We present experiments on the collective dynamics of macroscopic photoactive self-propelled particles subjected to spatiotemporally varying excitation. The particles move within an arena divided into two regions with different illumination intensities, creating alternating bright (more active) and dark (less active) zones. Under such conditions, the system exhibits a robust migration from the more active region toward the less active region, demonstrating a strong response to external modulation. This response depends sensitively on the frequency of the illumination pattern: at low frequencies, particles follow the changing landscape, whereas at higher frequencies, the response diminishes. We show that this behavior arises from the interplay between the imposed excitation and the intrinsic dynamics of the particle clusters that form spontaneously. To explain these features, we extend a kinetic model previously introduced in Lévay et al. [Phys. Rev. Lett. 135, 098301 (2025)], hence revealing the most important parameters governing the transition between the responsive and unresponsive regimes.

We investigate heat conduction in a one-dimensional chain of rigid rotors. The rotors are constrained to rotate in a plane about fixed pivot points and coupled by springs, such that in equilibrium, the neighboring rotors lie on opposite sides of the chain axis. The linearized limit of this model valid for small angular displacements was first introduced by Kane and Lubensky (KL) [Nat. Phys. 10, 39 (2014)] as a topological mechanical insulator hosting zero-energy vibrational edge modes. We show that the linearized KL chain behaves as a thermal insulator at low temperature in both the topological phases with a finite band gap, and the heat current falls exponentially with the chain length. When the gap vanishes at the topological phase transition, the KL chain becomes a good thermal conductor and conducts heat ballistically. The chain of rotors for arbitrary angular displacements hosts nonlinear solitary waves and distinct topological mechanical phases. Our numerical analysis shows normal (diffusive) heat conduction in all topological phases of the nonlinear chain. Nevertheless, a finite thermal conductivity is achieved for different system sizes in different topological phases of this nonlinear chain.

We present a comprehensive discussion of a transition from integrability to nonintegrability in an oval billiard with a static boundary. This transition is controlled by a deformation parameter $\epsilon$, which modifies the boundary shape from circular, corresponding to $\epsilon =0$ and an integrable dynamics, to oval for $\epsilon \ne 0$, where nonintegrability emerges. The deformation of the circular billiard gives rise to a chaotic layer that develops along a well-defined stripe in phase space. By introducing a set of transformations that isolate this chaotic stripe, we characterize the diffusive spreading of ensembles of trajectories and identify an observable, ${\omega }_{\mathrm{rms},\mathrm{sat}}$, which plays the role of an order parameter for the transition. For small deformations, the saturation value of the diffusion obeys the scaling law ${\omega }_{\mathrm{rms},\mathrm{sat}}\propto {\epsilon }^{\tilde{\alpha }}$, with a critical exponent $\tilde{\alpha }=0.507\left(2\right)$, vanishing continuously as $\epsilon \to 0$. The associated susceptibility, $\chi =d{\omega }_{\mathrm{rms},\mathrm{sat}}/d\epsilon$, diverges in the same limit, signaling the presence of critical behavior analogous to that observed in second-order (continuous) phase transitions in statistical mechanics.

Polymer physics models have been employed to elucidate the 3D organization of chromosomes in the cell nucleus. However, how well they capture chromatin architectures at the single-molecule level remains poorly understood. Here, we consider a minimal polymer model where folding is driven by sequence-specific self-interactions between cognate monomer types, leading to their separation into spatially segregated globular domains. Focusing on a key genomic region in human IMR90 cells, we demonstrate that the model accurately reproduces the distribution of individual chromatin conformations as validated by single-cell super-resolution microscopy experiments. The structural variability across cells is naturally explained by the predicted thermodynamic ensemble of domain-segregated states, hence providing a robust validation of the model basic ingredients with no additional molecular parameters.

An important goal of computational studies of protein-protein interfaces (PPIs) is to predict the binding site between two monomers that form a heterodimer. The simplest version of this problem is to rigidly redock the bound forms of the monomers, which involves generating computational models of the heterodimer and then scoring them to determine the most nativelike models. PPI scoring functions have been assessed previously using rank- and classification-based metrics; however, these methods are sensitive to the number and quality of models in the scoring function training set. We assess the accuracy of seven physical, statistical, or deep-learning-based PPI scoring functions by comparing their scores of computational models of PPIs to a measure of structural similarity to the x-ray crystal structure (i.e., the DockQ score) for a nonredundant set of heterodimers from the Protein Data Bank. For each heterodimer, we generate redocked models uniformly sampled over DockQ and calculate the Spearman correlation between the PPI scores and DockQ. For some targets, the scores and DockQ are highly correlated; however, for many targets, there are weak correlations. Several physical features explain the difference between difficult- and easy-to-score targets. Strong correlations exist between the score and DockQ for targets with highly intertwined monomers and many interface contacts. We also develop a new score based on only two physical features that matches the performance of current PPI scoring functions. In addition, we address the more general problem of flexible-body docking by generating and docking intermediate monomer conformations between their bound and unbound forms. We score the docked models and find that the Spearman correlations between the PPI scores and DockQ decrease strongly as the monomers are deformed from their bound conformations. These results emphasize that PPI docking predictions can be improved by focusing on correlations between the PPI score and DockQ and incorporating more discriminating physical features into PPI scoring functions.

