This research demonstrates that entropy-based measures, calculated from marginals of the Husimi functions, effectively identify and characterize quantum phase transitions in the Lipkin-Meshkov-Glick model. The study reveals that changes in entropy, particularly Wehrl entropy, marginal entropies, and mutual information, act as sensitive indicators of criticality, distinguishing between different transition orders and highlighting the breakdown of separability near critical points. These findings establish entropy analysis as a powerful, complementary tool to traditional methods for understanding quantum criticality in many-body systems.

In many biological processes, the size of a population changes stochastically with time, and recent work in the context of cancer and bacterial growth have focused on the situation when the mean population size grows exponentially. Here, motivated by the evolutionary process of genetic hitchhiking in a selectively neutral population, we consider a model in which the mean size of the population increases linearly. We are interested in understanding how the fluctuations in the population size impact the first passage statistics and study the fixation probability that a mutant reaches frequency one by a given time in a population whose size follows a conditional Wright-Fisher process. We find that at sufficiently short and long times, the fixation probability can be approximated by a model that ignores temporal correlations between the inverse of the population size, but at intermediate times, it is significantly smaller than that obtained by neglecting the correlations. We also study the distribution of the population size at which the mutant fixes; we find that it is qualitatively different in the full model and the uncorrelated model and decays algebraically with different exponents in the two models. Our analytical and numerical study of the correlation functions show that the conditional Wright-Fisher process of interest is neither a stationary nor a Gaussian process; we also find that the variance of the inverse population size initially increases linearly with time $t$ and then decreases as $t^{-2}$ at intermediate times followed by an exponential decay at longer times. Our work emphasizes the importance of temporal correlations in populations with fluctuating size that are often ignored in population-genetic studies of biological evolution.

Membrane filtration, a crucial and widely used industrial process, has attracted significant attention in mathematical modeling. Previous theoretical endeavors have posited the internal structure of membrane filters as a network of cylindrical pores, with fouling characterized as the gradual accumulation of fouling particles on the inner walls of these pores. Subsequently, membrane filter performance was evaluated employing metrics such as total throughput and accumulated foulant concentration throughout the filter's lifespan; and the correlation between such metrics and certain network properties, such as porosity and tortuosity, was analyzed. In this work, we analyze the correlation between the performance of such networks and their topological characteristics, with the objective of identifying the most pertinent topological features for membrane filter design for a fixed porosity setup. Persistent homology serves as our primary instrument for quantifying topological features. Specifically, we generate persistence diagrams for the pore networks utilizing thresholding based on the pore radii. The data encoded in these persistence diagrams are then statistically correlated with the performance metrics. We identify a strong correlation between total throughput and our topological measures and demonstrate explicitly that membrane topology significantly influences filtration performance, distinct from the effects of membrane geometry. We also report a strong positive correlation between total throughput and accumulated foulant concentration and find that, for fixed porosity setups as used in this work, tortuosity does not provide a useful measure for permeability.

Vector-borne diseases arise from the coupled dynamics of human mobility and mosquito ecology, producing outbreaks shaped by both spatial distributions and temporal patterns of movement. Here we develop a coarse-grained hub-leaf reduction that isolates the universal principles governing epidemic vulnerability in interconnected populations. By deriving and analyzing the epidemic vulnerability equation, we show how human and vector population ratios, together with mobility parameters that regulate time spent in hub and leaf locations, jointly determine the conditions for outbreak persistence. The analysis reveals that balanced flows of individuals between patches consistently minimize vulnerability, whereas disproportionate concentrations of vectors can shift the dominant risk to specific locations. Across parameter regimes, compensatory mobility emerges as a stabilizing mechanism, while skewed host-vector ratios elevate epidemic risk. These results establish general principles for the spatiotemporal determinants of vector-borne disease spread and provide a theoretical foundation for extending minimal models to more complex epidemiological settings.

