We generalize the Hunt-Crossley (HC) model to the case compatible with external potential fields, attributing to a small dimensionless parameter, and employ the perturbation method to derive the perturbation and asymptotic solutions of the coefficient of restitution. The numerical results reveal that the perturbation solution decreases with the impact velocity for higher velocities and asymptotically approaches the case without any external force, while dropping into a critical sticking velocity for lower velocities. Finally, we analyze the dissipative properties of the bouncing ball system and demonstrate that a localized dispersive structure consistent with experiments appears after mapping the chaotic phase diagram to the perturbation solution. The proposed model and its solutions may be applied to study other collision-related nonlinear dynamic systems.

The presence of chaos in classical Hamiltonian systems is witnessed by its maximal Lyapunov exponent, that quantifies the instability of motion through the exponential growth of indicators such as the trace of the stability matrix or the out-of-time-ordered correlator. On the other hand, integrable dynamics near unstable fixed points, which are in turn characterized by a stability exponent, can also induce such exponential growth. Following the paradigm of integrability breaking as driven by nonlinear resonances that hallmarks the genesis of chaos, the integrability-chaos transition is universally described by a periodic perturbation applied to a generic pendulum. Remarkably, this means that within the corresponding separatrix dynamics, which is an unavoidable a consequence of the resonance scenario, both instability exponents must play a role as both dynamical regimes coexist. We report here the universality of the transition from instability to Lyapunov exponents, thus completing the resonance scenario at the level of indicators based on exponential growth. To achieve this goal we obtain an analytical expression for the time evolution near separatrices, which enables us to derive an analytical expression for the exponent that characterizes chaos and its transition from local instability to global chaos. We support our claim for the universality of this mechanism by studying two paradigmatic examples of the integrability-to-chaos transition, namely, the kicked rotor and the kicked Bose-Hubbard dimer.

The dynamical behavior of water in magnesium perchlorate aqueous solutions is investigated through molecular dynamics simulations using the TIP4P/2005 water model and the recently extended Madrid-2019 force field. This study is motivated by the recent radar detection of liquid water underneath the Martian South Pole. We explore the supercooled regime for salt concentrations up to 24.4 wt %. In the region of mild supercooling we analyze the water oxygen self-intermediate scattering functions. Our results show that the relaxation dynamics of water is well described by the mode coupling structural relaxation in this region. Upon further cooling, a fragile-to-strong crossover is observed for all investigated concentrations. Below the crossover, activated processes maintain the ergodicity. Notably, the addition of magnesium perchlorate induces a downward shift in both the mode coupling temperature and the fragile-to-strong crossover temperature. This combined effect extends the range of existence of the supercooled liquid regime to lower temperatures compared to bulk water. These findings support the hypothesis that perchlorate aqueous solutions can persist in a thermodynamically metastable liquid state at the low-temperature conditions of the Martian subsurface.

We consider a minimalist model of polar chiral active matter: overdamped, self-propelled agents coupled through a localized Kuramoto-Sakaguchi interaction, which causes alignment. Intrinsic frustration drawn from a broad distribution constitutes a temperature for the ensemble. In the comoving frame of the local order parameter, the agent dynamics reduce exactly to the Adler equation, placing each agent in a tilted washboard potential: trapped agents are phase-synchronized, and we demonstrate thereby that synchronization (phase rigidity) is maintained by information supercurrents; agents that are running in this potential form a resistive bath. The model is therefore formally isomorphic to a disordered, resistively shunted Josephson array, and a Monte Carlo sweep over the frequency dispersion empirically recovers the disorder-broadened Adler-Ohmic crossover of the ensemble-averaged slip velocity. Lifting the dynamics from $S^1$ to $S^2$, the polar alignment torque (the Kuramoto term) is geometrically equivalent to the Gilbert-damping term of the Landau-Lifshitz-Gilbert equation; the mapping establishes an effortless azimuthal precession, yielding a Goldstone-mode dispersion that carries an effective inertia $\propto R^2$, where $R$ is the local order parameter. This furnishes a microscopic basis for the spin-wave transport assumed in inertial-spin models of flocking. Within its regime of validity, i.e., dry, polar, chiral agents under marginal synchronization with sufficient frustration, the model is well-described as a dissipative spintronic fluid.

