We develop two complementary generative mechanisms that explain when and why Benford's first-digit law arises. First, a probabilistic Turing machine (PTM) ensemble induces a geometric law for codelength. Maximizing its entropy under a constraint on halting length yields Benford statistics. This model shows a phase transition with respect to the halt probability. Second, a constrained partition model (Einstein-solid combinatorics) recovers the same logarithmic profile as the maximum entropy solution under a coarse-grained entropy-rate constraint, clarifying the role of nonergodicity (ensemble vs. trajectory averages). We also perform numerical experiments that corroborate our conclusions.

Edge localized modes (ELMs) and runaway electrons (REs) pose significant challenges for all tokamak devices. Both phenomena act as potent heat sources, potentially shortening the lifespan of plasma-facing materials (PFMs). These thermal loads can manifest in various detrimental effects, including melting, sputtering, cracking, blistering, and other forms of material degradation. While the ELMs are an intrinsic feature of H-mode operation in tokamaks, runaway electrons pose a potential threat across all tokamak device scales. In devices such as ITER, even with mitigation strategies, the ELMs can still impose considerable heat loads on the PFMs, reaching levels of approximately $1\mathrm{MJ}/{\mathrm{m}}^2$. Various methods exist to experimentally simulate the heat load effects of ELMs on PFMs. In this study, the thermal loads from runaway electrons in small-scale tokamaks are considered for this purpose. The presence of small-scale tokamaks, exemplified by the Damavand experiment, facilitates the investigation of runaway electron energy deposition. Analysis of the experimental data indicates that the RE populations generated by plasma instabilities within the Damavand tokamak discharges exhibit heat densities on the order of $\mathrm{MJ}/{\mathrm{m}}^2$ to $1\mathrm{c}{\mathrm{m}}^2$ area PFMs. Furthermore, considering an average RE energy of 1 MeV and the prevailing discharge current, calculations indicate that the average total energy of the REs population per discharge is approximately 1 kJ, which is subsequently deposited on the tokamak limiter. Considering the limiter's surface area and assuming that only 40% of the RE energy is transferred to it, the calculated heat load density reaches the order of $\mathrm{MJ}/{\mathrm{m}}^2$, comparable to that observed during the ELM events in large-scale fusion devices. This correspondence in heat flux levels enables the Damavand tokamak to investigate material behavior under intense thermal loads, offering valuable insights into the effects of the ELMs on the performance and durability of PFMs in large-scale tokamaks.

We present a numerical analysis of the translational motion of dimers composed of charged dielectric particles immersed in aqueous electrolytes under ac electric fields. The dimers consist of two spheres with different radii and are studied in two distinct configurations: (i) spheres connected by a negligibly thin wire, and (ii) spheres joined by a narrow neck. We explain their net motion as a consequence of steady electro-osmotic flows generated on the particle surfaces, a phenomenon known as concentration-polarization electrophoresis. Our numerical results are compared with recent experimental observations, and we discuss the similarities and discrepancies between the two.

Drying in confined systems is a critical process with broad implications, spanning applications from materials science to water management in microscale technologies. Nevertheless, the coupled dynamics of transport and gelation in confined drying of colloidal suspensions remains poorly understood. Here cellulose nanocrystals (CNCs) are employed as a model system to systematically investigate the temporal dynamics, kinetic behavior, and structural transformation of nanocrystal suspensions during capillary drying. We report a mechanism whereby CNC suspensions, upon exceeding a critical concentration (∼1 wt%), undergo a transition from a fluid-like state to a kinetically arrested gel state at the evaporation front. This transition is accompanied by pinning of the evaporation interface at the capillary opening and leads to the formation of a gel–film heterostructure, consisting of a CNC gel layer with a water concentration gradient and a thin surface film formed via interfacial slip. This heterostructure promotes directional water transport from the capillary interior to the interface and significantly enhances the effective evaporative area, thereby accelerating the overall drying process. These findings offer insights into confinement-driven drying behavior and establish a framework for regulating evaporation kinetics in colloidal systems.

