We study the statistical mechanics of two-dimensional “super-Coulombic” plasmas, namely, neutral plasmas with power-law interactions longer ranged than Coulomb. To that end, we employ numerically exact large-scale Monte Carlo simulations. Contrary to naive energy-entropy arguments, we observe a charge confinement-deconfinement transition as a function of temperature. Remarkably, the transition lies in the Berezinskii-Kosterlitz-Thouless (BKT) universality class. Our results corroborate recent dielectric medium and renormalization group calculations predicting effective long-scale Coulomb interactions in microscopically super-Coulombic gases. We explicitly showcase this novel dielectric screening phenomenon, capturing the emergent Coulomb potential and the associated crossover length scale. This is achieved by utilizing a new test charge based methodology for determining effective inter-particle interactions. Lastly, we show that this Coulomb emergence and the associated BKT transition occur universally across generic interactions and densities.

The dynamics of interacting domain walls, regarded as a system of particles which are biased to move towards their nearest neighbors and annihilate when they meet, have been studied in the recent past. We study the effect of the presence of a fraction $r$ of quenched impurities (which act as rigid walkers) on the dynamics. Here, in the case where two domain walls or one impurity and one domain wall happen to be on the same site, both get simultaneously annihilated. It is found that for any nonzero value of $r$, the dynamical behavior changes as the surviving fraction of particles $\rho \left(t\right)$ attains a constant value. $\rho \left(t\right)t^{\alpha }$ shows a universal behavior when plotted against $r^{\beta }{t}^{\alpha }$ with $\alpha ,\beta$ values depending on whether the particles are rigid or nonrigid. Also, the values differ for the biased and unbiased cases. The timescale associated with the particle decay shows that it varies with $r$ in a power-law manner with an exponent $\approx \frac{\beta }{\alpha }$ as expected.

Protein nanoclustering is a characteristic feature of their activated state and is essential for forming numerous subcellular structures. The formation of these nanoclusters is highly dependent on a series of posttranslational modifications, such as mono- and multiphosphorylation and dephosphorylation of residues. We theoretically simulate how a protein can be either mono- or multiphosphorylated on several residues in functional nanoclusters, depending on effective biophysical parameters (diffusion, dwell time, etc.). Moving beyond a binary view of phosphorylation, this approach highlights the interplay between mono- and multiphosphorylation, the cooperative effects generally associated with multiphosphorylation networks, and stresses the role of phosphatases in transforming graded phosphorylation signals into almost switchlike responses. The results are discussed in light of experiments that probe the distribution of phospho-residues.

This work presents a theoretical and numerical investigation of the modulational instability and rogue wave triplets of dust-acoustic waves in a dusty plasma composed of warm adiabatic dust grains with opposite polarity, $q$-nonextensive electrons, and nonthermal ions. The dynamics are modeled by deriving a nonlinear Schrödinger (NLS) equation using the reductive perturbation method. This equation leads to the growth rate of modulational instability of dust-acoustic waves. The analysis reveals that positively charged dust grains, the degree of electron nonextensivity, and the distribution of electrons (protons) on negatively (positively) charged dust grains critically influence the growth rate of instability. The ratio of dispersion to nonlinear coefficients in the NLS equation demarcates stable and unstable regions, distinguishing bright and dark solitons. This novel mechanism reveals a second stability regime in opposite polarity dusty plasma for the fast acoustic mode. We also explore the impacts of multiple physical parameters, which are sensitive in forming rogue wave triplets. These parameters result in three distinct peaks arranged in a triangular pattern, with unique rotational behavior that offers a new perspective on the dynamical behaviors of localized nonlinear waves. To validate the model, we benchmark the exact analytical solutions for rogue wave triplets with numerical results. This comparison demonstrates the accuracy of the model and provides deeper insight into nonlinear localized waves. This analysis has significant implications for rogue wave triplet formation in both space and laboratory plasma environments. These triplets may coalesce into super freak waves under specific conditions, particularly when key physical parameters approach zero.

