The Boltzmann distribution for an equilibrium system constrains the statistics of the system by the energetics. Despite the nonequilibrium generalization of the Boltzmann distribution being studied extensively, a unified framework valid for far-from-equilibrium discrete-state systems is lacking. Here, we derive an exact path-integral representation for discrete-state processes and represent it using the exponential of the action for stochastic transition dynamics. Solving the variational problem, the effective action is shown to be equal to the inferred entropy production rate (a thermodynamic quantity) and a nonquadratic dissipation function of the thermodynamic length (TL) defined for microscopic stochastic currents (a dynamic quantity). This formulates a far-from-equilibrium analog of the Boltzmann distribution, namely, the minimum action principle. The nonquadratic dissipation function is physically attributed to incorporating non-Gaussian fluctuations or far-from-equilibrium nonconservative driving. Further, an exact large deviation dynamical rate functional is derived. The equivalence of the variational formulation with the information geometric formulation is proved. The nonquadratic TL recovers the nonquadratic thermodynamic-kinetic uncertainty relation (TKUR) and the speed limits, which are tighter than the close-to-equilibrium quadratic formulations. Moreover, if the transition affinities are known, then the nonquadratic TL recovers the fluctuation relation (FR). The minimum action principle manifests the nonquadratic TKUR and FR as two faces corresponding to the thermodynamic inference and partial control descriptions, respectively. In addition, the validity of these results is extended to coarse-grained observable currents, strengthening the experimental/numerical applicability of them.

We investigate collective dynamics in a pulse-coupled adaptive Winfree network under the influence of a frustration (phase-lag) parameter. The coupling strengths coevolve according to a Hebbian adaptation rule and self-organize to support a wide variety of collective states. We observe frequency-clustered states, entrainment, bump states, bump-frequency cluster states, antipodal and multiantipodal cluster states, chimera states, and incoherent dynamics. Notably, we report the spontaneous emergence of entrainment, bump, and bump-frequency cluster states in an adaptive network without any external forcing. To systematically characterize these regimes, we introduce three complementary measures of incoherence based on (i) time-averaged frequencies, (ii) instantaneous phases, and (iii) mean frequencies per bin. These measures enable the construction of one- and two-parameter phase diagrams that clearly delineate transitions between distinct dynamical states. Furthermore, we analytically derive the stability condition for the frequency-entrained state, which shows excellent agreement with numerical simulations. Our results highlight the crucial role of frustration-mediated plasticity in shaping rich self-organized dynamics in pulse-coupled adaptive networks.

When exposed to a contagion phenomenon, individuals may respond to the perceived risk of infection by adopting behavioral changes, aiming to reduce their exposure or their risk of infecting others. The social cost of such adaptive behaviors and their impact on the contagion dynamics have been investigated in pairwise networks, with binary interactions driving both contagion and risk perception. However, contagion and adaptive mechanisms can also be driven by group (higher-order) interactions. Here, we consider several adaptive behaviors triggered by awareness of risk perceived through higher-order and pairwise interactions, and we compare their impact on pairwise and higher-order contagion processes. By numerical simulations and a mean-field analytic approach, we show that adaptive behaviors driven by higher-order information are more effective in limiting the spread of a contagion, than similar mechanisms based on pairwise information. Meanwhile, they also entail a lower social cost, measured as the reduction of the intensity of interactions in the population. Indeed, adaptive mechanisms based on higher-order information lead to a heterogeneous risk perception within the population, producing a higher alert on nodes with large hyperdegree (i.e., participating in many groups), on their neighborhoods, and on large groups. This in turn prevents the spreading process to exploit the properties of these nodes and groups, which tend to drive and sustain the dynamics in the absence of adaptive behaviors.

