How much information about an unknown parameter can be assigned to one realized outcome, and how is that information constrained by the sensitivity of the same outcome? We derive upper bounds on the pointwise mutual information in terms of the stochastic Fisher information, both for parameters in a bounded interval and for sufficiently regular differentiable priors, and state the corresponding saturation conditions. Averaging the pointwise inequality and applying Jensen's inequality twice yields the known mutual-information–Fisher-information bound, while making explicit the outcome dependence discarded by the ensemble description. We illustrate the classical result using the instantaneous position of an overdamped Langevin particle as the observed outcome. For a fixed, parameter-independent quantum measurement, the stochastic Fisher information is further bounded by the conditional quantum Fisher information (CQFI), whose probability-weighted mean is the quantum Fisher information. A thermal-qubit field-sensing example evaluates this finite-prior bound deterministically from exact $2\times 2$ matrices and, separately, decomposes the projected SLD second moment into population, coherent, and interference contributions. The interference contribution can be negative for an individual probe direction and has zero unweighted trace, but it is not itself an operational measure of readout quality. Neither the CQFI nor its mean selects a measurement basis: the latter is measurement-independent, whereas the relevant basis-dependent local objective is the classical Fisher information of the chosen measurement.

We study the effects of phase-frustrated, higher-order interactions in a system of coupled phase oscillators with two communities. We use dimensionality reduction techniques to derive a low-dimensional system of ordinary differential equations (ODEs) to describe the macroscopic behavior of the system. By analyzing this system we show that, in addition to the fixed point solutions present in a system of oscillators with higher-order interactions and community structure only, the system also exhibits oscillatory or chaotic synchronization behavior for some phase lag values. Moreover, some phase lag values give rise to multistability of solutions, where both fixed point solutions and oscillatory or chaotic behavior of the order parameters can be observed, depending on initial conditions.

The axial next-nearest-neighbor Ising model in two dimensions is studied using population annealing combined with a two-replica cluster algorithm. We are able to fully resolve the sequence of sharp specific heat peaks that characterize the finite-size incommensurate floating phase. We also show that the two-replica cluster algorithm is much more effective in equilibrating the system than either single-replica cluster methods or the Metropolis algorithm when these are combined with population annealing. We argue that the effectiveness of the algorithm is due to its ability to move groups of defect lines between replicas combined with resampling in population annealing, which removes replicas from the population that have larger numbers of defect lines.

The present work revisits hydrodynamic linear stability theory from the perspective of Lie symmetries. For the linearized Navier-Stokes equations of a two-component shear flow, the expected symmetries and equivalence transformations of the Navier-Stokes group are recovered, while additional ones arise due to linearization. The concept of symmetries and equivalence transformations in space and time is extended to spectral space, where the new definition of a spectral equivalence transformation is introduced. These are not fundamentally new transformations, as they correspond to space-and-time symmetries or equivalence transformations; however, they take on a different form that is used throughout the subsequent analysis. In particular, the Squire transformation is derived from such a symmetry generator of a spectral equivalence transformation with regard to the coupled Orr-Sommerfeld and Squire system, including the vorticity. As another step, these spectral generators are applied to an adjoint-projected residual functional. The variation of this functional is studied via the variation of the differential operator. This approach yields algebraic invariance conditions as well as derivative expressions. At a direct-adjoint eigenpair corresponding to an isolated eigenvalue, these derivatives determine the derivatives of the eigenvalue branch through the standard adjoint sensitivity relation and thus the group velocity. One specific result thereof is that the homogeneous Squire equation does not admit stationary-frame double saddle points in three dimensions (3D), which is a necessary criterion for a potential 3D absolute instability mechanism within the formalism of Briggs's theory.

Generalized local and multidimensional conservation laws of action, energy, momentum, and angular momentum are derived for stimulated Raman (SRS) and Brillouin backscattering (SBS) in a density gradient within the paraxial ray approximation. A Lagrangian density is given for which requiring the action be stationary reproduces the well-known envelope equations for SRS and SBS in density gradients in the absence of damping. Using Noether's theorem, the symmetries of the Lagrangian density are used to obtain local conservation laws for quantities that can easily be identified as the wave action, energy, and momentum. These multidimensional conservation laws reduce to the well-known one-dimensional Manley-Rowe relations and frequency and wave number matching conditions. Additional symmetries of the action lead to conservation laws for quantities that are identified as the orbital angular momentum and additional contributions to the energy and momentum of the wave from frequency and wave number shifts. Augmentation of the conservation laws in the presence of damping and extensions of the Lagrangian to include higher order corrections to the paraxial ray equation and nonlinear frequency shifts are also provided.