Hydrodynamic flows are often generated in colloidal suspensions. Since colloidal particles are frequently used to construct stochastic heat engines, we study how the hydrodynamic flows influence the output parameters of the engine. We study a single colloidal particle confined in a harmonic trap with time-periodic stiffness that provides the engine protocol, in the presence of an externally applied steady linear shear flow. The nature of the flow (circular, elliptic, or hyperbolic) is externally tunable. In the quasistatic limit, the work done by the flow field is shown to dominate over the thermodynamic (Jarzynski) work done by the trap, if there is an appreciable deviation from the circular flow. The work by the time-dependent trap is the sole contributor only for a perfectly circular flow. The work done by the elliptic flow is positive whereas in the case of hyperbolic flows, in the limit of low trapping strength, it can be negative, so as to allow for harnessing the work from the flow field. We also study an extended model, where a microscopic spinning particle (spinor) is tethered close to the colloidal particle, the latter being the working substance of the engine, such that the flow generated by the spinor influences the dynamics of the colloidal particle. We simulate the system and explore the influence of such a flow on the thermodynamics of the engine. We further find that for larger spinning frequencies, the work done by the flow dominates and the system cannot produce thermodynamic work.

A powerful strategy to accelerate quantum-walk-based search algorithms leverages on resetting protocols, where a detector monitors a target site and the evolution of the walker is restarted if no detection occurs within a fixed time interval. The optimal resetting rate can be extracted from the time evolution of the probability $S\left(t\right)$ that the detector has not clicked up to time $t$. We analyze $S\left(t\right)$ for a quantum walk on a one-dimensional lattice when the coupling between sites decays algebraically as $d^{-\alpha }$ with the distance $d$, for $\alpha \in (0,\infty )$. At long times, $S\left(t\right)$ decays with a universal power-law exponent that is independent of $\alpha$. At short times, $S\left(t\right)$ exhibits a plethora of phase transitions as a function of $\alpha$. From this, we provide a strategy to determine the optimal resetting rate. We identify two regimes: for $\alpha >1$, the resetting rate $r$ is bounded from below by the velocity with which information propagates causally across the lattice; for $\alpha <1$, instead, the long-range hopping tends to localize the walker: The optimal resetting rate depends on the size of the lattice and diverges as $\alpha \to 0$. Our strategy directly connects local measurement outcomes with the global dynamics encoded in $S\left(t\right)$. We derive simple models explaining our numerical results, shedding light on the interplay of long-range coherent dynamics, symmetries, and local quantum measurement processes in determining equilibrium. Our findings offer experimentally testable predictions and provide new physical insights on optimizing quantum search through resetting.

Quantum thermal states are known to be passive, as required by the second law of thermodynamics. This paper investigates the potential for work extraction by coupling a thermal bath to a qubit of either spin, fermionic, or topological type, which acts as a quantum thermal state at different temperatures. The amount of work extraction is derived from the work statistics under a cyclic nonequilibrium process. Although the work statistics of many-body systems are known to be challenging to calculate explicitly, we propose an effective field theory approach to tackle this problem by assuming the externally driven source couples to a specific quasiparticle operator of the thermal state. We show that the work statistics can be expressed succinctly in terms of this quasiparticle's thermal spectral function. We obtain the nonperturbative work distribution function (WDF) for the pure thermal bath without the qubit coupling. With qubit coupling, we get the second-order WDF, from which the physical regime of work extraction can be pinned down precisely to help devise quantum heat engines or refrigerators. Their efficiency or coefficient of performance can be inferred from the combination of the fluctuation theorem and the first law, and we find that the spin or topological qubit-bath system generally yields a far better heat engine or refrigerator than the other two alternatives due to the underlying quantum statistics.

Social media networks reveal highly asymmetric communication patterns, where a minority of individuals dominate speech while the majority primarily listen. Yet, the mechanisms governing the emergence and stability of such roles remain poorly understood. Here, we introduce a minimal agent-based model in which disparities in expression and attention give rise to emergent social structure. Persistent self-referential speech generates local dominance and hierarchical organization, whereas listener attention and memory sustain overall network cohesion. The model uncovers a feedback loop linking speaking activity, attention allocation, and memory, which sets the balance between social integration and fragmentation. Our results predict that greater listening propensity, social openness, and memory capacity promote cohesion and mitigate fragmentation, while excessive hub dominance can be curtailed by ensuring that all individuals engage in at least a minimal fraction of listening.

