Heat generation and conduction at moving interfaces are ubiquitous and fundamentally important. However, despite decades of progress on thermal transport across static interfaces, insights into moving interfaces remain rare due to the complex and ever-changing nature of most sliding contacts. Here, we take advantage of structural superlubricity and achieve simultaneous mechanical manipulation and thermal measurement of the heterointerface between gold micromesas and single-crystal graphite. We uncover a robustly high thermal conductance which is orders of magnitude higher than that in conventional moving contacts and remarkably insensitive to arbitrary interfacial rotation and thousands of cycles of sliding. In conjunction with atomistic simulations, we reveal the critical role of full atomic contact associated with the interfacial superlubricity and the stacking-insensitive out-of-plane phonon modes that dominate heat transfer. Altogether, our findings highlight diverse superlubric heterointerfaces as a pristine platform for exploring phonon dynamics in moving systems and managing heat in emerging devices including twistronics and slidetronics.

Quasicrystals extend topological concepts beyond periodic systems, but their exploration in mechanical wave systems remains elusive. Here, we experimentally realize two-dimensional quasicrystal water waves with fivefold rotational symmetry via the interference of multiple quasiplane waves. Although topologically indistinguishable in real space, these patterns are uniquely classified by higher-dimensional topological charge vectors that obey an angular-momentum-like conservation law. Using the water-wave amplitude and its in-plane gradient, we construct a synthetic three-dimensional vector field and demonstrate the emergence of skyrmions in water-wave quasicrystals. These skyrmions exhibit dynamically evolving boundaries and orientations, i.e., deformation and propagation due to phasonlike motion during the evolution of the quasicrystal water-wave field. Remarkably, the associated phase singularities can generate forces and torques that stably trap and drive the rotation of floating particles. We demonstrate in experiments the simultaneous manipulation of particles at multiple trapping sites in different ways, opening a path toward programmable control of particle dynamics. By bridging higher-dimensional topology with water-wave quasicrystals and skyrmions, our work not only advances the physics of topological hydrodynamics but also establishes a platform for on-demand particle control in aqueous environments, which is promising for applications in biomedicine, microfluidics, and lab-on-a-chip technologies.

Mechanical metamaterials achieve their extraordinary properties through their intricate architectures. While amorphous designs can minimize directional bias relative to their regular counterparts, their vast configuration space poses a significant challenge for conventional design strategies. Here, we introduce a physics-constrained, energy-based model framework to navigate this complexity with machine learning. We formulate a multiobjective energy function that encodes desired macroscopic properties—specifically, a target negative Poisson ratio and approximate isotropy—into the network’s topology. The design problem is then recasted as finding the ground state of this energy landscape, while operating within a mechanically stable or physics-constrained configuration space. We employ Boltzmann annealing as a physically consistent inference algorithm to identify the optimal low-energy configurations. The structures discovered and fabricated via 3D printing exhibit a highly negative Poisson ratio together with near-equal responses along principal axes (i.e., isotropy along both $x$ and $y$ axes). Remarkably, these optimized structures also reveal highly desirable emergent properties, including exceptional performance in specific energy absorption, impact resistance, and fracture toughness, significantly outperforming regular lattice counterparts. This work establishes a robust and interpretable machine-learning framework for the design of high-performance amorphous metamaterials.

Robust inference for stochastic dynamical systems is often hampered by sparse sampling and the absence of closed-form likelihoods. We introduce a Monte Carlo path-inference framework that leverages full-path statistics and bridge processes to deliver reliable parameter estimation and model selection from coarsely sampled time series, without requiring analytical solutions. Crucially, we couple mechanistic stochastic models with their inference procedures to quantify how experimental design—specifically, sampling frequency and dataset size—governs estimator precision and model distinguishability. This analysis reveals optimal sampling regimes and sharp, resolution-dependent limits beyond which competing models become empirically indistinguishable. We validate the approach across four disparate systems—trajectories of optically trapped particles, human microbiome dynamics, social-media topic mentions, and forest population time series—recovering parameters and identifying when inference is fundamentally constrained by measurement resolution, thereby clarifying ongoing debates about dominant noise sources in these systems. Together, these results establish path-based Monte Carlo as a practical, general tool for inference and model discrimination in complex systems and provide principled guidelines for designing measurements that maximize information under real-world constraints.