This study investigates the evolution mechanism of elastic instability in a bilateral double-cavity channel through numerical simulations and microfluidic experiments. Depending on the Weissenberg number ($\text{Wi}$), the flow is categorized into three regimes: stable symmetric vortex structures at low $\text{Wi}$ ($\text{Wi}\le 4.5$); periodic corner vortices with horizontal symmetry breaking at intermediate $\text{Wi}$ ($5\le \text{Wi}\le 7.5$); and strongly asymmetric flow at high $\text{Wi}$ ($\text{Wi}\ge 8.5$). Power spectral density and correlation analyses reveal that the periodic evolution of corner vortices indicates a potential breathinglike mechanism driven by hydrodynamic interactions between cavities. At high $\text{Wi}$, enhanced elastic stresses lead to pronounced asymmetry, as corner vortices gradually expand to fill the cavities, exacerbating the flow instability. Experimentally, polyacrylamide solutions with concentrations of 100, 200, and 300 ppm were employed for validation. Fluorescent particle tracking results qualitatively support the numerical predictions, consistently revealing the instability dynamics associated with symmetry breaking. Furthermore, a two-level multiresolution dynamic mode decomposition was conducted to uncover the multiscale dynamics of the instability. Level 0 modes capture low-frequency, large-scale structures, while Level 1 modes resolve localized high-frequency oscillations in the shear layers. At $\text{Wi}=2.5$, the flow remains fully symmetric and stable, with cavity modes exhibiting high coherence. At $\text{Wi}=5$, symmetry breaking arises between the left and right cavities, and the amplitudes of unstable modes in both levels increase to $O\left({10}^{-1}\right)$, indicating that both large-scale structures and high-frequency fluctuations play significant roles. At $\text{Wi}=25$, the flow becomes strongly unstable with an increased number of modes exhibiting positive growth rates. The dominant structures display marked asymmetry in both streamwise and transverse directions, while localized high-frequency oscillations are superimposed on large-scale recirculation patterns, revealing multiscale interactions between global vortex dynamics and localized shear-layer instabilities.

Progress towards achieving net gain from nuclear fusion is typically characterized by the triple product $nT\tau$. Although stellarators have several benefits for a reactor, such as the inherent steady-state capability and the lack of disruptions, the maximum achieved triple product has historically lagged behind that of tokamaks. In the large optimized stellarator Wendelstein 7-X, a triple product of $(1.10\pm 0.15)\times {10}^{20}{\mathrm{m}}^{-3}\mathrm{keV}\mathrm{s}$ has recently been achieved and held stable for 1.9 s. This marks an important step in stellarator core plasma performance and puts it in line with $H$-mode performance in similar sized tokamaks. The progress in Wendelstein 7-X performance is due to the suppression of ion-temperature-gradient turbulence by strong density gradients. In the record case, these are maintained by a fine balance of the core particle transport and central fueling using neutral beam injection. The duration of the scenario was limited in time only by technical restrictions of the neutral beam injectors and control of the divertor heat loads. This paper presents the result in the context of the leading magnetic confinement devices along with details of the scenario.

We introduce a family of classical stochastic processes describing diffusive particles undergoing branching and long-range annihilation in the presence of a parity constraint. The probability of a pair-annihilation event decays as a power-law in the distance between particles, with a tunable exponent. Such long-range processes arise naturally in various classical settings, and increasingly play a role in the study of quantum dynamics: for example, quantum state preparation or error correction processes aim to prepare ordered ground states, which requires removing pointlike excitations in pairs via nonlocal feedback operations conditioned on a global set of measurement outcomes. We analytically and numerically describe features of absorbing phases and phase transitions in this family of classical models as pairwise annihilation is performed at larger and larger distances. Notably, we find that the two canonical absorbing-state universality classes—directed percolation and parity conserving–are endpoints of a new line of universality classes with continuously varying critical exponents. These new classes follow from an interplay of long-range interactions and symmetries: decreasing the long-range exponent effectively weakens the local effects of global symmetry constraints. This competition significantly broadens known nonequilibrium phases and phase transitions.

We develop a closed-form analytical theory for the transport of a chiral active Brownian particle in three dimensions, moving through a fluctuating local density field that models steric and dynamical interactions in a dense active medium. The density field is modeled as an Ornstein-Uhlenbeck process with finite correlation time $\tau$ and fluctuation strength ${\sigma }_{\rho }^2$, capturing both spatial fluctuations and temporal memory. Within this framework, we derive exact expressions for the mean-square displacement and time-dependent diffusivity, revealing how chirality and density coupling jointly renormalize orientational persistence and generate nontrivial dynamical crossovers. The theory predicts (i) anomalously high initial diffusivity for particles starting in locally denser regions, arising from a transient active drift driven by local swim-pressure gradients; (ii) a finite crossover time $t_c$ for homogenizing density inhomogeneities, with a transient dependence of the dynamics on the initial local density environment which arises from the nonequilibrium evolution of density fluctuations and does not persist when averaging over stationary initial conditions (${\rho }_0={\rho }_{\infty }$); (iii) a nonmonotonic $t_c\left(\mathrm{\Omega }\right)$ with a global minimum at intermediate chirality, and a three-regime suppression of long-time diffusivity $D_{\infty }\left(\mathrm{\Omega }\right)$, consistent with microclustered phases observed in simulations; and (iv) a resonance like peak in the early-time oscillatory strength of the mean-square displacement at an optimal chirality ${\mathrm{\Omega }}^{*}$, set by the interplay of orientational diffusion, density-field decorrelation, and imposed rotation. The framework captures the qualitative dependence of $D_{\infty }$ on Pe and $\mathrm{\Omega }$, where Pe denotes the Péclet number, while uncovering chirality-dependent transport features in active matter, offering a qualitative perspective for understanding transport in biological systems and suggesting possible directions for designing active materials.