Gene expression involves a series of complex regulatory processes. It is known that self-feedback regulation plays an important role in it. However, self-feedback burst dynamics in single-cell sequencing data has not been extensively studied yet. Here we propose a single-cell stochastic burst model with coupled positive- and negative-feedback gene expression circuits and then analyze its dynamical behavior using mouse fibroblast scRNA-seq data. The burst dynamics parameters are inferred genomewide and the self-feedback regulation patterns are identified. The results show that positive feedback can restore a bimodal distribution of gene expression, while negative feedback and no feedback often lead to a unimodal distribution. Additionally, we analyze the effects of feedback regulation types on burst dynamics, namely, burst size, burst frequency, and noise. It is found that as the gene mean increases, the burst frequency and burst size of the three feedback types show an increasing trend, while noise shows a decreasing trend. On the other hand, the mean burst frequency of negative feedback is greater than that of positive feedback, while the mean burst size and noise of positive feedback are greater than those of negative feedback. This helps us understand the gene expression patterns, cell differentiation, and fate determination.

Hall magnetohydrodynamics (HMHD) extends ideal MHD by incorporating the Hall effect via the induction equation, making it more accurate for describing plasma behavior at length scales below the ion skin depth. Despite its importance, a comprehensive description of the eigenmodes in HMHD has been lacking. In this work, we derive the complete spectrum and eigenvectors of HMHD waves and identify their underlying topological structure. We prove that the HMHD wave spectrum is homotopic to that of ideal MHD, consisting of three distinct branches: the slow magnetosonic-Hall waves, the shear Alfvén-Hall waves, and the fast magnetosonic-Hall waves, which continuously reduce to their ideal MHD counterparts in the limit of vanishing Hall parameter. Contrary to a recent claim [Mahajan, Sharma, and Lingam, Phys. Plasmas 31, 090701 (2024)], we find that HMHD does not admit any additional wave branches beyond those in ideal MHD. The key qualitative difference lies in the topological nature of the HMHD wave structure: it exhibits nontrivial topology characterized by a Weyl point—an isolated eigenmode degeneracy point—and associated nonzero Chern numbers of the eigenmode bundles over a 2-sphere in $\mathbf{k}$-space surrounding the Weyl point.

Accurately predicting thermophysical properties across various physical states is essential for both industrial and scientific applications. However, experimental data often exhibit variability and noise, requiring robust modeling approaches. In this work, we employ machine learning (ML) techniques to predict methane's thermophysical properties in liquid, vapor, and supercritical phases, including isobaric and isochoric heat capacities, density, specific volume, Joule-Thomson coefficients, enthalpies, sound speed, and shear viscosities, applying an approach recently developed [ACS Eng. Au 5, 226 (2025)]. We explore various ML algorithms, including Adaptive Boosting, Bagging, Decision Trees, Extra Trees, Gradient Boosting, Histogram-based Gradient Boosting Regression Tree, $K$-Nearest Neighbors, Light Gradient Boosting Machine, $\mathit{Nu}$-Support Vector Regression, Random Forest, Extreme Gradient Boosting, and Artificial Neural Networks. The ML models, which use raw experimental data without removing outliers, produce predictions that are closer to those obtained from the equations of state (EOS) employed by the National Institute of Standards and Technology than to the same raw experimental data used as input for developing the EOS. These results highlight ML's potential to identify and generalize complex patterns, smooth inherent noise, and manage the variability of different thermophysical properties. They indicate that ML models, particularly Extra Trees and Gradient Boosting, can offer a scalable alternative for thermophysical property predictions, offering consistency and efficiency over traditional methods. Although our approach does not eliminate preprocessing, it demonstrates that ML can effectively manage noisy data independently, offering a more efficient and cost-effective alternative to conventional pre- and postprocessing techniques.

In the quantum world, the process of energy storage can be enhanced thanks to various nonclassical phenomena. This inspiring fact suggests quantum batteries as plausible sources of power for future quantum devices, at least in principle. However, thermodynamically not all of the energy stored in a quantum battery is useful for doing work. By considering a class of models based upon quantum continuous variables, here we show how the maximum extractable energy from a bosonic quantum battery can be intimately related to Heisenberg's uncertainty principle. We found that realizing minimum uncertainty essentially guarantees that all of the energy stored in a Gaussian quantum battery can be withdrawn and used to do work. For a standard system where the charger and battery are coupled linearly, this criterion is satisfied rather trivially. However, our theoretical results demonstrate that—for a quantum battery with nonlinear coupling—a state of minimum uncertainty can also be achieved nontrivially via the generation of quantum squeezing. We characterize the charging performance of our proposed continuous-variable quantum batteries in detail, and we hope that our theory may be useful in the design of a new generation of efficient quantum batteries harnessing bosonic excitations, such as those built with photonic architectures.