Coarse graining (CG) is an important task for efficient modeling and simulation of complex multiscale systems, such as the conformational dynamics of biomolecules. This work presents a projection-based coarse-graining formalism for general underdamped Langevin dynamics. Following the Zwanzig projection approach, we derive a closed-form expression for the coarse-grained dynamics. In addition, we show how the generator extended dynamic mode decomposition method, which was developed in the context of Koopman operator methods, can be used to model the CG dynamics and evaluate its kinetic properties, such as transition timescales. Finally, we combine our approach with thermodynamic interpolation, a generative approach to transform samples between thermodynamic conditions, to extend the scope of the approach across thermodynamic states without repeated numerical simulations. Using a two-dimensional model system, we demonstrate that the proposed method allows to accurately capture the thermodynamic and kinetic properties of the full-space model.

Glasses are traditionally characterized by their rugged landscape of disordered low-energy states and their slow relaxation towards thermodynamic equilibrium. Far from equilibrium, dynamical forms of glassy behavior with anomalous algebraic relaxation have also been noted, for example, in networks of coupled oscillators. Due to their disordered and high-dimensional nature, such systems have been difficult to study theoretically, but data-driven methods are emerging as a promising alternative that may aid in their analysis. Here, we characterize glassy dynamics using the dynamic mode decomposition, a data-driven spectral computation that approximates the Koopman spectrum. We show that the gap between oscillatory and decaying modes in the Koopman spectrum vanishes in systems exhibiting algebraic relaxation, and thus, we propose a model-agnostic signature for robustly detecting and analyzing glassy dynamics. We demonstrate the utility of our approach through both a minimal example of a one-dimensional ODE and a high-dimensional example of coupled oscillators.

We study the one-dimensional (1D) swarmalator model with time-delayed interactions. Delay preserves the familiar static states—sync, async, and phase wave—but generates two new families of nonstatic states. One bifurcates from the phase wave at $\tau ={\tau }_c(J,K)$; the other bifurcates from the async state at $K_c=-\pi /\tau$ and includes a limit cycle, an irregular unsteady regime, and a partially synchronized state. We derive both bifurcation boundaries analytically. A surprising result is that the stability of the sync state is independent of $\tau$; it depends only on the coupling strength.

We introduce an evidence-driven Bayesian formulation of physics-informed neural networks that enables automatic optimization of loss weights between residuals of partial differential equations, boundary conditions, and observational data. Unlike existing Bayesian Physics-Informed Neural Network approaches based on sampling or variational inference, the proposed method uses a Laplace approximation to compute model evidence analytically, enabling efficient hyperparameter tuning and model comparison without posterior sampling. We demonstrate the method on the heat, wave, and Burgers' equations, obtaining solutions in agreement with exact or reference results. In the Burgers' equation example, we further show that the framework naturally integrates information from governing equations and noisy measurements, providing predictive uncertainties within a unified Bayesian setting.

We investigate a trapping mechanism for passive Brownian particles based on mixtures with self-propelled dipolar colloids. Active dipoles, whose magnetic moment is oriented perpendicularly to their propulsion direction, spontaneously form dynamic chains that collapse into clusters through dipole-dipole interactions. These transient structures efficiently capture nearby passive particles, forming dense phases at relatively low global packing fractions. Using Brownian dynamics simulations, we analyze how the capture efficiency depends on the Péclet number ($\mathrm{Pe}$) and dipolar interaction strength ($\lambda$). We demonstrate that an external magnetic field, applied briefly to align the active dipoles, significantly enhances trapping efficiency, with capture fractions exceeding 50% under optimal conditions. Our results reveal a nontrivial competition between activity and dipolar forces, governed by the ratio $\lambda /\mathrm{Pe}$, and offer insights into designing self-organized trapping strategies for passive colloids.