The transmembrane voltage, $V_{i=0}$, which is the potential drop required to nullify the electrical current ($i=0$), is a key characteristic of water desalination and energy harvesting systems that utilize macroscopically large nanoporous membranes, as well as for physiological ion channels subjected to asymmetric salt concentrations. To date, existing analytical expressions for $V_{i=0}$ have been limited to simple scenarios under simplifying assumptions. In this work, we derive two expressions for $V_{i=0}$. First, we consider the much simpler scenario of two species. Then, we can consider an electrolyte composed of an arbitrary number of species. The difference in the models is that the latter solution utilizes an ad hoc assumption of a linear concentration profile, while the former solution does not require such an ad hoc assumption. However, to derive a closed-form solution, another assumption is needed. In both models, we explicitly assume that the system is locally electroneutral. We show that both electroneutral models display remarkable correspondence with the numerical simulations of the one-dimensional Poisson-Nernst-Planck equations that do not assume electroneutrality. We show how the interplay between diffusion coefficients and ionic valencies significantly varies the system response and why it is essential to account for all system parameters. Importantly, we show that the new models can be reduced to several known models. Ultimately, this model can be used to improve experimental interpretation of ion transport measurements.

This work establishes a direct connection between semiclassical Thomas-Fermi theory and Tsallis statistics. The kinetic energy term of the Thomas-Fermi framework is shown to be associated with the Tsallis entropy $S_q$, while the particle interactions play the role of internal energy $U$, allowing the Thomas-Fermi-Lenz functional to be interpreted as a free-energy functional within a generalized thermostatistical setting. Accordingly, the minimization of the energy functional is equivalent to a maximum-entropy principle. The entropic index $q$ is found to depend on spatial dimension: $q=(d+2)/d$ in the nonrelativistic case, $q=(d+1)/d$ in the ultrarelativistic limit, and $q=3$ under strong magnetic fields. A time-dependent hydrodynamic formulation leads to a nonlinear diffusion equation consistent with a nonlinear Fokker-Planck description. An anomalous diffusion characterized by a universal subdiffusive regime, independent of the spatial dimension, was identified. The time-dependent and time-independent results reveal a correspondence between Thomas-Fermi theory and Tsallis statistics, indicating that the former can be viewed as a generalized thermostatistics; Tsallis statistics is not assumed, it emerges from Thomas-Fermi theory.

The $N$-queens problem asks for the number $Q\left(N\right)$ of ways to place $N$ mutually nonattacking queens on an $N\times N$ chessboard. Simkin [M. Simkin, Adv. Math. 427, 109127 (2023)] proved $Q\left(N\right)\sim {(N/e^{\gamma })}^N$, and subsequent work [P. Nobel, A. Agrawal, and S. Boyd, Optim. Lett. 17, 1229 (2023)] refined the constant to $\gamma =1.94400\left(1\right)$, settling the asymptotic behavior of this classical combinatorial problem. In this work, we pursue a thermodynamic-integration route in an unrestricted lattice-gas ensemble. We map the $N$-queens problem to a lattice gas with pairwise repulsive interactions along shared rows, columns, and diagonals, and we perform extensive Monte Carlo simulations for $N=8-1024$ with ${10}^8$ sweeps per temperature point. The specific heat per queen $C_v/N$ converges to a size-independent function with a broad, nondivergent maximum at $T^{*}\approx 0.235\mathrm{J}$, associated with a defect-proliferation crossover. This convergence, combined with the trivially exact high-temperature entropy $S\left(\infty \right)/N=\frac{1}{N}ln\left(\genfrac{}{}{0pt}{}{N^2}{N}\right)$, enables a thermodynamic integration of $C_v/T$ that extracts the ground-state entropy and yields ${\gamma }_{\mathrm{MC}}=1.946\pm 0.003$ at $N=1024$, within $0.1\%$ of the precise combinatorial value. The Simkin-Nobel value enters only as a benchmark; the thermodynamic route requires no prior knowledge of $Q\left(N\right)$. We further present a transfer-matrix-based tensor-network formulation that encodes the nonattacking constraints into a rank-9 site tensor with 17 nonzero elements, providing a complementary exact-enumeration route.

