We present an exact analysis of a spin-pseudospin sawtooth chain that incorporates three distinct valence states of copper ions and serves as a minimal model for one-dimensional cuprates composed of corner-sharing copper triangles. The model includes magnetic exchange and electrostatic coupling constants both along the base sites and between base and apex sites capturing the competition between spin and charge degrees of freedom. Using the transfer-matrix method, we derive exact expressions for the free energy and obtain an analytical condition defining the pseudocritical line associated with pronounced thermodynamic anomalies. The ground-state analysis reveals, besides an antiferromagnetic phase, three frustrated phases characterized by distinct residual entropies. At finite temperatures, these zero-temperature phase boundaries evolve into narrow entropy ridges signaling pseudotransitions between the corresponding quasiphases. The specific heat and the avoided-crossing scale exhibit sharp but continuous peaks at the pseudocritical temperature, whereas the physical correlation length may be controlled by a different subleading eigenvalue. Local correlation functions uncover a cooperative rearrangement from charge-dominated to magnetically correlated regimes. Our results demonstrate that the sawtooth geometry promotes frustration and short-range coherence leading to pronounced pseudotransition behavior.

Upon breaking the integrability, the equations of generalized hydrodynamics (GHD) are supplemented by a Boltzmann collision term. Such terms are typically complicated and stem from a perturbative treatment of integrability-breaking terms in the Hamiltonian. In our work, we study a simplified version of the collision operator in a form of relaxation time approximation familiar from kinetic theory. We explicitly compute transport coefficients which characterize the Navier-Stokes (NS) hydrodynamic regime emerging at large space-time scales. We also thoroughly study the crossover between GHD and NS hydrodynamic descriptions, identifying relevant characteristic space-time scales for the transition. In particular, we show how the emergence of NS hydrodynamics is visible in the dynamics of conserved and nonconserved charge densities and in hydrodynamic two-point functions.

We consider the number of ways all the sites of a kagome lattice can be covered by nonoverlapping linear rigid rods where each rod covers three sites. We establish a two-to-one correspondence between the configurations of trimers on the kagome lattice to the covering by dimers of a related hexagonal lattice to show that entropy of coverings per trimer $s_{\text{tri,kag}}$ equals the entropy per dimer $s_{\text{dim,hex}}$, and is given by $s_{\text{tri,kag}}=s_{\text{dim,hex}}=\frac{1}{2\pi }{\int }_0^{2\pi /3}ln(2+2cosk)dk\approx 0.323065947...$.

The role of quantum entanglement in thermodynamical systems remains elusive. Does entanglement result in thermodynamic advantages or does it impose fundamental limitations? Here, we unambiguously quantify the amount of heat and work in a quantum system that is due to the presence of entanglement. This is achieved by constraining the system's nonequilibrium dynamics to separable states, thereby isolating the impact entanglement has on thermodynamic effects. Unlike thermodynamic entanglement measures, which signify a loose connection between entanglement and thermodynamic properties, imposing a constraint constitutes an active intervention into a system—answering how much of a system's thermodynamics is caused by (not correlated with) its quantumness. We benchmark our theory by applying the constrained dynamics to several multipartite systems, including quantum batteries and quantum refrigerators.

Deterministic chaos is usually associated with local spectral expansion: Jacobian eigenvalues are expected to exceed unity somewhere on the attractor. We show that this view is incomplete in dimensions $d>1$. For non-normal Jacobians, pointwise spectral stability can suggest everywhere local contraction, while nonorthogonal eigenvectors still allow transient singular-vector amplification. We construct four low-dimensional deterministic maps realizing this mechanism: partition-reinjected, phase-prescribed, feedback-driven, and affine-reinjected non-normal routes to chaos. In all cases, the sampled one-step Jacobian remains spectrally stable at every point on the attractor away from switching boundaries, with the eigenvalues of the common planar core fixed inside the unit disk. Nevertheless, increasing non-normality raises the maximal Lyapunov exponent from negative to positive values, corresponding to sustained asymptotic chaos, not transient chaos. Across the four classes, the common signature is spectral radius ${\rho }_{\mathrm{traj}}^{max}<1$, singular value ${\sigma }_{\mathrm{traj}}^{max}>1$, maximal Lyapunov exponent ${\lambda }_1>0$, and an increase of attractor dimension. These examples identify non-normality and recurrent reinjection of transiently amplified directions as a deterministic route to chaos distinct from eigenvalue instability.

We study the large-deviation properties of minimum spanning trees for two ensembles of random graphs with $N$ nodes. First, we consider complete graphs. Second, we study Erdős-Rényi (ER) random graphs with edge probability $p=c/N$ conditioned on being connected. By using large-deviation Markov-chain sampling, we can obtain the distribution $P\left(W\right)$ of the spanning-tree weight $W$ down to probability densities as small as ${10}^{-300}$. For the complete graph, we confirm analytical predictions with respect to the expectation value. For both ensembles, the large-deviation principle is fulfilled. For the connected ER graphs, we observe a remarkable change of the distributions at the value of $c=1$, which is the percolation threshold for the original ER ensemble.