We investigate the motion amid grains of an intruder undergoing an imposed force that oscillates with a given frequency. For that, we made use of discrete numerical simulations where the intruder was a larger disk on which a force oscillating in direction was applied, and the grains consisted of smaller disks. All disks were placed on a surface with basal friction over which they could slide, the system was confined in the sliding directions, and we varied the system packing fraction, oscillation frequency, and magnitude of the forcing. The results show intermittent and very complex motions of the intruder depending on both the packing fraction and frequency of oscillation: It can move sideways while slowly progressing forward, it can be blocked during a long period after and/or before start moving, or it can simply be blocked after a given time. Interestingly, we find that the displacement velocity is much higher when the system packing fraction is above a given threshold, contrary to intuition. The results show that there is an optimal frequency that minimizes the transit time for some ranges of packing fraction, and we propose a model based on the system elasticity that explains this behavior and agrees with the numerical simulations. Our findings shed new light on how to better explore oscillating motion to move objects within granular media.

Understanding how quantum chaotic systems generate entanglement can provide insight into their microscopic chaotic dynamics and can help distinguish between different classes of chaotic behavior. Using von Neumann entanglement entropy, we study a nonentangled state evolved under three variants of the Sachdev-Ye-Kitaev (SYK) model with a finite number of Majorana fermions $N$. All the variants exhibit linear entanglement growth at early times, which at late times saturates to a universal value consistent with random matrix theory (RMT), but their growth rates differ. We interpret this as a large-$N$ effect, arising from the enhanced nonlocality of fermionic operators in SYK and binary SYK, absent in spin operators of the spin-SYK model. Numerically, we find that these differences emerge gradually with increasing $N$. Although all variants are quantum chaotic, their entanglement dynamics reflect varying scrambling rates and indicate that the entanglement production rate serves as a fine-grained probe of scrambling beyond conventional measures. To probe its effect on the thermalization properties of these models, we study the two-point autocorrelation function, finding no differences between the SYK variants, but deviations from RMT predictions for $N\ge 24$, particularly near the crossover from exponential decay to saturation regime.

Near equilibrium, the symmetric part of the time-integrated steady-state covariance, i.e., the time integral of correlation functions, is governed by the fluctuation-dissipation theorem, while the antisymmetric part vanishes due to Onsager reciprocity. Far from equilibrium, where these principles no longer apply, we develop a unified formalism for both symmetric and antisymmetric components of integrated covariances. We derive exact, computationally tractable expressions for these quantities, valid in arbitrary nonequilibrium steady states of Markov jump processes and Fokker-Planck equation. Both components are expressed in terms of excess observables, a notion central to both statistical physics and reinforcement learning. Furthermore, we establish thermodynamic upper bounds for antisymmetric covariances in terms of (pseudo-)entropy production and cycle affinities. Finally, we show that the speed-up of self-averaging induced by nonequilibrium drivings which preserve kinetics (activity) is bounded by the cycle affinities (thermodynamic forces).

The occupation number is a key observable for diagnosing thermalization, as it connects directly to standard statistical laws such as Fermi-Dirac, Bose-Einstein, and Boltzmann distributions. In the context of spin systems, it represents the population of the sublevels of the magnetization in the $z$ direction. We use this quantity to probe the onset of thermalization in an isolated one-dimensional quantum spin-1 Ising model with transverse and longitudinal fields and in its classical counterpart. Thermalization is achieved when the long-time average of the occupation number converges to the microcanonical prediction as the chain length $L$ increases, consistent with the emergence of ergodicity. However, the finite-size scaling analysis in the quantum model is challenged by the exponential growth of the Hilbert space with $L$. To overcome this limitation, we turn to the classical model, which enables access to much larger system sizes. By tracking the dynamics of individual spins on their three-dimensional Bloch spheres and employing tools from random matrix theory, we establish a quantitative criterion for classical ergodicity in interacting spin systems. We find that deviations from classical ergodicity decay algebraically with system size. This power-law scaling then provides a quantitative bound on the approach to thermal equilibrium in the quantum model.

We derive and analyze the amplitude equation for roll patterns in the generalized Active Model B (AMB) with chemical reactions in $d=1$. We start from the generalized $\mathrm{AMB}+$, which differs from the original $\mathrm{AMB}+$ introduced by Tjhung et al. [Phys. Rev. X 8, 031080 (2018)] through the inclusion of an additional quadratic term $g{\varphi }^2$ in the equilibrium part of the current. The model incorporates a rotation-free active current with strength $\lambda$ and a rotational current with strength $\xi$. In $d=1$, generalized $\mathrm{AMB}+$ reduces to generalized AMB with an effective rotation-free active current of strength ${\lambda }_{\mathrm{eff}}=\lambda -\frac{\xi }{2}$, while the rotational current is absent. The inclusion of a chemical reaction with rate $\mathrm{\Gamma }$ removes the conservation constraint and introduces a preferred wave number that governs the pattern formation below a critical reaction rate ${\mathrm{\Gamma }}_c$. We argue for the analytical form of the amplitude equation based on symmetry considerations and explicitly derive it using multiscale analysis. By taking different limits of $g$, $\lambda$, and $\xi$, we recover amplitude equations for several well-known physical models as special cases and determine the nature of transitions close to the onset of instability. We find that, for $g=0$, the transition is always supercritical, whereas for $g\ne 0$, the transition between the supercritical and subcritical regimes depends sensitively on the model parameters. Furthermore, we derive the condition for the Eckhaus instability from the stability analysis of the amplitude equation as well as from the phase-diffusion equation and find that it is independent of $g$.