Symmetry-breaking order at low temperatures is often accompanied by slow relaxation dynamics, due to diverging free-energy barriers arising from interfaces between different ordered states. Here we extend this correspondence to classical topological order, where the ordered states are locally indistinguishable, so there is no notion of interfaces between them. We study the relaxation dynamics of the three-dimensional (3D) classical ${\mathbb{Z}}_2$ lattice gauge theory (LGT) as a canonical example. We prove a lower bound on the mixing time in the deconfined phase, $t_{\text{mix}}=exp\left[\mathrm{\Omega }\left(L\right)\right]$, where $L$ is the linear system size. This bound applies even in the presence of perturbations that explicitly break the one-form symmetry between different long-lived states. This perturbation destroys the energy barriers between ordered states, but we show that entropic effects nevertheless lead to diverging free-energy barriers at nonzero temperature. Our proof establishes the LGT as a robust finite-temperature classical memory. We further prove that entropic effects lead to an emergent one-form symmetry, via a notion that we make precise. We argue that the exponential mixing time follows from universal properties of the deconfined phase, and numerically corroborate this expectation by exploring mixing timescales at the Higgs and confinement transitions out of the deconfined phase. These transitions are found to exhibit markedly different dynamic scaling, even though both have the static critical exponents of the 3D Ising model. We expect this entropic mechanism for memory and emergent symmetry to also bring insight into self-correcting quantum memories.

At finite temperature, an attractive pair potential does not by itself define a bond between two particles. Specifically, two particles initialized near a potential minimum can remain localized over one observation window and escape over another; therefore, bonding is an observation-time-dependent localization problem. Here, we treat bonding as finite-time localization and ask when thermal fluctuations delocalize this state. We measure localization by a fluctuation-derived stiffness, $k_{\mathrm{eff}}=1/\left(\beta \langle u^2\rangle \right)$, where $\langle u^2\rangle$ is the variance of the particle separation. For isotropic particle–particle and one-dimensional particle–wall interactions, we derive a nonequilibrium theory based on the finite-time escape problem that yields the nonequilibrium probability density function for the separation coordinate, drawing on ideas from Becker-Döring theory, and thus $k_{\mathrm{eff}}$ as a function of temperature and observation time ${\tau }_{\mathrm{obs}}$. We find that as temperature increases or as the sampled region grows, the configuration-space volume outside the well dominates the fluctuations and $k_{\mathrm{eff}}$ drops rapidly, signaling the melting of finite-time bonds at a temperature $T^{*}$. Langevin simulations show the same loss of stiffness for particle–particle and particle–wall potentials, and the theory captures this behavior without any adjustable parameters. The temperature $T^{*}$ marks finite-time escape from the localized state and therefore depends on the observation window. Although the nonequilibrium probability density function is obtained exactly, evaluating $k_{\mathrm{eff}}$ from its moments requires numerical quadrature. To provide a simplified analytical representation of this behavior, we introduce a constrained Boltzmann distribution restricted to a finite region of configuration space of size $R_{\mathrm{eq}}$, where $R_{\mathrm{eq}}$ is determined from the nonequilibrium theory. We show that both the nonequilibrium theory and constrained Boltzmann-like representation quantitatively capture the melting of finite-time bonds, with the latter providing an approximate coarse-grained description of bond interactions.

In this study, we investigate the charging dynamics of a multiqubit quantum battery, characterized by the SU(2) algebra and driven by a finite-dimensional SU(1,1) bosonic charger. To enable systematic exploration of the parameter space, we develop and validate a neural-network surrogate model that replicates the exact quantum dynamics with high fidelity, yielding computational savings of up to 2 orders of magnitude compared with direct simulation. The dynamical blockade described below is the central physical result of this work, and the surrogate model is the computational means by which we characterize it across the full parameter space. Our framework reveals a many-body charging blockade: when the battery dimensions are comparable to the charger's excitation number, charging efficiency falls well below its kinematic limit despite ample energy remaining in the charger. We identify the physical underpinnings of this blockade as the saturation of the charger's emission rate, which confines the system to a low-excitation subspace before the battery can access its most absorptive states. This mechanism is intrinsic to finite chargers and absent in conventional infinite-mode models. This blockade is robust across a range of Bargmann indices and persists in a standard Dicke charger, confirming that it is a general feature of finite-dimensional charging rather than a property specific to the SU(1,1) algebra. We further show that a large number of charger excitations improves efficiency and reduces variance at the same time, whereas the blockade regime degrades both metrics together. These findings identify a many-body constraint on collective quantum charging and provide guidelines for designing high-performance quantum energy storage systems.