The efficient separation of chiral particles is a crucial topic in active matter, where intrinsic rotational motion can generate rich nonequilibrium collective behaviors. So far, few investigations have explored the separation of binary chiral mixtures by guiding particle motion through local noise shielding. Based on a model of self-propelled chiral particles, this article proposes a scheme to achieve particle separation by setting up circular noise-shielded regions for each of two types of chiral particles. The results indicate that the separation process of binary chiral mixtures can be characterized by the evolution from unimodal to bimodal in the probability distribution of interparticle distances. The intrinsic mechanism of separation can be analyzed through the pair correlation function, which shows short-range correlations for homochiral particle pairs and long-range correlations for heterochiral particle pairs. The optimal self-propelled velocity exists to achieve maximum separation, which can be further understood through the spatial correlation of velocity orientation. Moreover, the separation coefficient versus chirality strength curve exhibits the continuous-transition-like behavior from mixing to separation, where the transition value of the chirality strength linearly depends on the self-propelled velocity. The leading scale of this transition point is set by the geometric comparability between the orbital radius and the noise-shielded region's radius, while collective effects provide a subleading correction. These results may have significant implications for understanding nonequilibrium collective dynamics and particle sorting mechanisms.

Ice formation, a crucial phase transition for life on Earth, mainly occurs through heterogeneous nucleation on a solid substrate. Despite the importance of this phenomenon, the correlation between the structure of the substrate and its ability to induce ice nucleation remains poorly understood. In this work we use molecular dynamics simulations with an atomistic model of water to investigate how the lattice mismatch affects the ability of the substrate to nucleate ice. To unambiguously quantify the mismatch, we use substrates with a stretched ice structure. We put the substrate in contact with supercooled water and determine the temperature at which ice spontaneously nucleates during the course of the simulations. We find that the nucleation temperature decreases by $\sim 5–6$ K for each percent by which the substrate lattice is stretched relative to that of ice. This trend is similar to that previously obtained with a coarse-grained water model [Camarillo et al., J. Chem. Phys. 160, 134505 (2024)]. The substrate induces a fluctuating network of subcritical icelike clusters from which a spherical-cap-shaped supercritical nucleus eventually emerges stochastically. Using classical nucleation theory, we combine previously reported homogeneous nucleation rates with heterogeneous nucleation rates computed in this work to estimate key heterogeneous nucleation parameters, including the nucleation barrier, the kinetic prefactor, and the contact angle. The latter is consistent with a microscopic visualization of nucleation trajectories, supporting the applicability of classical nucleation theory to describe a microscopic phenomenon such as heterogeneous ice nucleation.

We study the outcome of adaptive learning among many players engaged in sets of two-strategy, two-player games. We are interested in typical games and therefore generate the payoff matrices randomly at the outset. These payoff matrices then remain fixed throughout the learning process. This provides a game-theoretic foundation for the Sherrington-Kirkpatrick (SK) game recently introduced by Garnier-Brun et al. [Phys. Rev. X 14, 021039 (2024)]. The original model studied by these authors corresponds to the special case with no bias toward either strategy. Here, we determine the stability of learning in SK games with general random biases and show that the nature of the stable state is affected by random fields. We also introduce a grand-canonical version of the SK game, in which players may choose to abstain. For this extended model, we again determine the stability of learning. Our analysis confirms that complex situations involving many players are often unlearnable, even if each player chooses between only two actions. The rate at which players forget past payoffs and the competitiveness of the game emerge as key parameters determining whether learning converges to a unique fixed point, whether multiple fixed points arise, or whether the dynamics remain persistently volatile.

We provide an equitable partition that gives an exact, minimal representation for the graph Cartesian product formed from quantumlike bits that preserves the relevant spectral and topological properties. We show that this result follows from the fact that the operations of taking the Cartesian product of graphs and constructing equitable partition of the graphs commute. Numerical simulations illustrate the preserved emergent eigenstates in the reduced structures. Additionally, we provide a construction of the minimal structure without passing through the Cartesian product. Finally, we frame quantumlike structures in the language of topology and fibrations.

Empirical regularities described by parametrized families of probability distributions can shape how complex systems are interpreted and explained. A recurring problem is to determine the extent to which these descriptions are supported by observations, and how they can be used to characterize the underlying system. Here we introduce a general framework for constructing constrained surrogates capable of representing arbitrary families of continuous distributions. We demonstrate its utility by providing explicit algorithms for several canonical distributions in statistical physics, including continuous power-law, lognormal, exponential, and truncated Gaussian distributions. These constrained surrogates enable unbiased estimation and accurate tests of model validity based on arbitrary (physically meaningful) sample statistics, without requiring specification or estimation of model parameters. We show how these theoretical advantages translate into more informative and nuanced conclusions in applications ranging from bushfire magnitudes and word usage in texts to brain connectomes and city populations.