We introduce configuration space path integrals for quantum fields interacting with classical fields. We show that this can be done consistently by proving that the dynamics are completely positive directly, without resorting to master equation methods. These path integrals allow one to readily impose space-time symmetries, including Lorentz invariance or diffeomorphism invariance. They generalize and combine the Feynman-Vernon path integral of open quantum systems and the stochastic path integral of classical stochastic dynamics while respecting symmetry principles. We introduce a path integral formulation of general relativity where the space-time metric is treated classically. The theory is a candidate for a fundamental theory that reconciles general relativity with quantum mechanics. The theory is manifestly covariant, and may be inequivalent to the theory derived using master equation methods. We prove that entanglement cannot be created via the classical field, reinforcing proposals to test the quantum nature of gravity via entanglement generation.

Knits and crochets are mechanical metamaterials with a long history that can typically be produced from a single yarn. Despite the simplicity of the manufacturing process, they exhibit a wide range of structural configurations with diverse mechanical properties and application potentials. Although there has been recent growing interest in textile-based metamaterials, a rigorous topological characterization of what makes a structure knittable has been lacking. Here, we introduce a general criterion based on topological constraints that distinguish knits and crochets from other textile structures. We demonstrate how the introduction of topological defects and their propagation makes this classification practical. Our approach highlights a fundamental link between manufacturing processes and structural fragility. Within this framework, we show how the rationalization of defect propagation unlocks the design of fabrics with controllable damage resistance.

The thermal noise of mirror coatings for gravitational-wave detectors critically depends on the elastic properties of the constituent materials. Data analyses and theoretical models typically assume each material is homogeneous and isotropic, but isotropy has never been explicitly verified. Using Brillouin light scattering (BLS), we demonstrate that ion-beam-sputtered ${\mathrm{SiO}}_2$—a material still viable for future mirror coatings—exhibits cylindrical elastic symmetry, with in-plane isotropy but a notable 6% compressive anisotropy along the film normal. This anisotropy remains unchanged after the postdeposition heat treatment currently used in ground-based detectors ($500°\mathrm{C}$, 10 h) but is nearly eliminated at $900°\mathrm{C}$. Infrared reflectivity experiments support these findings by directly revealing heterogeneities in the distribution of bridging and nonbridging oxygen structures along the growth axis. While BLS measures the real part of the elastic constants at gigahertz frequencies, the data reveal negligible contributions from mechanical relaxations in the kilohertz to gigahertz range, making BLS a valid substitute for low-frequency properties obtained from standard anisotropy-insensitive techniques. Our results highlight that restoring isotropy through heat treatment—by softening the material, enabling more than 7% out-of-plane expansion, and smoothing out structural heterogeneities—may play a key role in reducing thermal noise. This proof-of-concept study extends beyond silica, providing critical insights for the design of future coatings.