The eigenstate thermalization hypothesis (ETH) explains how generic quantum many-body systems thermalize internally. It implies that local operators' time-averaged expectation values approximately equal their thermal expectation values, regardless of microscopic details. The ETH's range of applicability therefore impacts theory and experiments. Murthy et al. [Phys. Rev. Lett. 130, 140402 (2023)] recently showed that non-Abelian symmetries conflict with the ETH. Such symmetries have excited interest in quantum thermodynamics lately, as they are equivalent to conserved quantities that fail to commute with each other and noncommutation is a quintessentially quantum phenomenon. Murthy et al. proposed a non-Abelian ETH, which we support numerically. The numerics model a one-dimensional next-nearest-neighbor Heisenberg chain of 18 qubits. We represent local operators with matrices relative to an energy eigenbasis. The matrices bear out seven predictions of the non-Abelian ETH. We also prove analytically that the non-Abelian ETH exhibits a self-consistency property. The proof relies on a thermodynamic-entropy definition different from that of Murthy et al. This work initiates the observation and application of the non-Abelian ETH.

Constructing both basic and dynamic logic gates within a unified noise-driven system remains a challenge due to the lack of a comprehensive theoretical framework describing the underlying stochastic dynamics. In this work, we utilize the mean first-passage time theory to develop a robust theoretical framework for such systems. We propose a unique analytical criterion that allows for the determination of reliable parameter ranges without the need for extensive numerical simulations. This approach significantly reduces the time required for parameter scanning and enables more efficient identification of the operational stability of logic gates under noise. Validated by these analytical results, our numerical simulations uncover a key insight: by dissecting the types of logic signal input transitions, we identify the specific transition that predominantly determines the reliability of the logic gates. This discovery provides a criterion for the precise control of noise-driven dynamics, offering a comprehensive theoretical foundation for the design of flexible logic systems with improved reconfigurability and reliability.

Spectral fluctuation analysis within the random matrix theory (RMT) framework is a powerful probe of complexity in networked systems, yet its extension to multilayer architectures remains unresolved. In general multilayer networks, the adjacency matrix possesses a heterogeneous block structure with unequal variances across layers, causing eigenvalue spacing statistics to deviate from RMT predictions even when each individual layer is perfectly random. We demonstrate that this variance mismatch is the central obstacle to observing spectral universality in multilayer systems and introduce a general blockwise normalization scheme that restores the correct variance structure across all blocks. Using higher-order spacing ratios, we show that once properly normalized, multilayer networks exhibit universal spectral fluctuations consistent with RMT across a broad class of configurations, including purely intralayer, interlayer, and multiplex structures. Focusing on the bilayer case, we introduce a crossover model parametrized by the relative interlayer to intralayer coupling strength, which captures the continuous transition from two independent Gaussian orthogonal ensembles (GOEs) to a single GOE. We find that this crossover sharpens with increasing system size, suggesting that in the large-system limit, arbitrarily weak interlayer coupling may be sufficient to induce global spectral correlations. Applying the framework to empirical multilayer networks derived from protein-crystal structures, we demonstrate that structural coupling drives analogous spectral transitions, directly linking the emergence of universality to physically meaningful organization. These results establish spectral universality as a robust feature of multilayer networks and provide a quantitative framework for understanding how structure and coupling govern collective behavior in complex interconnected systems.

We study an ecology-inspired model for a population of bounded size, whose dynamics is governed by random birth, death, and immigration events. Stochastic fluctuations in the number of individuals give rise to a succession of alternating active and vacant periods, where the population is, respectively, extant and extinct. Using both analytical and numerical techniques, we characterize the statistics of the two kinds of period, quantifying their duration and frequency, and the typical population sizes in active periods. In sharp contrast to the deterministic mean-field behavior, governed by logistic dynamics, active periods may exhibit pronounced bimodality: either short durations with very small populations, or much longer durations with population sizes close to the maximum. We also investigate how these results change when the population evolves on random networks of three classes: Erdős-Rényi, regular, and geographic. The main effect of the network structure is to induce population clustering, with individuals aggregated into localized groups. This, in turn, limits population growth and increases the frequency of vacant periods.