporal chaotic systems characterized by nonlocal dissipative interactions. Controlling such systems presents significant challenges due to the interplay between nonlinear convection and fractional diffusion. This study investigates a model-free feedback control framework to stabilize the F-KSE. By formulating the control problem as a high-dimensional optimization task, a continuous control law is derived without assuming prior knowledge of the governing equations. Numerical experiments demonstrate that the proposed controller effectively suppresses chaotic wave shedding, forcing the system into a near-trivial stationary state with an energy reduction consistently exceeding 96% (reaching a peak of 98.55% across the diffusive regime). Spectral analysis reveals that the stabilization is achieved through broadband suppression of dominant instability modes. Most notably, a sensitivity analysis demonstrates that a single control policy, trained at a specific fractional order ($\alpha =1.85$), exhibits universal robustness across the regime $\alpha \in [1.0,2.0]$ without retraining. This suggests the data-driven agent identifies a dominant stabilization mechanism that primarily counteracts energy-containing structures driven by the convective nonlinearity. The resulting policy is largely invariant to the underlying dissipative structure.

Visibility graphs are spatial interpretations of time series. When derived from the time evolution of physical systems, the graphs associated with such series may exhibit properties that can reflect aspects such as ergodicity, criticality, or other dynamical behaviors. It is important to describe how the criticality of a system is manifested in the structure of the corresponding graphs or, in a particular way, in the spectra of certain matrices constructed from them. In this paper, we show how the critical behavior of an Ising spin system manifests in the spectra of the adjacency and Laplacian matrices constructed from an ensemble of time evolutions simulated via Monte Carlo (MC) Markov chains, even for small systems and short MC steps. In particular, we show that the number of spanning trees—or its logarithm—which represents a kind of structural entropy or topological complexity here obtained from Kirchhoff's theorem, can, in an alternative way, describe the criticality of the spin system. These findings parallel those obtained from the spectra of correlation matrices, which similarly encode signatures of critical and chaotic behavior.

We examine how heterogeneous swarms, mixing exploratory and exploitative agents with distinct decision rules, consistently outperform homogeneous ones where each agent balances exploration and exploitation individually, performing experiments in two contrasting deployment scenarios. Using odor fields from state-of-the-art direct numerical simulations of the 3D Navier-Stokes equations, we find that policy diversity typically allows the group to reach the source of the odor more efficiently by mitigating the detrimental effects of spatiotemporal turbulent correlations. These findings provide insights into collective search behavior and offer promising strategies for the design of robust, bioinspired search algorithms in engineered systems.