Tipping occurs when an abrupt transition is observed in a system's long-term behavior. This study demonstrates tipping in ecological systems using a unidirectional, three-species coupled system, where only the first subsystem experiences a ramp-like parameter drift. Using a model of bacteria, phytoplankton, and fish populations, we explore how environmental changes, coupling strength, and nonlinearity drive sudden transitions. This study identifies three crucial tipping phenomena based on the coupling strength: tipping cascade, cascade hopping, and indirect tipping. While prior research has focused on tipping cascade and cascade hopping, this work introduces indirect tipping as a critical phenomenon, where the tertiary subsystem tips even when both the primary and secondary subsystems do not tip. The results emphasize the vulnerability of coupled systems to minor changes and highlight the necessity of closely observing systems that appear untipped in coupled systems.

Community detection in hypergraphs is both instrumental for functional module identification and intricate due to higher-order interactions among nodes. We define a hypergraph Ricci flow that directly operates on higher-order interactions of undirected hypergraphs and proves the long-time existence of the flow. Building on this theoretical foundation, we develop HyperRCD, a Ricci-flow-based community detection approach that deforms hyperedge weights through curvature-driven evolution, which provides an effective mathematical representation of higher-order interactions mediated by weighted hyperedges between nodes. Extensive experiments on both synthetic and real-world hypergraphs demonstrate that HyperRCD exhibits remarkable enhanced robustness to topological variations and competitive performance across diverse datasets.

Material renewability in active living systems, such as in cells and tissues, can drive the large-scale patterning of forces, with distinctive phenotypic consequences. This is especially significant in the cell cytoskeleton, where multiple species of myosin bound to actin, apply differential contractile stresses and undergo differential turnover, giving rise to patterned force channeling. Here we study the dynamical patterning of stresses that emerge in a hydrodynamic description of a renewable active actomyosin elastomer comprising two myosin species. Our analytical framework also holds for an actomyosin elastomer with a single myosin species. We find that a uniform active contractile elastomer spontaneously segregates into spinodal stress patterns, followed by a finite-time collapse into tension carrying singular structures that display self-similar scaling and caustics. Our numerical analysis carried out in one dimension shows that these singular structures move and merge and gradually result in a slow coarsening dynamics. We discuss the implications of our findings to the emergence of stress fibers and the spatial patterning of actomyosin. Our study suggests that with state-dependent turnover of crosslinkers and myosin, the in vivo cytoskeleton can navigate through the space of material parameters to achieve a variety of functional phenotypes.

A theory for Abelian plasma permeated by photons has been developed considering QED generalized in Podolsky electrodynamics framework for consideration of higher order terms in electromagnetic theory. The theory traces out photonic degrees of freedom in plasma and accounts for plasma dynamics mediated by photons by calculated effective Hamiltonian. New modes of propagation have been predicted along with suppression of fields and collective behavior. Non-Markovian behavior is also discovered for plasma states and interactions in finite plasma system. This finds applicability in solid-state plasma, plasma confinement of magnetic and inertial nature, and laser-plasma interaction when theory is reduced to local interactions.

A theory of the magnetic response of single-domain particles suspended in a fluid to a linearly polarized harmonic field of arbitrary amplitude is developed for the case when a stationary magnetizing field is present. The theory regards magnetically hard particles without internal diffusion of the magnetic moment. The dependence of the magnetic relaxation spectrum of such particles on the magnitude of the applied field is analyzed. It is shown that their dynamic magnetic susceptibility comprises a countable set of Debye-type terms. However, the longest-lived relaxation mode predominates both in the longitudinal and transverse cases, and the dynamic magnetic susceptibility can be found up to good accuracy by means of a relatively simple formula for any direction of the bias field. The dynamic magnetic hysteresis of the particles in strong alternating fields is studied. It is demonstrated that the characteristics of the cyclic remagnetization curve strongly depend on the amplitude and frequency of the field. It is shown that the bias field can qualitatively change the magnetic response of the particles. In particular, it definitely leads to shrinkage of the hysteresis loop. Additionally, both vertical and horizontal shifts of the latter are expected if the angle between alternating and stationary fields is not right. The case of transverse biasing is special: the magnetization curve should always remain symmetric with respect to the origin.