In 2016, x-ray microcalorimeter spectroscopy with the Hitomi soft x-ray spectrometer observed strong spectrum lines of Fe XXIV-XXVI in galaxy NGC 1275 at the center of the Perseus cluster of galaxies. Special attention was paid to the $\mathrm{K}\alpha$ lines of the Fe plasmas [Aharonian et al., Nature (London) 535, 117 (2016)]. The dominant spectral component was treated as a collisional ionization equilibrium plasma using the SPEX code. However, it was found that the ratio of Fe XXV $\mathrm{He}\alpha$ resonant and forbidden lines is lower than the observed one. This difference could be attributed to the insufficient consideration of radiation field effects in the spectral modeling approach. To address this issue, we recalculated the emission spectra under astrophysical conditions using the nonlocal thermodynamic equilibrium collisional-radiative code. Our analysis reveals a pronounced sensitivity of the emission spectra to the radiative temperature and distribution. Furthermore, we performed a detailed investigation of the atomic processes involving photon interactions and their effects on the emission spectra of Fe plasmas. The recalculated spectra show excellent agreement with the measured spectra, highlighting the significant role of the radiation field in shaping the spectral characteristics of astrophysical plasmas.

Metastasis of cancer cells is closely associated with their ability to undergo mechanical softening under shear stress. A statistical-thermodynamic model has been developed to demonstrate the crucial role of entropic effects in this process. The model establishes a quantitative relationship between the reorganization of the cytoskeleton's orientation and alterations in mechanical properties, as well as entropy production. This elucidates the phenomenon of mechanical softening in cells under loads ranging from 0.09 to 0.63 Pa. The validation of the model was undertaken using experimental data from A431 cells, which demonstrated high accuracy (root mean square error of 0.0069) and noise resistance. Thermodynamic analysis revealed a nonlinear relationship between entropy production and orientation deformation. It is proposed that a new marker for metastatic potential be established, with the marker being defined as “dissipative process frequency.” This parameter demonstrates remarkable stability across different loading conditions (variation of 7.35%). The reliability of the marker was confirmed through Monte Carlo simulations, which yielded a coefficient of variation of less than 12.1%. The present study establishes a fundamental connection between cytoskeletal thermodynamics and the mechanical properties of cancer cells, offering novel opportunities for metastasis diagnosis based on dissipative characteristics.

We investigate the long-term relaxation of a distribution of $N$ point vortices in two-dimensional hydrodynamics. To focus on the regime of weak collective amplification, we embed these point vortices within a static background potential and soften their pairwise interaction on small scales. Placing ourselves within the limit of an average axisymmetric distribution, we stress the connections with generic long-range interacting systems, whose relaxation is described within angle-action coordinates. In particular, we emphasize the existence of two regimes of relaxation, depending on whether the system's profile of mean angular velocity (frequency) is a nonmonotonic (respectively, monotonic) function of radius, which we refer to as profile (1) [respectively, profile (2)]. For profile (1), relaxation occurs through two-body nonlocal resonant couplings, i.e., $1/N$ effects, as described by the inhomogeneous Landau equation. For profile (2), the impossibility of such two-body resonances submits the system to a “kinetic blocking.” Relaxation is then driven by three-body couplings, i.e., $1/N^2$ effects, whose associated kinetic equation has only recently been derived. For both regimes, we compare extensively the kinetic predictions with large ensemble of direct $N$-body simulations. In particular, for profile (1), we explore numerically an effect akin to “resonance broadening” close to the extremum of the angular velocity profile. Quantitative description of such subtle nonlinear effects will be the topic of future investigations.

We focus on the Feigenbaum-Coullet-Tresser point of the dissipative one-dimensional $z$-logistic map $x_{t+1}=1-a{\left|x_t\right|}^z(z\ge 1)$. We show that sums of iterates converge to $q$-Gaussian distributions $P_q\left(y\right)=P_q\left(0\right){exp}_q(-{\beta }_q{y}^2)=P_q\left(0\right){[1+(q-1){\beta }_q{y}^2]}^{1/(1-q)}(q\ge 1;{\beta }_q>0)$, which optimize the nonadditive entropic functional $S_q$ under simple constraints. We propose and justify heuristically a closed-form prediction for the entropic index, $q\left(z\right)=1+2/(z+1)$, and validate it numerically via data collapse for typical $z$ values. The formula captures how the limiting law depends on the nonlinearity order and implies finite variance for $z>2$ and divergent variance for $1\le z\le 2$. These results extend edge-of-chaos central limit behavior beyond the standard ($z=2$) case and provide a simple predictive law for unimodal maps with varying maximum order.