Extracellular ion concentrations directly influence neuronal excitability, synaptic transmission, and the generation of electrical signals. Capturing the ionic dynamics is essential for modeling both healthy and pathophysiological brain function. Here we explore how variations in ion concentration in the extracellular space affect the generation and propagation of traveling fronts of activity in cortical tissue. To this end, we develop a neural field model in which neuronal excitability is modulated by the local extracellular ionic concentration. Using an interface dynamics approach, we derive an analytic expression for the speed of propagating activity fronts. We demonstrate that increasing the ionic diffusion coefficient leads to a reduction in front speed. In addition, analysis of stationary bump solutions reveals that increases in the diffusion rate reduces the size of a region of high activity required to initiate a propagating front.

We report a seeding mechanism for the current filamentation instability that was identified using an experimental platform where a relativistically intense 2-ps (full width at half maximum) long-wavelength infrared pump laser both produces and interacts with a plasma that is overdense to the pump yet transparent to a near-infrared probe laser. This platform enables simultaneous high spatial resolution measurements of the self-generated magnetic filaments using Faraday rotation polarimetry and density filaments using interferometry. Supporting simulations show that the highly nonlinear dependence of the ionization rate on the local sheath electric field produced by pump-laser-heated hot electrons gives rise to $20\text{−}\mu \mathrm{m}$-scale filaments of cold electrons that form a return current, generating local azimuthal magnetic fields that can last for over 100 picoseconds.

We develop an analytical theory of coherent (scaled quadratically with the number of particles) radiation and coherent radiation friction in a head-on collision of a dense charged particle bunch with an intense laser pulse. We demonstrate that the low-frequency coherent radiation in the forward and backward directions dominates the energy-momentum losses of a mildly relativistic bunch and can result in a substantial enhancement of the overall radiation friction as compared to the incoherent case. We derive the scaling laws for the average momentum losses of the bunch over the collision with respect to laser intensity, pulse duration, and particle bunch parameters, and show their robustness with respect to laser polarization and the shape of the particle distribution in the bunch.

A theoretical study is presented of nematic liquid crystals confined between two concentric cylindrical surfaces under a radially inhomogeneous electric field, focusing on the interaction among elastic anisotropy, cylindrical geometry, and flexoelectric surfaces. Two alignment regimes are considered: planar under positive dielectric anisotropy, and homeotropic under negative dielectric anisotropy, both with strong anchoring at the inner and outer cylinders. The molecular reorientation behavior is related to measurable electrical quantities by modeling the nematic cell as an equivalent parallel $\mathit{RC}$ circuit and deriving expressions for resistance, capacitance, and time-dependent current under a linearly ramped voltage. Numerical results reveal how the flexoelectric coefficients (magnitude and sign), the elastic anisotropy ratio, and the geometry (inner and outer radii) influence the threshold behavior and post-threshold dynamics of the director field, thereby affecting the electrical response. In particular, it is shown that the electrical response of cylindrical nematic devices can be controlled by adjusting flexoelectric coefficients and the elastic anisotropy in this geometry.

The origin of some mesophases of the ferroelectric nematic realm is not yet well understood. In this work, we study the highly polar liquid crystal MIO, a close structural analog of the prototypical ferroelectric nematogen DIO, which exhibits a ferroelectric smectic A to ferroelectric smectic C (${\mathrm{SmA}}_{\text{F}}–{\mathrm{SmC}}_{\text{F}}$) phase transition. Calorimetric, dielectric, and light-scattering experiments reveal that it is a second-order phase transition with mean-field behavior and is driven by the softening of the tilt elastic constant accompanied by the divergence of the amplitude of the associated dielectric mode.

Amorphous particulate matter constitutes a wide range of natural and synthetic materials. Despite this ubiquity, the way in which these systems' disordered microstructure couples to their often subtle and complex dynamical behavior is not yet fully understood, with profound consequences for phenomena ranging from landscape evolution to cellular unjamming during tumor metastasis. With this paper, we introduce tools from linear control theory that quantify system response to external input, and demonstrate their utility in elucidating the dynamics of jammed amorphous materials under stress. Our results indicate that average controllability, the response of a system to perturbation, strongly correlates with particle rearrangement in systems subject to quasistatic shear, implying that average controllability is an accurate predictor of rearrangement dynamics in certain contexts. Moreover, we show that the timescale over which average controllability is calculated can be tuned to optimize its predictive capacity for particle rearrangement. Values of the optimal timescale provide physical insight into the system; namely, that multiple rearranging particles participate on average in vibrational eigenmodes of lower and lower energy as the system is sheared until the rearrangement event. Broadly, our study demonstrates that linear control theory is a promising mathematical framework for predicting and designing mechanical response in disordered media.