Models of complex dynamical systems like the Earth’s climate often involve large numbers of uncertain parameters. Comprehensive exploration of the parameter space is typically prohibitive due to excessive computational costs, and systematic gradient-based parameter optimization is not feasible because such models are typically not differentiable. This is especially problematic in cases where the models intend to describe highly nonlinear and possibly abrupt dynamics, where sensitivity to parameter changes is high. Components of Earth’s climate system, such as the North Atlantic Overturning Circulation, the polar ice sheets, or the Amazon rainforest, are at risk of undergoing critical transitions in response to anthropogenic climate change. However, estimates of the critical forcing thresholds are highly uncertain because the parameter spaces of complex climate models cannot be fully explored. Concerns have been raised that the above Earth system components are too stable in state-of-the-art models. Here, we introduce a method for efficient, systematic, and objective calibration of dynamical complex system models, targeted at adjusting system stability. Given a number of physical or observational constraints, our method moves the system in a direction where the system loses or gains stability, guided by indicators of “critical slowing down”. In contrast to a brute force approach, where the computational cost would exponentially increase with the number of parameters, our method scales polynomially and thus evades the curse of dimensionality. We successfully apply our method to a conceptual double-fold bifurcation model and a physically plausible reduced-order model of the global ocean circulation. Our method can efficiently adjust stability biases across a range of complex system models, helping to reveal hidden instabilities and resulting state transitions they induce. In particular, it can help us to explore and improve the representation of key multistable components of the Earth system in climate models.

The restricted Boltzmann machine (RBM) is a neural network based on the Ising model, well known for its ability to learn probability distributions and stochastically generate new content. However, the high computational cost of Gibbs sampling in content generation tasks imposes significant bottlenecks on electronic implementations. Here, we propose a photonic restricted Boltzmann machine (PRBM) that leverages photonic computing to accelerate Gibbs sampling, enabling efficient content generation. By introducing an efficient encoding method, the PRBM eliminates the need for computationally intensive matrix decomposition and reduces the computational complexity of a single dot product in Gibbs sampling from $O(N)$ to $O(1)$. Moreover, with the advantage of photonic computation of non–von Neumann computing architecture, we physically encode the model parameters onto the phases of different wavelength light fields on a spatial light modulator, substantially enhancing computation efficiency for large-scale RBMs. We experimentally validate the photonic-accelerated Gibbs sampling by simulating a two-dimensional Ising model, where the observed phase transition temperature closely matches the theoretical predictions. Beyond physics-inspired tasks, the PRBM demonstrates strong performance in generating and restoring diverse content, including images and temporal sequences. The scalability and reduced training cost of the PRBM framework underscore its potential as a promising pathway for advancing photonic computing in generative artificial intelligence.

Triboelectric charging of insulating particles through contact is critical in diverse physical and engineering processes, from dust storms and volcanic eruptions to industrial powder handling. However, many experiments over the years have consistently revealed counterintuitive charging patterns, including variable impact charge under identical conditions, charge sign reversal with repeated impacts, and bipolar charging of differently sized particles. Existing computational models cannot predict these patterns; they either rely on oversimplified heuristics or require inaccessible detailed surface properties. We present a stochastic scaling model (SSM) for particle charging that unifies same-material (particle-particle) and different-material (particle-wall) charging in a single theoretical framework. The model is grounded in a physics-based stochastic closure by the mean, variance, skewness, and minimum impact charge measured in a highly controlled reference experiment. To test the SSM, we implemented it in an open-source Lagrangian-Eulerian computational fluid dynamics solver. When simulating 300 000 insulating particles transported by turbulent wall-bounded flows, the SSM takes less than 0.01% of the CPU time. By scaling the statistical parameters of the reference impact to each collision, the new model reproduces the complex charging patterns observed in experiments without requiring surface-level first-principles inputs. The SSM offers a physically grounded route to large-scale simulations of electrostatic effects across many fields of particle-laden flows.

A major challenge of AI plus science lies in its inherent incompatibility: Today’s AI is primarily based on connectionism, while science depends on symbolism. To bridge the two worlds, we propose a framework to seamlessly synergize Kolmogorov-Arnold networks (KANs) and science. The framework highlights KANs’ usage for three aspects of scientific discovery: identifying relevant features, revealing modular structures, and discovering symbolic formulas. The synergy is bidirectional: science to KAN (incorporating scientific knowledge into KANs), and KAN to science (extracting scientific insights from KANs). We highlight major new functionalities in pykan: (1) MultKAN, KANs with multiplication nodes, (2) kanpiler, a KAN compiler that compiles symbolic formulas into KANs; (3) tree converter, convert KANs (or any neural networks) into tree graphs. Based on these tools, we demonstrate KANs’ capability to discover various types of physical laws, including conserved quantities, Lagrangians, symmetries, and constitutive laws.