Diffusion with multipole-moment conservation gives rise to transport laws that generalize Fick's law and has attracted growing attention following experimental advances in strongly tilted optical lattices. It was recently shown that conserving complete multipole-moment groups leads to subdiffusive dynamics governed by a nonlinear diffusion equation, raising the question of whether hydrodynamic equations would also be nonlinear when the conservation law is imposed only at the subsystem level. Here we show that subsystem symmetries generically produce nonlinear hydrodynamic equations with shear-only transport, in which any localization present in the initial marginal distributions is preserved at long times by the conservation of those marginals. A linear regime emerges only as a limiting case for small fluctuations around a uniform background. We derive the deterministic and fluctuating parts of the hydrodynamic equations in arbitrary dimensions and obtain the corresponding maximum-entropy equilibrium distributions under constrained marginals. We also show that marginal-conserving diffusion provides a concrete hydrodynamic realization of partial multipole-moment conservation, and we offer an information-theoretic interpretation in which total correlation decays monotonically even when pairwise mutual information does not.

The complexity of many natural systems stems from the abundance of interactions that go beyond simple pairwise networks. While higher-order interactions (HOIs) are fundamental to the dynamics of complex networks, their role in shaping ecological communities through species dispersal remains poorly understood. Here, using chaotic tritrophic dynamics, we explore how synchronization emerges in networks characterized by both dyadic and three-body interactions. In random networks, HOIs reduce extreme asynchrony by promoting partial clustering, but never produce complete synchrony. By contrast, in globally connected networks, stronger HOIs drive the system from asynchronous states to full synchrony, with important consequences for community persistence. Employing the master stability function, we further demonstrate that global synchrony remains stable once a critical coupling threshold is crossed. Our findings reveal that HOI-mediated dispersal introduces topology dependence governed by the local triadic structure of the landscape network, which critically shapes the system's collective emergent dynamics.

Chimera states are one of the most intriguing phenomena in nonlinear dynamics, characterized by the coexistence of coherent and incoherent behavior in systems of coupled identical oscillators. Despite extensive studies and numerous observations in different settings, the development of reliable and systematic methods to classify chimera states and distinguish them from other dynamical patterns remains a challenging task. Existing approaches are often limited in scope and lack robustness. In this work we propose a method based on Fourier analysis combined with statistical classification to identify chimera behavior. The method is applied to a system of topological signals coupled via the Dirac operator, where it successfully captures the rich dynamical regimes exhibited by the model. We demonstrate that the proposed approach is robust with respect to variations in network topology and system parameters. Beyond the specific model considered, the framework provides a general and automated tool for distinguishing different dynamical regimes in complex systems.

We investigate how the nature, rather than just the strength, of coupling controls synchronization between self-sustained oscillators. By parametrizing the coupling between two van der Pol oscillators as $J{e}^{i\theta }$ at fixed overall strength $J$, we continuously tune from purely coherent ($\theta =0$) to purely dissipative ($\theta =\pi /2$) coupling. We find that dissipative coupling yields a substantially wider frequency-locking window than coherent coupling in both the weakly and strongly nonlinear regimes. In the weakly nonlinear regime, hybrid coherent-dissipative coupling unlocks an unbalanced synchronization (U-sync) regime with strongly asymmetric amplitudes, extending the locking window far beyond the conventional balanced-synchronization (B-sync) boundary. A systematic bifurcation analysis, supported by Matcont numerical continuation, identifies the synchronization boundaries as saddle-node bifurcations in the strongly nonlinear regime for all coupling angles, and as saddle-node (for purely dissipative coupling) or Hopf (otherwise) bifurcations in the weakly nonlinear regime. We confirm the predicted synchronization enhancement and both the B-sync and U-sync regimes experimentally using coupled self-sustained LC resonators with tunable coherent-dissipative coupling. Our results establish the coupling angle as a practical tuning knob for synchronization engineering and suggest design principles, based on the dissipative-to-coherent ratio of each pairwise link, for controlling synchronization robustness and amplitude distributions in oscillator networks.

We numerically studied active Brownian particles with attractive interactions. Contrary to our intuition, the attractive force between particles disrupts the formation of a single cluster observed in motility-induced phase separation, giving rise to a multicluster state. This transition is driven by a decrease in effective motility caused by the persistent cohesion between particles. We also found that the self-propulsion directions spontaneously align within each cluster in the multicluster state, despite the absence of explicit alignment interactions. This study revealed the intricate role of attractive interactions in the aggregation of motile systems.