We perform an extensive investigation of the localization properties of the eigenmodes of the Laplace and adjacency matrices for one-dimensional random geometric graphs. We evaluate the density of states, the probability distribution of the participation ratio, and its relation to the eigenvalues. By disentangling the influence of system size, graph component size distribution, mean degree of nodes, network motifs, and degeneracy, we provide a comprehensive understanding of this system. We compare our findings to ordered graphs with the same mean degree and to one-dimensional tight-binding models.

Growing evidence suggests that the macroscopic functional states of urban road networks exhibit multistability and hysteresis, but microscopic mechanisms underlying these phenomena remain elusive. Here, we demonstrate that in real-world road networks, the recovery process of congested roads is not spontaneous, as assumed in existing models, but is hindered by connected congested roads, and such hindered recovery can lead to the emergence of multistability and hysteresis in urban congestion dynamics. By analyzing real-world urban traffic data, we observed that congestion propagation between individual roads is well described by a simple contagion process as an epidemic, but the recovery rate of a congested road decreases drastically by the congestion of the adjacent roads unlike an epidemic. Based on this microscopic observation, we proposed a simple model of congestion propagation and dissipation, and found that our model shows a discontinuous phase transition between macroscopic functional states of road networks when the recovery hindrance is strong enough through a mean-field approach and numerical simulations. Our findings shed light on an overlooked role of recovery processes in the collective dynamics of failures in networked systems.

The aggregation of amyloid-$\beta 42$ ($\mathrm{A}\beta 42$) peptide, a key pathological event in Alzheimer's disease, is strongly influenced by its solvent environment. While cosolvents are often used in experimental studies, their specific role in modulating the conformational stability and aggregation propensity of $\mathrm{A}\beta 42$ remains poorly understood. We perform molecular dynamics simulations to investigate the effects of three organic solvents—ethanol (EtOH), dimethyl sulfoxide (DMSO), and acetonitrile (ACN)—on the structural dynamics of $\mathrm{A}\beta 42$. Our results reveal a distinct dichotomy: EtOH and DMSO exert a stabilizing effect by promoting the $\alpha$-helical content, reducing Coil formation, and extending the lifetime of intramolecular hydrogen bonds. In contrast, ACN destabilizes the native state and accelerates the formation of aggregation-prone $\beta$-sheet structures. We attribute these opposing effects to the solvents' differential disruption of the peptide's hydrophobic core and their specific interactions with the protein backbone. This work elucidates the microscopic mechanisms by which solvent environment directs $\mathrm{A}\beta 42$ conformational sampling, with implications for understanding aggregation pathways and designing modulating agents.

Biomolecular condensates are essential for cellular organization and result from phase separation in systems far from thermodynamic equilibrium. Among various models, chemically active droplets play a significant role, and consist of proteins that switch between attractive and repulsive states via nonequilibrium chemical reactions. While field-based simulations have provided insights into their behavior, these coarse-grained approaches fail to capture molecular-scale effects, particularly in crowded cellular environments. Macromolecular crowding, a key feature of intracellular organization, strongly influences molecular transport within condensates, yet its quantitative impact remains underexplored. This study investigates the interplay between chemically active droplets and crowders by using particle-based models, that provide molecular insight, and a field-based model, that complements this picture. Surprisingly, crowding reduces droplet size while expanding the overall dense phase volume, challenging equilibrium-based expectations. This effect arises from the interplay between depletion interactions, diffusion hindrance, and nonequilibrium particle fluxes. Our findings provide a step towards a more comprehensive understanding of chemically active droplets in complex, realistic cellular environments.