Layers composed of lateral connections are ubiquitous in biological systems from subcellular membranes to epithelial sheets. Such layers are often found in nonflat environments, such as the ellipsoidal Drosophila embryo. Here we build on Lou et al. [Phys. Rev. Lett. 130, 108401 (2023)] to provide a more complete description of the impact on three-dimensional (3D) cell shape of mechanical forces within a curved domain. We construct a generalizable model for the emergence of stress anisotropy as a function of depth in different curvature settings. We principally consider an epithelial monolayer to explain how the interplay between layer curvature and cell mechanics determines the stress anisotropy. We show that this can lead to irregular cellular shapes in 3D. Though here we principally focus on axisymmetric geometries, our framework is general and can be extended to a diverse set of biologically relevant systems.

Continuous spin models with long-range interactions of the form $r^{-\sigma }$, where $r$ is the distance between two spins and $\sigma$ controls the decay of the interaction, exhibit enhanced order that competes with thermal fluctuations, leading to a wide variety of phases and types of phase transitions. Here, we identify that the true long-range ordered phase encompasses distinct scaling regimes, which we term enhanced long-range ordered (EnLRO) and reduced long-range ordered (ReLRO) regimes. In the former regime, the spin-spin correlation function decays exponentially to a finite value, whereas in the latter regime it decays algebraically to a finite value. In the one-dimensional XY model, the crossover from EnLRO to ReLRO regimes occurs around $\sigma \approx 1.575$, while in two dimensions, the crossover happens near $\sigma \approx 3.2$. Applying finite-size scaling analysis, we extract the critical exponents that characterize the order-to-disorder phase transitions in the EnLRO and ReLRO regimes, constructing comprehensive phase diagrams. The analysis is further extended to the one- and two-dimensional long-range Heisenberg models, where we find the EnLRO-ReLRO crossover at $\sigma \approx 1.575$ and $\sigma \approx 3.22$, respectively. The similar crossover points suggest that the distinction between EnLRO and ReLRO regimes is a generic feature in continuous spin models with long-range interactions. The persistence of EnLRO regime can be attributed to the interplay between the short-range spin wave and the long-range order.

Thouless pumps are time-periodic one-dimensional systems that capture the physics of the two-dimensional quantum Hall effect via the quantized pumping of particles under adiabatic modulation. Recent work in photonics has shown that nonlinearity can act to quantize the displacement of light in the form of soliton motion. Here we use a mechanical system, namely, coupled pendulums described by the Frenkel-Kontorova model, to propose and observe quantized nonadiabatic Thouless pumping using topological kink solitons. The pumping proceeds by a qualitatively different mechanism compared to Thouless' original proposal as the pump is nonadiabatic and dissipation is necessary. In the presence of an additional potential gradient along the pump, we predict and observe the emergence of quantized transport against the pumping direction as a function of the period and show the emergence of a rich plateau structure; this quantization is unique to dissipative systems and cannot be described by the Chern number. Finally, we experimentally demonstrate the robustness of the process by pumping the soliton through a tunable nonlinear defect.

Understanding the mechanisms that shape bacterial community composition has implications in the ecology and evolution of both natural and synthetic microbial communities. Quorum sensing (QS), the regulation of cellular activity through signal exchange as a response to cell density, is a common mechanism of gene regulation in bacteria. The potential implications of QS in microbial community dynamics remain poorly understood. To investigate the impact of QS on community dynamics, QS-based changes in cellular activity were incorporated into a Lotka-Volterra (LV) model. Simulations approximated the dynamics of a multispecies bacterial community undergoing serial dilutions. The effects of QS were incorporated as an instantaneous and random change on interspecies interactions upon exceeding a threshold cell density. The addition of QS to the standard LV model increased the percentage of surviving species within the community, often benefiting both QS and non-QS species. This community benefit remained, even if incorporating reasonable energetic costs of QS. Competitive effects from QS cheater strains were tested: A noncheater strain was always outcompeted by cheaters when growing in a single population, while in a community context, the change of interspecies interactions due to QS increased the survival likelihood of the noncheater strain. Antifragile regimes, where variability enhances diversity, were promoted by QS, QS increased the variability of interactions, and higher variability increased community diversity. Our model generalizes prior ecological LV models with density-dependent interactions and shows that antifragile regimes induced from responses to a community's states (for example, through QS) might be an important mechanism to stabilize complex communities.