Probabilistic computing with p-bits is emerging as a computational paradigm for machine learning and for facing combinatorial optimization problems (COPs) with the so-called probabilistic Ising machines (PIMs). From a hardware point of view, the key elements that characterize a PIM are the random number generation, the nonlinearity, the network of coupled probabilistic bits, and the energy-minimization algorithm. Regarding the energy-minimization algorithm in this work we show that PIMs using the simulated quantum annealing (SQA) schedule exhibit better performance as compared to simulated annealing and parallel tempering in solving a number of COPs, such as maximum satisfiability problems, the planted Ising problem, and the traveling salesman problem. Additionally, we design and simulate the architecture of a fully connected CMOS-based PIM that is able to run the SQA algorithm having a spin-update time of 8 ns with a power consumption of 0.22 mW. Our results also show that SQA increases the reliability and the scalability of PIMs by compensating for device variability at an algorithmic level enabling the development of their implementation combining CMOS with different technologies such as spintronics. This work shows that the characteristics of the SQA are hardware agnostic and can be applied in the codesign of any hybrid analog-digital Ising machine implementation. Our results open a promising direction for the implementation of a new generation of reliable and scalable PIMs.

Time estimation is a fundamental task that underpins precision measurement, global navigation systems, financial markets, and the organization of everyday life. Many biological processes also depend on time estimation by nanoscale clocks, whose performance can be significantly impacted by random fluctuations. In this work, we formulate the problem of optimal time estimation for Markovian stochastic processes, and present its general solution in the asymptotic (longtime) limit. Specifically, we obtain a tight upper bound on the precision of any time estimate constructed from sustained observations of a classical, Markovian jump process. This bound is controlled by the mean residual time, i.e., the expected wait before the first jump is observed. As a consequence, we obtain a universal bound on the signal-to-noise ratio of arbitrary currents and counting observables in the steady state. This bound is similar in spirit to the kinetic uncertainty relation but provably tighter, and we explicitly construct the counting observables that saturate it. Our results establish ultimate precision limits for an important class of observables in nonequilibrium systems and demonstrate that the mean residual time, not the dynamical activity, is the measure of freneticity that tightly constrains fluctuations far from equilibrium.

A broad class of systems, including ecological, epidemiological, and sociological ones, are characterized by populations of individuals assigned to specific categories, e.g., a chemical species, an opinion, or an epidemic state, that are modeled as compartments. Because of interactions and intrinsic dynamics, the system units are allowed to change category, leading to concentrations varying over time with complex behavior, typical of reaction-diffusion systems. While compartmental modeling provides a powerful framework for studying the dynamics of such populations and describe the spatiotemporal evolution of a system, it mostly relies on deterministic mean-field descriptions to deal with systems with many degrees of freedom. Here, we propose a method to alleviate some of the limitations of compartmental models by capitalizing on tools originating from quantum physics to systematically reduce multidimensional systems to an effective one-dimensional representation. Using this reduced system, we are able not only to investigate the mean-field dynamics and their critical behavior, but we can additionally study stochastic representations that capture fundamental features of the system. We demonstrate the validity of our formalism by studying the critical behavior of models widely adopted to study epidemic, ecological, and economic systems.