We study site percolation on a square lattice with random compact diamond-shaped neighborhoods. Each site $s$ is connected to others within a neighborhood in the shape of a diamond of radius $r_s$, where $r_s$ is uniformly chosen from the set $\{i,i+1,...,m\}$ with $i\le m$. The model is analyzed for all values of $i=0,...,7$ and $m=i,...,10$, where $\overline{z}(i,m)$ denotes the average number of neighbors per site and $p_c(i,m)$ is the critical percolation threshold. For each fixed $i$, the product $\overline{z}(i,m)p_c(i,m)$ is found to converge to a constant as $m\to \infty$. Such behavior is expected when $i=m$ (single diamond sizes), for which the product $z\left(i\right)p_c\left(i\right)$ tends toward $2^d{\eta }_c$, where ${\eta }_c$ is the continuum percolation threshold for diamond-shaped regions or aligned squares in two dimensions ($d=2$). This case is further examined for $i=1,...,10$, and the expected convergence is confirmed. The particular case $i=m$ was first studied numerically by Gouker and Family in 1983. We also study the relation to systems of deposited diamond-shaped objects on a square lattice. For monodisperse diamonds of radius $r$, there is a direct mapping to percolation with a diamond-shaped neighborhood of radius $2r+1$, but when there is a distribution of object sizes, there is no such mapping. We study the case of the deposition of mixtures of diamonds of radius $r=0$ and $r=1$, and contrast it with the $(i,m)=(1,2)$ model and also the continuum percolation of disks of two sizes.

Size-bidisperse granular material flowing down a rough incline, or chute, may develop a Rayleigh-Taylor instability even when the two particle species have the same density. Unlike fluid instability, which occurs under quiescent conditions, the granular material must be flowing for the instability to occur. Initially, size segregation results in a monodisperse layer of large particles above a monodisperse layer of small particles with an interfacial layer of mixed particles that has a higher volume fraction and, hence, is denser than the monodisperse layers above and below it. The interfacial layer destabilizes via a Rayleigh-Taylor instability and forms dense descending plumes of mixed particles and ascending plumes of less dense pure small particles. As a result of these plumes, the upper layer of large particles breaks and accumulates above the descending plumes; the small-particle plumes reach the free surface. The instability evolves into persistent longitudinal rolls corresponding to streamwise bands, or stripes, of small and large particles at the free surface. The appearance of the instability depends on the particle and mixture properties as well as the flow conditions. In all cases, the propensity for the appearance of the instability and subsequent band formation can be traced back to the total particle volume fraction, or packing density, in the mixed-particle layer, which depends on the particle size ratio, fraction of each particle species, and thickness of the flow.

Electrostatic interactions fundamentally govern the structure and transport of electrolytes. In concentrated electrolytes, however, electrostatic and steric correlations, together with ion-solvent coupling, give rise to complex behavior, such as underscreening, that remains challenging to explain despite extensive theoretical effort. Using molecular dynamics simulations of primitive electrolytes with and without space-filling solvent particles, we elucidate the structural and dynamical crossovers and their connection that emerge with increasing salt concentration. Explicit-solvent electrolytes exhibit a screening transition from a charge-dominated dilute regime to a density-dominated concentrated regime, accompanied by dynamical crossovers in ion self-diffusion and ion-pair lifetimes. These dynamical crossovers display a marked discontinuity, unlike the smoother variation of the screening crossover, which originates from short-range ion-counterion structures. The pronounced growth of ionic clusters leads to a percolation transition only at higher concentrations, whereas the onset of the structural and dynamical crossovers is associated primarily with local ion pairing or small aggregates. Both structural and dynamical behaviors are found to depend sensitively on ion-solvent coupling: implicit-solvent electrolytes exhibit a screening transition between two charge-dominated regimes, accompanied by qualitatively distinct dynamical behavior. Finally, we demonstrate that the diffusion-corrected ion-pair lifetime provides a consistent descriptor linking ionic structure and dynamics across electrolyte systems.