Three-dimensional (3D) asymmetries and their associated residual kinetic energy (RKE) are a major performance-degradation mechanism in inertial-confinement fusion (ICF) implosions at the National Ignition Facility (NIF). These asymmetries can be diagnosed with the three neutron imaging systems fielded with orthogonal views to the implosion, as well as a suite of real-time neutron activation diagnostics (RTNADs) and neutron spectrometers. Conventional tomographic reconstructions are typically used to reconstruct the 3D morphology of the hot spot and surrounding dense fuel in an implosion using neutron images, but the reconstruction problem is ill-posed with only three imaging lines of sight. In this work a 3D reconstruction technique has been developed and used to overcome these limitations by combining information from the neutron images, RTNAD data, and neutron spectra to infer RKE. Markov chain Monte Carlo is used along with a group of neural networks to fit a physics model to the observed data to robustly reconstruct the 3D morphology of the hot spot and dense fuel in a NIF implosion. Bayesian statistics provides quantification of the uncertainty in the inference. Initial inferences find that the normalized RKE on several NIF experiments is between 2% and 5% of the total implosion energy, and is inversely related to the yield of an implosion, as expected. This technique is being developed to help guide designs toward minimizing asymmetries in ICF implosions and achieving higher performance.

We investigate the asymptotic failure of the network arising solely from intrinsic fluctuations in the flux passing through its nodes. By modeling the flux as random walkers and the node failure induced by large fluctuations as extreme events, it is shown that three distinct nodal failure regimes can be identified before a complete network failure takes place. Further, the approach to network failure through these three regimes is shown to be qualitatively similar for square lattice, all-to-all, scale-free, and Erdos-Renyi networks. We obtain approximate analytical description of the approach to failure for an all-to-all network. This network failure scenario is also demonstrated on a real flight transportation network.

We investigate a deformable spin-1/2 Ising chain subjected to either a longitudinal or a transverse magnetic field, which incorporates a magnetoelastic coupling linearly dependent on a lattice distortion parameter. Within the harmonic and static adiabatic approximations, the variational Gibbs free energy is evaluated exactly using transfer-matrix and Jordan-Wigner fermionization techniques and then minimized self-consistently with respect to the lattice distortion parameter. This approach enables a unified description of magnetic and elastic properties including the magnetization, magnetic susceptibility, lattice distortion, inverse compressibility, and relative change in the sound velocity. In a longitudinal magnetic field, the deformable Ising chain displays a line of discontinuous thermal phase transitions terminating at a critical point. The discontinuous transitions are accompanied by metastable states, which give rise to a hysteresis loop at low temperatures. In contrast, the deformable Ising chain in a transverse field undergoes exclusively a continuous quantum phase transition at zero temperature with no indication of thermal phase transitions. The magnetic susceptibility and inverse compressibility exhibit cusp- and dip-like anomalies at discontinuous phase transitions, while a diverging susceptibility and vanishing inverse compressibility characterize the continuous phase transitions. An elastic softening of the deformable chain near thermal and quantum phase transitions manifests itself also through a significant sound attenuation.

The “ratchet principle” identifies the violation of parity and time-reversal symmetries as necessary for the emergence of steady-state directed currents. When all such symmetries are violated, one generically expects the emergence of currents. We study stochastic systems in the presence of asymmetric fluctuation sources, which violate these symmetries and yet fail to display steady currents. We show that this stems from a hidden conservation law for momentum. For underdamped and overdamped Brownian dynamics, we show that thermal fluctuations cannot power the momentum sources required to sustain directed currents, even when time-reversal symmetry is broken due to an inhomogeneous temperature field. While active Brownian and run-and-tumble particles display interaction-induced directed currents in asymmetric activity landscapes, we show that effective momentum conservation prevents this in Active Ornstein-Uhlenbeck particles: not all inhomogeneous active fluctuations can power transport. For each of the systems considered in this article, we numerically test for the emergence of interaction-induced directed currents. We then characterize time-reversal (a)symmetry in position space using a combination of path-integral and operator methods. When the existence of effective momentum conservation is ruled out, we develop perturbation theories to characterize the onset of interaction-induced directed currents.

We show that the statistics of chaotic systems can be predicted by constructing an associated sequence of periodic differential operators and computing their densities of states. For such operators, the density of states is well understood and can be computed straightforwardly, often yielding explicit formulas. As a case study, we investigate a nonlinear recursion relation that maps naturally onto a family of periodic operators generated by a Fibonacci tiling rule. This correspondence enables us to derive an explicit formula for the limiting statistics of the chaotic system and to demonstrate that the clustering near critical values is equivalent to the van Hove singularities in the operators' densities of states.