We study the emergence of strong interactions between dissipative coherent structures (pulses) in spatially extended systems. Focusing first on a prototypical model problem from fluid dynamics, that of liquid film flowing down a vertical plane, we show that under certain conditions, a two-pulse system undergoes a transition from a regime of decaying oscillatory dynamics to one with self-sustained oscillations. Intriguingly, such a transition is not governed by the standard Hopf bifurcation. Instead, a novel governing mechanism for transition to oscillatory dynamics is unraveled via a peculiar and atypical Hopf bifurcation in which a complex-conjugate resonance pair crosses the imaginary axis in the complex plane. Prior to crossing the essential spectrum (including at the bifurcation point), this resonance pair does not appear in the standard $L_{\mathbb{C}}^2$-based spectral analysis but reveals itself when appropriate weighted functional spaces are used. We show that such a resonance pair originates from the splitting of a resonance pole of the single-pulse system. While this object is not part of the classical spectrum, it plays a vital role in shaping the system’s dynamics. We further demonstrate that this resonance-pole mechanism extends to a broad range of systems. Specifically, in the generalised Kuramoto-Sivashinsky equation—a model prototype applicable across a wide range of fields from fluid dynamics to geophysics and plasma physics—we observe the same bifurcation and resulting oscillatory pulse interactions. By contrast, in the FitzHugh-Nagumo model—a central model prototype in reaction-diffusion systems—the resonance pole splits into real eigenvalues, and monotonic pulse interactions occur. In addition, we illustrate that the resonance pole may induce oscillatory interactions in three-pulse systems and eventually lead to chaotic dynamics in strongly interacting multipulse systems, which can be quantified in terms of a positive Lyapunov exponent.

Current progress in artificial intelligence is centered around so-called large language models that consist of neural networks processing long sequences of high-dimensional vectors called tokens. Statistical physics provides powerful tools to study the functioning of learning with neural networks and has played a recognized role in the development of modern machine learning. The statistical physics approach relies on simplified and analytically tractable models of data. However, simple tractable models for long sequences of high-dimensional tokens are largely underexplored. Inspired by the crucial role models such as the single-layer teacher-student perceptron (also known as generalized linear regression) played in the theory of fully connected neural networks, in this paper, we introduce and study the bilinear sequence regression (BSR) as one of the most basic models for sequences of tokens. We note that modern architectures naturally subsume the BSR model due to the skip connections. Building on recent methodological progress, we compute the Bayes-optimal generalization error for the model in the limit of long sequences of high-dimensional tokens and provide a message-passing algorithm that matches this performance. We quantify the improvement that optimal learning brings with respect to vectorizing the sequence of tokens and learning via simple linear regression. We also unveil surprising properties of the gradient descent algorithms in the BSR model.

This work describes a blueprint for a process that accelerates progress in science by quantitatively answering the following question: What is the optimal combination of fundamental-science and application-driven experiments to maximally reduce pertinent data uncertainties? Answering this question entails solving a high-dimensional and complex optimization problem that is best solved with advanced statistic techniques often classified as machine learning. We apply this process within the framework of nuclear data with the aim to select an experiment combination that will reduce uncertainties in ${}^{239}\mathrm{Pu}$ nuclear data for neutron energies between 1 and 600 keV. In this field, fundamental-physics driven data, called differential, look at one nuclear physics observable at a time. They are contrasted to application-driven, integral, data where one or few resulting values inform a broad set of nuclear data across several nuclides and energies. The candidates for integral experiments are criticality measurements that were refined by a genetic algorithm to be maximally sensitive to ${}^{239}\mathrm{Pu}$ fission cross sections in the desired energy range. Twenty-three candidate differential experiments were investigated and span multiple nuclear physics observables (e.g., total, capture cross sections) for isotopes appearing in the integral experiments. The optimal combination among these candidate experiments was investigated via generalized least squares fitting, augmented with Gaussian processes to ameliorate statistical irregularities in data, and the D-optimality criterion. The latter evaluates for each pair of candidates the joint reduction in uncertainties of all 12200 nuclear data appearing in the integral experiments compared to the knowledge we have from 168 past experiments, theory, and nuclear data. We chose as differential measurements those that investigate ${}^{63}\mathrm{Cu}$ and ${}^{239}\mathrm{Pu}$ total cross sections, based on D-optimality rank and feasibility constraints. Two integral (criticality) experiments were selected: An experiment with ${\mathrm{Al}}_2{\mathrm{O}}_3$ and graphite interleaved with Pu and a thick Cu reflector explores 1–30 keV, while we target the 30–600 keV range with an experiment that swaps boron in place of graphite with a different geometry.