We experimentally and numerically investigate the clogging behavior of granular materials in a two-dimensional vertical pipe. The nonmonotonicity of the clogging probability found in a cylindrical vertical pipe [López et al., Phys. Rev. E 102, 010902(R) (2020)] is also observed in the two-dimensional case. We numerically demonstrate that the clogging probability strongly correlates with the friction coefficient $\mu$ in addition to the pipe-to-particle diameter ratio $D/d$. We thus construct a clogging-flowing $D/d\text{−}\mu$ phase diagram within the $2<D/d<3$ range. Finally, by analyzing the geometrical arrangements of particles and using a simple analysis of forces and torques, we are able to predict the clogging-flowing transition in the $D/d\text{−}\mu$ phase diagram and explain the mechanism of the observed counterintuitive nonmonotonicity in more detail. We demonstrate that for pipe clogging, friction-mediated force and torque equilibrium are essential for arch formation.

We uncover a previously unreported solid-solid phase transition in tetrachloro-$m$-xylene (TCMX), a hexasubstituted benzene derivative exhibiting orientational disorder. Differential scanning calorimetry and powder x-ray diffraction reveal a weak but reproducible phase transition near $437\text{K}$, corresponding to a continuous, second-order symmetry change from monoclinic $P{2}_1/n$ (phase II) to orthorhombic $Pnnm$ (phase I). Despite this structural reorganization, quasielastic neutron scattering demonstrates that molecular dynamics remain governed by discrete ${60}^{\circ }$ in-plane reorientational jumps consistent with the pseudosixfold molecular symmetry. The activation energy is unaffected, while only slight variations in relaxation times and effective rotational radii are detected. Molecular dynamics simulations reproduce the transition and clarify its microscopic origin. In phase II, weak orientational correlations between adjacent molecular columns are present, but these constraints vanish in phase I, restoring higher symmetry without altering the underlying reorientational mechanism. This study establishes TCMX as a rare example of a disorder-disorder transition in which molecular dynamics are preserved while collective orientational correlations reorganize. More broadly, our results highlight how subtle symmetry changes govern emergent behavior in disordered crystals, advancing the understanding of plastic phases and phase transitions in complex condensed matter systems.

The presence of correlated noise, arising from a mixture of independent fluctuations and a common noisy input shared across the neural population, is a ubiquitous feature of neural circuits, yet its impact on collective network dynamics remains poorly understood. We analyze a network of quadratic integrate-and-fire neurons driven by Gaussian noise with a tunable degree of correlation. Using the cumulant expansion method, we derive a reduced set of effective mean-field equations that accurately describe the evolution of the population's mean firing rate and membrane potential. Our analysis reveals a counterintuitive phenomenon: increasing the noise correlation strength suppresses the mean network activity, an effect we term correlated-noise-inhibited spiking. Furthermore, within a specific parameter regime, the network exhibits metastability, manifesting itself as spontaneous, noise-driven transitions between distinct high- and low-activity states. These results provide a theoretical framework for reducing the dynamics of complex stochastic networks and demonstrate how correlated noise can fundamentally regulate macroscopic neural activity, with implications for understanding state transitions in biological systems.

We present a theoretical investigation of the mixing dynamics of two constituent fluids within a soft rotating microfluidic channel. We solve a coupled system of transport equations, governing the mixing dynamics in this endeavor, with the associated symmetric and antisymmetric boundary conditions using the variational calculus approach. Our theoretical framework, developed in the context of centrifugal microfluidics, demonstrates strong agreement with full-scale simulated data and analytical solutions in the limiting case. Beginning with the characterization of flow velocity, including Coriolis force-induced secondary flows across different aspect ratios of the fluidic channel, we provide a comprehensive analysis of the underlying mixing phenomena. Through Poincaré map analysis, we qualitatively visualize fluid stream mixing, while mixing entropy analysis offers a quantitative evaluation of mixing performance. Our findings suggest that a lower aspect ratio in the rotating channel enhances mixing efficiency compared to higher aspect ratios. Additionally, our analysis highlights that the Coriolis force modulated emergence of vortex structures in the flow field significantly improves mixing in rotating channels, even at higher aspect ratios, relative to nonrotating channels of identical configuration. The insights from this study hold significant implications for the optimized design of rotational fluidic platforms, largely used in laboratory-on-a-chip applications, including point-of-care diagnostics.