Synchronization control in networked dynamical systems requires regulating not only whether coherence is achieved but also when and to what extent it emerges. We propose a physics-informed neural network framework for continuous-time synchronization regulation, in which system trajectories and control inputs are jointly parameterized and constrained by the governing dynamics. Macroscopic synchronization objectives are imposed directly at the trajectory level by enforcing persistence conditions on the order parameter after a prescribed target time. This formulation enables simultaneous control of synchronization time and coherence level without assuming any explicit feedback law or solving a strict optimal control problem. Numerical studies on networked Kuramoto oscillators demonstrate smooth synchronization with reduced transient control effort and competitive cumulative cost relative to analytical baselines. The framework remains effective in nongradient and frustrated dynamics, highlighting physics-informed neural control as a flexible trajectory-level approach to synchronization regulation. This perspective enables controlled access to nontrivial collective states, including chimera and chaotic dynamics.

Water-wave focusing is a significant technology for enhancing wave energy density, which can effectively improve the efficiency of the wave energy converter. To achieve parabolic focusing of water waves using a straight boundary, the space transformation method (STM) was employed to map a parabolic reflector onto a straight configuration. Initially, a straight reflector was designed using the STM by spatially compressing the domain of a parabolic reflector. The spatial transformation relationship between the parabolic and straight reflectors was established. Subsequently, leveraging the form invariance of the governing equation for water waves, the ideal effective parameters, including anisotropic water depth and gravitational acceleration within the transformed region, were derived. To circumvent the impracticality of altering gravitational acceleration, a set of simplified anisotropic parameters was obtained by incorporating the scale factor of gravity acceleration into the adjusted water depth. Finally, the Helmholtz equation was solved via the finite element method to analyze the focusing performance of three configurations: the original parabolic reflector, the ideal straight reflector, and the simplified straight reflector. The results demonstrate that the proposed straight reflector successfully focuses water waves at designated points corresponding to those of the parabolic reflector. Moreover, the wave distribution of the ideal straight reflector in the unmodified region beyond the transformed reflector area is identical to that generated by the parabolic reflector.

The development of hydrodynamic instabilities may be significantly affected by the presence of suprathermal high-energy particles (HEPs). These effects are particularly pronounced in high-energy-density plasmas. We develop a single-equation diffusion-type turbulence model that describes the turbulent mixing arising from the growth of instability at the interface of a material that strongly emits HEPs. We derive a basic governing equation of this model and its self-similar solutions, which allow us to constrain the growth rate of the mixing zone width $h_{\text{turb}}$. We show that key turbulence characteristics, including the spectrum and the mixing zone dynamics, depend primarily on the ratio of HEP free paths in the active and passive materials. In particular, the model predicts an asymptotic behavior $h_{\text{turb}}\sim t^{1/3}$ when the HEP free path in the active material exceeds that in the passive material, and $h_{\text{turb}}\sim t^{2/5}$ in the opposite case. We compare the predictions of the derived model with three-dimensional simulations of instability development and find good agreement between the simulated evolution of the mixing zone width and that obtained by numerical integration of the model equation. The asymptotic growth rates inferred from the self-similar solutions are also observed in the simulations.

Relaxation dynamics of supercooled liquids approaching glassy arrest remain a central challenge in integrated electronic architectures, where conventional rheometry becomes incompatible. Here, we demonstrate that an ambipolar ${\mathrm{PdSe}}_2$ field-effect transistor functions as an electrical probe capable of resolving ion-specific relaxation dynamics in fragile ionic glass formers and semiquantitatively inferring rheological parameters within an operating device environment. Temperature evolution of the transfer curve hysteresis and time-resolved current transients under ionic-gate pulse reveal a non-Arrhenius fragile slowdown. We track the continuous reduction of dynamically equilibrated liquid regions approaching the glass transition through an electrically accessible quantity $p_{\text{eq}}\left(T\right)$, quantifying the fraction of the mobile ions able to relax within the experimental timescale. Upon cooling, $p_{\text{eq}}$ collapses sharply as mobile regions fragment into percolating fractal clusters, consistent with a reduction of configurational entropy predicted for fragile glass formers. This approach enables temperature-dependent scaling of viscosity and extraction of characteristic temperatures marking the ergodic-to-nonergodic crossover, within a solid-state device architecture where conventional rheological characterization is inapplicable. Further, polymer confinement of the ionic liquid shifts these characteristic temperatures upward, demonstrating the sensitivity of this method to structural constraints imposed by the polymer matrix.