We present an analytical investigation of the global helicity budget associated with the salt-fingering instability within the two-dimensional, three-component framework. Our analysis shows that in the region of parameter space corresponding to salt fingering, helicity amplification occurs when the Rayleigh ratio—quantifying the relative strength of salinity to temperature gradients—exceeds a critical threshold. This finding provides a possible theoretical explanation for the spontaneous emergence of helicity, observed in recent numerical simulations.

Filtering methods are fundamental tools for extracting the backbone of complex networks. Systems displaying group interactions, however, open the way to new types of filtering approaches. Here, we introduce a statistical filtering method for higher-order networks that identifies statistically validated maximal interacting sets—maximal sets of nodes that consistently interact together within group interactions. Using properly designed benchmarks, we show that our approach is highly effective in systems where the maximal sets are likely to be diluted into interactions of larger sizes that include occasional participants. Applications to real-world data reveal that the identified sets of nodes are characterized by higher levels of similarity and topical coherence, highlighting the ability of our method to provide new insights on the organization of real-world higher-order networks.

Neural circuits exhibit structured connectivity, including an overrepresentation of reciprocal connections between neuron pairs. Despite important advances, a full understanding of how such partial symmetry in connectivity shapes neural dynamics remains elusive. Here we ask how correlations between reciprocal connections in a random, recurrent neural network affect phase-space complexity, defined as the exponential proliferation rate (with network size) of the number of fixed points that accompanies the transition to chaotic dynamics. We find a striking pattern: partial antisymmetry strongly amplifies complexity, while partial symmetry suppresses it. These opposing trends closely track changes in other measures of dynamical behavior, such as dimensionality, Lyapunov exponents, and transient path length, supporting the view that fixed-point structure is a key determinant of network dynamics. Thus, positive reciprocal correlations favor low-dimensional, slowly varying activity, whereas negative correlations promote high-dimensional, rapidly fluctuating chaotic activity. These results yield testable predictions about how connection reciprocity may shape neural dynamics and function.

Photonic and polaritonic systems offer a fast and efficient platform for accelerating machine learning (ML) through physics-based computing. To gain a computational advantage, however, polaritonic systems must meet the following: (1) exploit features that specifically favor nonlinear optical processing; (2) address problems that are computationally hard and depend on these features; and (3) integrate photonic processing within broader ML pipelines. In this work, we propose a polaritonic machine learning approach for solving graph-based data problems. We demonstrate how lattices of condensates can efficiently embed relational and topological information from point cloud datasets. This information is then incorporated into a pattern recognition workflow based on convolutional neural networks (CNNs), leading to significantly improved learning performance compared to physics-agnostic methods. Our extensive benchmarking shows that photonic machine learning achieves over 90% accuracy for Betti number classification and clique detection tasks, a substantial improvement over the 35% accuracy of bare CNNs. Our study introduces a distinct way of using photonic systems as fast tools for feature engineering, while building on top of high-performing digital machine learning.

Vibrational properties of ordered athermal solids near yielding remain poorly understood. We show that yielding in a sheared crystal is governed not by a single localized instability but by directionally extended multimode softening that forms a cross-shaped low-frequency region in wave number space. Near yielding, the acoustic dispersion $\omega \sim k$ is replaced by $\omega \sim k^2$ along the soft direction, and the vibrational density of states crosses over from Debye to non-Debye scaling, with a diverging length scale. We analytically derive these scaling laws.

Stochastic fluctuations often act as promoters of activity in excitable and oscillatory systems, giving rise to phenomena such as coherence resonance. Here, we show that in the low-intensity regime, noise plays a dual role in weakly coupled neuronal units: It can both inhibit collective spiking and, with increasing intensity, restore coordinated activity. For a ring of diffusively coupled, oscillatory FitzHugh-Nagumo neurons, we demonstrate how the interplay of noise and coupling strength organizes a rich set of collective dynamical states. We systematically classify emergent dynamical scenarios by an in-depth time-series analysis that integrates multiple complementary measures. We are able to automatically identify five distinct dynamical clusters in parameter space: pure noise, quiescent state, noisy synchronization, complete synchronization, and intermittent switching. Our workflow provides a general, automated framework for characterizing collective dynamics in coupled oscillator networks.

This work presents a general thermodynamic approach to describe particle diffusion on a lattice, a model used to study transport processes in solids and on surfaces. By treating each lattice site as an open thermodynamic system, the effects of microscopic particle interactions are represented through the chemical potential. A fundamental relationship between the Onsager matrix $\left(L\right)$ and its ideal-system counterpart ($L_{\text{id}}$, where interactions are neglected) using the determinant of the covariance matrix is demonstrated. This framework allows for the calculation of transport coefficients using the combination of their ideal values and thermodynamic properties. The general result is successfully applied to reproduce the Darken equation for substitutional diffusion in solids and to derive the nondiagonal diffusion matrix of the Zhdanov model for surface diffusion of Langmuir particles. In the last case, analytical predictions are further validated through numerical simulations across various interaction potentials.