We develop a rotational gauge invariance for classical many-body ensembles with orientational degrees of freedom and, from it, derive a hierarchy of exact, closure-free Ward identities on the orientation sphere $S^2$ and on $SO\left(3\right)$. A master local identity generated by orientation-dependent infinitesimal rotations yields (i) a global rotational hyperforce relation, (ii) an exact one-body torque balance, (iii) a pair-level first-order identity, and (iv) a second-order Hessian rotational sum rule that expresses the orientational curvature of the pair density in terms of torque-torque and torque-gradient correlators. The $SO\left(3\right)$ formulation provides mode-resolved constraints in Wigner-$D$ harmonics and a Parseval-type identity linking the angular variance of the one-body density to the torque variance. The theory yields operational, parameter-free estimators: in isotropic rod fluids the nematic structure factor is fixed by a projected torque kernel, giving a sharp criterion for the isotropic-nematic spinodal; in polar liquids the Kirkwood factor and hence the dielectric constant follows from the torque kernel; for polyhedra and patchy particles, torsional moduli at contact and bond-angle or twist laws emerge directly; and for chiral media we obtain a parity sum rule and a microscopic expression for the cholesteric pitch. These Ward identities provide symmetry-based constraints that connect microscopic torques to orientational structure and macroscopic response across a broad class of anisotropic colloids and molecular fluids.

A binary system of particles that move in opposite directions under an applied field can exhibit disordered states as well as laned states where the particles organize into oppositely moving high-mobility lanes to reduce collisions. Previous studies of laning transitions generally focused on particles with purely repulsive interactions. Here we examine laning transitions for oppositely moving pattern-forming systems of particles with competing attractive and repulsive interactions, which in equilibrium form crystal, stripe, and bubble states. In addition to multiple types of laned states, we find jammed crystals, stripes, and bubbles, and generally observe a much richer variety of phases compared to the purely repulsive system. In the stripe-forming regime, the system can dynamically reorder into oppositely moving stripes that are aligned in the direction of the drive. The bubble phase can produce strongly polarized jammed states of elongated bubbles where particles in the individual bubbles segregate to opposite sides of the bubbles. We also find disordered states, segregated laned bubble states where the bubbles pass each other in lanes, and segregated bubbles that move through one another. In the compact bubble regime, we obtain a plastic bubble state in which the oppositely driven particles remain trapped in the bubbles but the bubbles move past each other at a slow velocity due to a net imbalance in the bubble population. At higher drives, individual particles begin to jump from bubble to bubble. We show that the different phases and the transitions between them produce signatures in the velocity-force and differential mobility curves. We demonstrate that the force for escaping from the jammed state is nonmonotonic, with stripes exhibiting the lowest unjamming force.

We study bent-core nematic (BCN) systems in two-dimensional (2D) and three-dimensional (3D) settings, focusing on the role of cybotactic clusters, phase transitions, confinement effects, and applied external fields. We propose a generalized version of Madhusudana's two-state model for BCNs [Phys. Rev. E 96, 022710 (2017)] with two order parameters: ${\mathbf{Q}}_g$ to describe the ambient ground-state (GS) molecules and ${\mathbf{Q}}_c$ to describe the additional ordering induced by the cybotactic clusters. The equilibria are modeled by minimizers of an appropriately defined free energy, with an empirical coupling term between ${\mathbf{Q}}_g$ and ${\mathbf{Q}}_c$. We demonstrate two phase transitions in spatially homogeneous 3D BCN systems at fixed temperatures: a first-order nematic-paranematic transition followed by a paranematic-isotropic phase transition driven by the GS-cluster coupling. We also numerically compute and give heuristic insights into solution landscapes of confined BCN systems on 2D square domains, tailored by the GS-cluster coupling, temperature, and external fields. This benchmark example illustrates the potential of this generalized model to capture tunable director profiles, cluster properties, and potential biaxiality induced by antagonistic ${\mathbf{Q}}_g$ and ${\mathbf{Q}}_c$ profiles.