We highlight the importance of long-range correlations in active matter systems of self-propelling particles even in the absence of global order or steric interactions by demonstrating that long-range density fluctuations are reduced. We show this analytically for a one-dimensional lattice process employing a Poisson representation. Within this framework, we are able to derive the fluctuating hydrodynamics for the Poisson fields. The emergent imaginary noise indicates the non-Poissonian nature of the number fluctuations and manifests in a nontrivial structure factor $S\left(k\right)$, which we are computing analytically. Numerically, we corroborate the relevance of these findings for off-lattice Vicsek-type models with antialigning interactions for which we observe apparent nonuniversal hyperuniformity, which we suggest to interpret as a reduction with integer power law to a finite value.

Using discrete element simulations based on molecular dynamics, we investigate the mechanical behavior of two-dimensional sheared, dry, frictional granular media in the “dense” and “critical” regimes. We find that this behavior is partitioned between transient stages and a final stationary stage. While the latter is macroscopically consistent with the predictions of the viscous $\mu \left(I\right)$ rheology, both the macroscopic behavior during the transient stages and the overall microscopic behavior suggest a more complex picture. Indeed, the simulated granular medium exhibits a finite elastic stiffness throughout its entire shear deformation history, although topological rearrangements of the grains at the microscale translate into a partial degradation of this stiffness, which can be interpreted as a form of elastic damage. When letting the system relax under constant volume at different stages of shear deformation, the relaxation of stresses follows a compressed exponential, also highlighting the role of elastic interactions in the medium, with residual stresses that depend on the level of elastic damage. The relations we establish between elastic and relaxation properties point to a complex rheology, characterized by a damage-dependent transition between a viscoelastoplastic and a viscous behavior.

This study combines broadband dielectric spectroscopy experiments with molecular dynamics (MD) simulations to investigate the impact of nanoparticle (NP) inclusions on pretransitional phenomena in liquid-crystal (LC) systems, specifically focusing on the relationship between nanoparticles, topological defects, and prenematic behavior. Our experimental results, using ${\mathrm{SiO}}_2$-doped 4-Cyano-4′-pentylbiphenyl composites, demonstrate that while NP additions do not significantly alter the isotropic-nematic transition temperature ($T_c$), prenematic effects exhibit universal behavior, confirmed by identical critical exponents across all samples. This indicates that the fundamental character of prenematic fluctuations remains unperturbed by the nanoparticles at these concentrations. Crucially, the observed systematic decrease in dielectric permittivity with increasing NP concentration is elucidated by MD simulations. These simulations reveal that nanoparticles act as "seeds” for topological defects, specifically forcing the surrounding LC molecules into a "hedgehog” configuration. This static, defect-induced structure leads to a local antiparallel alignment and cancellation of molecular dipoles. This provides a direct microscopic mechanism for the macroscopic dielectric response, successfully bridging the micro-macro scales and highlighting the nanoparticle-induced local ordering as a key factor in modifying the dielectric properties of the composite system.

We study the dynamics of an overdamped Brownian particle in a repulsive scale-invariant potential $V\left(x\right)\sim -x^{n+1}$. For $n>1$, a particle starting at position $x$ reaches infinity in a finite, randomly distributed time. We focus on the short-time tail $T\to 0$ of the probability distribution $P(T,x,n)$ of the blowup time $T$ for integer $n>1$. Krapivsky and Meerson [Phys. Rev. E 112, 024128 (2025)] recently evaluated the leading-order asymptotics of this tail, which exhibits an $n$-dependent essential singularity at $T=0$. Here we provide a more accurate description of the $T\to 0$ tail by calculating, for all $n=2,3,\cdots$, the previously unknown large preexponential factor of the blowup-time probability distribution. To this end, we apply a WKB (after Wentzel, Kramers and Brillouin) approximation—at both leading and subleading orders—to the Laplace-transformed backward Fokker-Planck equation governing $P(T,x,n)$. For even $n$, the WKB solution alone suffices. For odd $n$, however, the WKB solution breaks down in a narrow boundary layer around $x=0$. In this case, it must be supplemented by an “internal” solution and a matching procedure between the two solutions in their common region of validity.