When a granular material composed of elongated grains is sheared in a split-bottom shear cell, a pressure difference develops within the material. This pressure difference depends on the interparticle friction, which affects shear localization and particle alignment. At high friction, alignment is confined to a narrow shear band, leading to localized increases in packing density and pressure. At low friction, the particles align over a wider region, leading to a nearly uniform packing density and pressure throughout the material. In contrast, assemblies of spherical particles exhibit a uniform packing density and pressure, independent of the friction coefficient. Elongated grains behave similarly to the Weissenberg effect in non-Newtonian fluids, where the normal stress differences are associated with pressure variations, in contrast to the nearly uniform pressure field observed for spherical particles.

Microcanonical inflection-point analysis (MIPA) identifies third-order transitions from derivatives of the microcanonical entropy, yet this classification has lacked a direct canonical counterpart accessible from measurable fluctuations without reconstructing the density of states. Here we establish such a fluctuation-based canonical framework for MIPA-type third-order transitions using a cumulant-ratio diagnostic. Its signed extrema identify the corresponding canonical signatures and, in the single-saddle regime, are asymptotically linked to microcanonical classification. Because the diagnostic depends only on energy cumulants, it avoids explicit density-of-states reconstruction and is accessible from measurable fluctuations. Physically, it is a canonical fluctuation-asymmetry observable whose extrema mark high- and low-energy tail reorganizations of the canonical energy distribution. Benchmarks on Ising, Potts, and nonreciprocal Ising models support the framework.

Lee-Yang theory offers a unifying framework for understanding classical phase transitions and dynamical quantum phase transitions through the analysis of partition functions and Loschmidt echoes. Recently, this framework was extended to characterize quantum phase transitions of quantum Ising models by introducing the concepts of non-Hermitian parity-symmetry breaking and fidelity zeros. Here, we generalize the theory by studying a broad class of quantum models, including the XY, the XXZ, the XYZ, and the ${\mathbb{Z}}_p$ clock models in one dimension, subject to a complex magnetic field. For the XY, XXZ, and XYZ models, we find that the complex field breaks parity symmetry and induces oscillations of the ground state between the two parity sectors, giving rise to fidelity zeros within the ordered phases. For the ${\mathbb{Z}}_3$ clock model, the complex field splits the real part of the ground-state energy between the neutral sector $(q=0)$ and the charged sectors $(q=1,2)$, while preserving the degeneracy within the charged sector. Fidelity zeros arise only after projecting out one of the charged sectors. For the ${\mathbb{Z}}_4$ and ${\mathbb{Z}}_5$ clock models, the ground states are instead projected to oscillate between the neutral sector ($q=0$) and the charged sectors $q=2$ and $q=1$, respectively, giving rise to fidelity zeros. Finite-size scaling of these zeros yields critical exponents in full agreement with analytical predictions, demonstrating that this approach is applicable not only to the Ising model with ${\mathbb{Z}}_2$ symmetry, but also to more general Heisenberg-type models and systems with higher discrete symmetries.

We investigate the fragment-size distribution produced by a hierarchical generalization of Gilbert's two-dimensional random tessellation. The study is motivated by experimental data on fragmentation processes, obtained by Kooij and coworkers [S. Kooij et al., Nat. Commun. 12, 2521 (2021)], where the reasons for which experimental data can exhibit a scale-free behavior resulting in power distributions (for unstressed materials) or exponential distribution with a characteristic length scale (for stressed material) are analyzed in great detail. We study two tessellation models, Dichotomous Gilbert (DG) and Hierarchical Gilbert (HG), which implement different hierarchical splitting rules. Both models generate fragment-area distributions well described by a truncated power-law function, namely a power multiplied by a stretched exponential function or generalized Gamma function. The Gilbert's classic tessellation model gives rise, on the contrary, to a simple exponential distribution. To further characterize the underling complexity, we perform a multifractal analysis of the fragment areas. The results demonstrate that Gilbert's hierarchical fragmentation reveals a multifractal scaling.

Inspired by the phenomenologies of an open totally asymmetric simple exclusion process (TASEP) with Langmuir kinetics (Lk) and finite resources that dynamically control the entry and exit rates of the TASEP lane, we study the stationary densities and phase transitions in a TASEP with Lk connected to both ends of a particle reservoir. The resulting phase diagrams in the plane of the control parameters are significantly different from those in an open TASEP with Lk. In particular, some of the phases admissible in the open TASEP with Lk model are no longer possible. Intriguingly, our model is closely related to a TASEP coupled with Lk on a ring with a point defect, but admits more phases than the latter. Phenomenological implications of our results are discussed.