Simon’s problem is to find a hidden period (a bitstring) encoded into an unknown 2-to-1 function. It is one of the earliest problems for which an exponential quantum speedup was proven for ideal, noiseless quantum computers, albeit in the oracle model. Here, using two different 127-qubit IBM Quantum superconducting processors, we demonstrate an algorithmic quantum speedup for a variant of Simon’s problem where the hidden period has a restricted Hamming weight $w$. For sufficiently small values of $w$ and for circuits involving up to 58 qubits, we demonstrate an exponential speedup, albeit of a lower quality than the speedup predicted for the noiseless algorithm. The speedup exponent and the range of $w$ values for which an exponential speedup exists are significantly enhanced when the computation is protected by dynamical decoupling. Further enhancement is achieved with measurement error mitigation. This case constitutes a demonstration of a bona fide quantum advantage for an Abelian hidden subgroup problem.

Network flows are pervasive, including the movement of people, transportation of goods, transmission of energy, and dissemination of information; they occur on a range of empirical interconnected systems, from designed infrastructure to naturally evolved networks. Despite the broad spectrum of applications, because of their domain-specific nature and the inherent analytic complexity, a comprehensive theory of network flows is lacking. We introduce a unifying treatment for network flows that considers the fundamental properties of packet symmetries, conservation laws, and routing strategies. For example, electrons in power grids possess interchangeability symmetry, unlike packages sent by postal mail, which are distinguishable. Likewise, packets can be conserved, such as cars in road networks, or dissipated, such as Internet packets that time out. We introduce a hierarchy of analytical field-theoretic approaches to capture the different scales of complexity required. Mean-field analysis uncovers the nature of the transition through which flow becomes unsustainable upon unchecked growth of demand. Mesoscopic field theory accurately accounts for complicated network structures, packet symmetries, and conservation laws and yet is capable of admitting closed-form solutions. Finally, the full-scale field theory allows us to study routing strategies ranging from random diffusion to shortest path. Our theoretical results indicate that flow bottlenecks tend to be near sources for interchangeable packets and near sinks for distinguishable ones, and that dissipation hinders the maximum sustainable throughput for interchangeable packets but can enhance throughput for distinguishable packets. Finally, we showcase the flexibility of our multiscale theory by applying it in two distinct domains of road networks and the C. elegans neuronal network. Our work paves the way for a more unifying and comprehensive theory of network flows.

Within multicellular living systems, cells coordinate their positions with spatiotemporal accuracy to form various tissue structures and control development. These arrangements can be regulated by tissue geometry, biochemical cues, as well as mechanical perturbations. However, how cells pack during dynamic three-dimensional multicellular architectures formation remains unclear. Here, examining a growing spherical multicellular system, human lung alveolospheres, we observe an emergence of hexagonal packing order and a structural transition of cells that comprise the spherical epithelium. Surprisingly, the cell packing behavior on the spherical surface of lung alveolospheres resembles hard-disks packing on spheres, where the less deformable cell nuclei act as effective “hard disks” and prevent cells from getting too close. Nucleus-to-cell size ratio increases during lung spheroids growth; as a result, we find more hexagon-concentrated cellular packing with increasing bond orientational order. Furthermore, by osmotically changing the compactness of cells on alveolospheres, we observe a more ordered packing when nucleus-to-cell size ratio increases, and vice versa. These more ordered cell packing characteristics are consistent with reduced cell dynamics, together suggesting that better cellular packing stabilizes local cell neighborhoods and may regulate more complex biological functions such as cellular maturation and tissue morphogenesis.