We investigate the amplitude modulation of ion-acoustic wave packets in an unmagnetized electronegative plasma composed of cold positive ions, Boltzmann electrons, and negative ions following a Schamel trapped-particle distribution. The trapped-particle description is relevant to weakly collisional electronegative plasmas supporting Bernstein–Greene–Kruskal (BGK)-type potential structures and ion-hole equilibria, where a fraction of the negative-ion population can become trapped in the self-consistent wave potential. Unlike conventional analytic closures (Boltzmann, Tsallis, $\kappa$-distributed, nonthermal), which we show can only produce a cubic envelope nonlinearity regardless of their parametrization, this nonanalytic trapped-particle response naturally yields a generalized Schamel nonlinear Schrödinger equation combining the familiar cubic term with a genuinely noninteger ${\left|\mathrm{\Psi }\right|}^{1/2}\mathrm{\Psi }$ contribution. Derived through both a long-wavelength (Gardner-Schamel) limit and the full modulated-wave-packet limit, the resulting dispersion, cubic, and fractional coefficients are obtained in closed form. Two results stand out. First, the maximum modulational growth rate depends nonmonotonically on the negative-ion concentration, exhibiting an interior optimum that maximizes the instability above a critical temperature ratio, and, near the long-wavelength threshold, a finite concentration window outside of which the instability vanishes entirely. Second, a split-step Fourier analysis shows that the trapped-ion population breaks the time-symmetry of the Peregrine and Akhmediev rogue-wave solutions, causing them to build up faster than they decay, a signature invisible in the peak amplitude alone. These results extend previous electronegative plasma models and provide testable predictions for nonlinear wave localization in plasmas containing trapped particles.

The freely jointed chain is often applied to model the thermodynamics of single polymer chains, but the traditional formulation of the model lacks internal energy changes due to bond stretching. For this reason, the extensible freely jointed chain model includes a potential energy function, typically harmonic, that governs the length of each link in the chain. Among the other quantities of interest that are subject to thermal fluctuations, these link lengths and energies too fluctuate about their ensemble-average values. Since a plethora of models for polymer chains and networks incorporate chain dissociation as a function of either link length or energy, these fluctuations are crucial to understand and quantify. Motivated by this fact, fluctuations in link length and energy are analyzed within a freely jointed chain under an applied force. These fluctuations are quantified through their average values, standard deviations, and probability distributions. Across all values, asymptotically correct analytic relations and their less ergonomic exact counterparts are introduced. The asymptotic relations are verified to be accurate through direct comparison and to be correct within transcendentally small terms through error analysis. In certain cases, the fluctuations are shown to be approximately normally distributed. Hereafter, model components predicated on link length or energy ought to account for these fluctuations.

We investigate the expansion dynamics of two-dimensional colloidal assemblies interacting through a competing potential that supports unconventional local ordering. The systems are initially prepared under logarithmic confinement and subsequently released, generating a nonequilibrium decompression process. We show that expansion is not a simple disordering mechanism. Instead, the system undergoes a rich structural reorganization in which an initially dominant hexagonal core progressively shrinks while square local environments emerge and proliferate in the surrounding region. By combining real-space analysis, structure factors, bond-orientational order parameters, mean-square displacement, and dynamic exponents, we demonstrate that the expansion process promotes the formation and reorganization of square domains whose orientations initially reflect the sixfold geometry of the central hexagonal nucleus. This orientational-domain organization strongly influences the evolution of global order through cancellation effects between domains with different orientations. Finite-temperature simulations and independent thermal realizations further show that the structural conversion is robust, whereas the detailed late-time mobility events are trajectory dependent. As a consequence, substantial amounts of square local order may remain hidden from conventional global order parameters, demonstrating that local and global measures of structural order can become strongly decoupled during nonequilibrium expansion.

Dielectric relaxation times of powdered amorphous ices have served as kinetic benchmarks for the glass dynamics of water. To examine the effect of sample geometry on the dielectric spectra, we measured in situ dielectric spectra of bulk and emulsified high- and low-density amorphous ices at $P\simeq 0.01\mathrm{GPa}$. The emulsified samples showed loss maxima in the measurement window, while the bulk samples showed none. This is consistent with the qualitative peak-shift trends calculated using series-capacitor and Maxwell-Wagner-Sillars approximations for ice and oil. Caution is needed when using the dielectric results obtained from emulsionlike samples (e.g., powder) as kinetic benchmarks.