We derive the first two moments of generic positive stochastic functionals in terms of the one- and two-time probability density functions of the underlying random walk, and we prove ergodicity of observables in stationary random walks. These general results are applied to the half-occupation time and the occupation time in an interval of a Gaussian random walk, for which we obtain exact analytic expressions for the first two moments. We then extend the analysis to scaled Brownian motion and fractional Brownian motion, computing the ergodicity breaking parameter and establishing a simple scaling form for the probability densities of occupation times. Within the framework of infinite ergodic theory, we further identify universal properties of positive observables. All analytical predictions are fully confirmed by numerical simulations.

Rotating equilibrated systems are widespread, but relatively little attention has been devoted to studying them from the first principles of statistical mechanics. We fill this gap by studying a Brownian particle coupled with a thermal bath made of rotating harmonic oscillators. We show that the Langevin equation that describes the dynamics of the Brownian particle contains (due to rotation) long-range correlated noise. In contrast to the usual situation of (nonrotating) equilibration, the rotating Gibbs distribution is recovered only for a weak coupling with the bath. In the presence of a uniform magnetic field, the stationary state is not Gibbsian, even under weak coupling. In this context, we clarify the applicability of the Bohr-van Leeuwen theorem to classical systems in rotating equilibrium, as well as the concept of work done by a changing magnetic field. We show that the Brownian particle under a rotationally symmetric potential reaches a stationary state that behaves as an effective equilibrium, characterized by a free energy. As a result, no work can be extracted via cyclic processes that respect the rotation symmetry. However, if the external potential exhibits asymmetry, then work extraction via slow cyclic processes is possible. This is illustrated by a general scenario involving a slow rotation of a non-rotation-symmetric potential. We study sedimentation equilibrium and show that centrifugal instability is prevented by a finite friction.

Efficient allocation is important in nature and human society, where individuals frequently compete for limited resources. The Minority Game (MG) is perhaps the simplest toy model to address this issue. However, most previous solutions assume that the strategies are provided a priori and static, failing to capture their adaptive nature. Here we adopt the reinforcement learning paradigm to the MG, where individuals' decision-making is guided by their experience and the expectation of future rewards. By regulating the balance between exploration and exploitation in individual decision-making, the study reveals diverse collective behaviors. We find that the optimal allocation is reached when individuals appreciate both the experience and the rewards in the future and can balance the exploitation of their experiences with exploration by randomly acting. When the balance of the exploitation and exploration is broken, only partial coordination is observed; in some scenarios, anticoordination may occur, a phenomenon where the coordination is even worse than the scenario where every individual acts purely randomly. Mechanism analysis reveals a symmetry-breaking of action preferences that underlines optimal coordination, where resource utilization reaches its maximum, and the dynamics behind its destabilization. These findings are robust to the population size and the resource capacity. Our work thus provides a different solution to the MG and valuable insights into the resource allocation problems in general.

Feedback in cellular processes is typically inferred through cellular responses to experimental perturbations. Modular response analysis provides a theoretical framework for translating specific perturbations into feedback sensitivities between cellular modules. However, in large-scale drug perturbation studies the effect of any given drug may not be known and may not only affect one module at a time. Here, we analyze the response of gene expression models to random perturbations that affect multiple modules simultaneously. In the deterministic regime we analytically show how cellular responses to infinitesimal random perturbations can be used to infer the nature of feedback regulation in gene expression, as long as the effects of perturbations are statistically independent between modules. We numerically extend this deterministic analysis to the response of average abundances of stochastic gene expression models to finite perturbations. By sampling simple models of stochastic gene expression, we identify example systems that violate the bounds predicted within a deterministic framework. We show these violations persist even in the limit of infinitesimal perturbations and are due to the inherently stochastic dynamics of biochemical feedback circuits. These discrepancies demonstrate how deterministic analyses can fail to correctly describe the response of cellular averages to perturbations even in the linear response regime.