Molecular dynamics (MD) simulations have demonstrated that viscous effects arising from thermal motion and molecular rearrangement play a substantial role in collisions between submicron-sized particles. However, most of these simulations have been conducted at fixed temperatures, and the influence of temperature has not been specifically evaluated. In this study, we perform MD simulations of head-on collisions between particles with a radius of 30 nm to examine the temperature dependence of collisions at impact velocities below a few percent of the sound velocity. The results indicate that the coefficient of restitution decreases with increasing temperature, demonstrating that high-temperature collisions cause considerable dissipation of the particles' kinetic energy. We further find that the hysteresis of the interparticle force and contact radius—the difference between the loading and unloading phases—increases with temperature and accounts for the observed temperature dependence of the coefficient of restitution. This hysteresis is attributable to atomic rearrangement: at higher temperatures, stronger atomic random motion promotes more frequent rearrangement. Compression at the contact area forces atoms outward, producing cracks throughout the particles and expanding the contact area. These processes lead to plastic deformation, indicating that greater energy dissipation occurs through plastic deformation at higher temperatures. Atoms that enlarge the contact area also contribute to the attractive force between particles, further enhancing the hysteresis. Finally, we also validate the stress-dependent dissipation model developed in our previous study by fitting it to the MD simulation results and show that the model successfully reproduces the MD simulation.

Many bacteria share the fascinating ability to sense Earth's magnetic field—a process known as magnetotaxis. These bacteria synthesize magnetic nanoparticles, called magnetosomes, within their own cell body and arrange them to form a linear magnetic chain. The chain, which behaves like a compass needle, aligns the microorganisms with the geomagnetic field. Here, we measure the magnetic hysteresis of an individual bacterium of the species Magnetospirillum gryphiswaldense via ultrasensitive torque magnetometry. These measurements, in combination with transmission electron microscopy and micromagnetic simulations, reveal the magnetic configurations of the magnetosomes, their progression as a function of applied field, as well as the total remanent magnetic moment and effective magnetic anisotropy of a chain within a single bacterium. Knowledge of these properties is crucial both for understanding the mechanisms behind magnetotaxis and for the design of systems exploiting magnetotactic bacteria in biomedical applications.

Electrolyte-filled channels with modulated wall charge distribution subjected to an applied DC electric field form time-independent vortices whose sense of circulation is determined by the field direction [Phys. Rev. Lett. 75, 755 (1995)]. In this paper, we show that an electrolyte in a channel or cylindrical capillary subjected to an external alternating (AC) electric field gives rise to various laminar flow structures, including vortices whose sense of circulation changes with the period of oscillation of the applied AC field. The introduction of a period of oscillation lifts certain degeneracies associated with its time-independent counterpart. Although in general the mass flux vanishes, the charge flux is nonzero. The flow is accompanied by a longitudinal (oscillating) advective current that displays hysteresis accompanied by a diverging and negative self-similar conductance that depends on the applied voltage [Nano Lett. 10, 2674 (2010)]. We show that this behavior can be interpreted with respect to a “memory retention time” that depends on frequency, viscosity, and the Debye length and could thus form the impetus for investigating control protocols of signal carriers.

The recently proposed physics-based framework by Huo and Johnson [arXiv:2504.04600]. models the attention mechanism of large language models as an interacting two-body spin system, offering a first-principles explanation for phenomena like repetition and bias. Building on this hypothesis, we extract the complete query-key weight matrices from a production-grade GPT-2 model and derive the corresponding effective Hamiltonian for every attention head. From these Hamiltonians we obtain analytic phase boundary and logit gap criteria that predict which token should dominate the next-token distribution for a given context. A systematic evaluation on 144 heads across 20 factual-recall prompts reveals a strong negative correlation between the theoretical logit gaps and the model's empirical token rankings ($r\approx -0.70, p<{10}^{-3}$). Targeted ablations further show that suppressing the heads most aligned with the spin-bath predictions induces the anticipated shifts in output probabilities, confirming a causal link rather than a coincidental association. Taken together, our findings provide the first strong empirical evidence for the spin-bath analogy in a production-grade model. In this work, we utilize the context-field lens, which provides physics-grounded interpretability and motivates the development of novel generative models bridging theoretical condensed-matter physics and artificial intelligence.