The behavior of particles subject to a nonlinear drag force in a medium (nonlinear Brownian motion) is usually treated by means of the Fokker-Planck equation proposed by Klimontovich [Phys. Usp. 37, 737 (1994)]. However, the derivation of such an equation appears to be questionable since it involves unproved assumptions and does not take into account any relation between the assumptions and approximations leading (in kinetic theory) to a velocity-dependent friction coefficient and those necessary to obtain an appropriate kinetic equation. In spite of this, as far as we know, the limits of validity of the said equation have not yet been investigated. Such circumstances pose the general problem: what is (if any) the appropriate (approximate) differential kinetic equation which is really compatible with the Langevin equation for nonlinear Brownian motions? To adequately solve this problem, previous papers dealing with the behavior of heavy particles in light gases are reexamined. The study leads to the final conclusions that (1) the heavy-particle speed dependence of the friction coefficient (and of the fluctuating force), in the Langevin equation, makes it very difficult to derive an appropriate Fokker-Planck equation for nonlinear Brownian motion, particularly in the most general three-dimensional case, and (2) the searched appropriate (approximate) differential kinetic equation for the heavy particles really exists and is the fourth-order equation following from the Boltzmann equation for a quasi-Rayleigh gas. Then it is shown that, on the contrary, the equation for the heavy-particle mean velocity relaxation following from the Fokker-Planck equation proposed by Klimontovich conflicts with that directly derived from the Langevin equation, a circumstance which now proves the inadequacy of the Klimontovich approach. Subsequently, some relaxation processes of particular interest are studied. So both the correct time-dependent mean velocity and the mean distance traveled by an anisotropic swarm of heavy particles are obtained, and the results are discussed assuming an interaction force between heavy- and gas-particles proportional to inverse powers of their mutual distance. Moreover, the correct relaxation equation for the heavy-particle mean-square speed is also achieved, and the difference with the corresponding result following from the Klimontovich theory is pointed out. An approximate method of solution of the said correct relaxation equation is also proposed. Finally, the limits of validity of the present theory are discussed.

This work presents a quantum graph neural network architecture in which each edge of the input graph carries a $d$-level quantum system and the model acts on the associated line graph. The set of circuits generated by the model is dense in the unitary group of the total Hilbert space, subject to an irrationality condition on the angular parameters. The model constructively separates pairs of 1-WL-indistinguishable graphs whose line graphs are $k$-WL-distinguishable, making it a quantum model that lies beyond the 1-WL ceiling. The function class realizable at dimension $d$ admits a strictly positive residual loss floor, which yields a criterion for adaptive expansion of the local dimension. Numerical validation confirms the impossibility of separation by node-based architectures for $\mathrm{SRG}(16,6,2,2)$, establishes the 3-WL distinguishability of its line graphs, and demonstrates direct separation by the edge-qudit architecture between the Petersen graph and the pentagonal prism. Taken together, these results establish the structural expressivity of edge qudits as an advantage over existing node-based architectures.

The melting of stripe-forming systems involves changes in connectivity that are not fully captured by conventional structural and orientational descriptors. We investigate a two-dimensional model with competing interactions whose low-temperature phase consists of one-particle-thick stripes. Molecular dynamics simulations along seven heating isochores are analyzed using thermodynamic, orientational, dynamical, and graph-based observables. Heating produces a multistage reconstruction in which the loss of stripe alignment and the reorganization of filament connectivity occur over distinct temperature ranges. Density controls whether the disordered filaments fragment into finite polymerlike clusters or remain joined in a dynamically fluid, system-spanning network. The topological observables distinguish these outcomes, which are not resolved by the thermodynamic and orientational responses alone. Thus, the same ordered stripe microphase can melt into topologically distinct fluids selected by density.

I derive the impedance response of an ideal electrolyte containing an arbitrary number of mobile ionic species between blocking planar electrodes, described by the Poisson-Nernst-Planck equations. By transforming the linearized equations to a charge-salt description, the response is written in terms of a multi-component diffusion-migration matrix and its eigenvalues and eigenvectors. When all diffusivities are equal, the charge mode decouples from the neutral concentration subspace and the classical binary-electrolyte result is recovered. In contrast, unequal diffusivities couple charge relaxation to one or more neutral composition modes. For a ternary electrolyte with two cations and one anion, this coupling produces additional diffusive features and broadens the crossover between resistive and capacitive regimes. The results found in this paper provide a minimal continuum explanation for why mixed electrolytes can display impedance spectra that cannot be interpreted as a simple binary electrolyte with an averaged diffusion coefficient.