Hierarchy significantly shapes interactions in social structures by organizing individuals or groups based on status, power, or privilege. This study investigates how hierarchy affects structural balance as temperature variations, which measure an individual's average irrationality in society. To address this question, we develop a two-layer balance model, the “leader layer,” which maintains structural balance exclusively through intralayer interactions. Conversely, the “follower layer” maintains structural equilibrium through both inter- and intralayer interactions. The Hamiltonian of the leading layer is independent, while the follower layer depends on its parameters as well as those of the leading layer. Analytical results from the mean-field approximation and exact Monte Carlo simulations show that instability arises in the equilibrium states of the follower layer when the temperature is below the critical threshold ($T<T_c$), which is different from the structural Heider equilibrium. Furthermore, our findings indicate that the critical temperature is elevated in the follower layer.

Power-law (PL) distribution functions (DF) are prevalent in highly diverse systems. The systems range in size from nanometer to mega light years, in complexity from dust grains to living organisms, and characterize the distribution of various events in nature and in various human activities. To gain some insight on why PL DF are so prevalent, we explore the conditions leading to the formation of a PL DF in a simple system of colliding hard sphere. We follow the time evolution of the energy DF through direct Monte Carlo simulations. In statistical equilibrium, the DF evolves into the Maxwell-Boltzmann DF. A transition to a PL DF occurs when the following occurs: (1) The system is initially far from equilibrium. For example, a mix of light and heavy particles with the same velocity. (2) The system dynamics is scale free, which holds in the intermediate asymptotic regime, far from the initial and the final equilibrium states. The scale-free dynamics leads to a DF which evolves in a self-similar form. (3) The system is open with a scale-free boundary condition. For example, a constant injection of particles far from equilibrium. The DF PL index is set by the time dependence of the self-similar DF and by the boundary condition. The PL index is independent of the self-similar DF form. Conditions (1)–(3) are common in a great variety of systems, which may explain why PL DF are so prevalent in nature.

In thin film deposition from vapor at constant substrate temperature, the surface roughness may reach large values as the thickness increases or as multilayer islands form in the initial growth stages. Here, we use kinetic Monte Carlo (KMC) simulations of four models of thin film deposition with dynamically changing substrate temperature to search for conditions to reduce the roughness of a variety of surface morphologies of applied relevance. At constant temperature, these models lead to: (1) kinetic roughening of the film surfaces; (2) growth of uncorrelated mounds whose widths increase with the temperature; (3) mound coarsening with selection of slopes that increase with the temperature; and (4) growth of multilayer islands on a foreign substrate and their coalescence to form a continuous film. In all simulations, we consider linearly increasing and linearly decreasing temperatures. With models 2 and 4, time-increasing temperature during the deposition produces final surfaces with smaller roughness than those produced by deposition at any temperature in the same range. This occurs because narrow mounds or islands nucleate at the lowest temperatures and, as the temperature increases, the larger diffusion lengths of the adsorbed species lead to rapid filling of the gaps or valleys, allowing faster coalescence of mounds and islands, and consequent surface smoothening. This physical interpretation shows that deposition in time-increasing temperature may be a route for producing smoother films when high densities of islands or mounds are formed at the lowest temperatures (which is the common feature of models 2 and 4). In the simulations of models 1 and 3, as well as with time-decreasing temperature in all models, a similar effect is not observed, but nontrivial evolutions of the roughness (e.g., nonmonotonic variations) may be found, which significantly differ from the growth modes observed in constant temperature deposition. A method to interpolate the roughness evolution of KMC simulations at constant temperatures is also proposed, but for all models, we show that the growth history in time-varying temperature cannot be quantitatively predicted by interpolation of data obtained in constant temperature growth.

The association between tie strength and network structure is a fundamental topic in the analysis of complex social systems. We study this association by analyzing tie strength using higher-order networks, an increasingly relevant model which can encode group interactions between three or more individuals. First, we introduce three measures based on algebraic topology which characterize the network context and influence of an edge. Our experimental results across 15 datasets indicate that these measures outperform standard network proxies in estimating tie strength as a function of the unweighted network topology. These measures can further replicate and explain a puzzle wherein certain bridging ties are surprisingly strong. We then consider a single centrality measure which combines the three initial measures, is highly inversely correlated with tie strength, and can be interpreted through an information exchange process that highlights ties that have access to useful information. In this sense, we are able to illuminate the information advantages of weak ties due to their network position.

Markov processes are widely applied in modeling random phenomena, and the corresponding models can be analyzed within an established theoretical framework. It is thus desirable to have reliable tests for the (non-)Markovianity of a physical or biological system at hand. One such test, suggested by Engbring et al. [Phys. Rev. X 13, 021034 (2023)], is based on a nonlinear fluctuation-dissipation relation (NL-FDR) that compares spontaneous fluctuations with the response to (nonweak) external perturbations. A violation of this NL-FDR indicates non-Markovianity. However, estimating the relevant statistics for the variable conjugated to the perturbation from finite experimental data can be challenging. Comparing noisy estimates of the spontaneous and the response statistics can lead to apparent deviations from the prediction of the NL-FDR. So, when is a violation of the NL-FDR due to non-Markovian features of the system and when is it due to a finite sample size? We consider this question for the simplest Markovian example, the overdamped harmonic oscillator with thermal white noise and subject to a constant force perturbation. We derive analytical expressions for the variances of the estimators for the spontaneous correlation function and for the time-dependent mean response. We confirm previous findings that there is an optimal amplitude for the perturbation at which the test of non-Markovianity is most reliable. In terms of the original variable, the optimal amplitude is such that the response to the perturbation is of the order of one standard deviation of the spontaneous fluctuations. Put differently, the optimal amplitude neither corresponds to the linear-response regime of very weak perturbations nor to the regime of very strong perturbations where the response is largely deterministic. At large amplitudes, we encounter heavy-tailed distributions of certain estimators, which we discuss.

We consider Rayleigh particles in a periodically modulated optical trap formed by two counterpropagating Gaussian beams. It is shown that for certain values of the parameters the system exhibits transient chaos which manifests itself in particle acceleration and subsequent directional ejection out of the trap. The escape flights are terminated at a distance of hundreds of wavelengths from the trap center and the particles return to the trap under the action of the Stokes force. The particle escape is shown to be a threshold effect that can be potentially employed for particle sorting.

We study the hydrodynamic behavior of two-dimensional chiral dry Malthusian flocks, that is, chiral polar-ordered active matter with neither number nor momentum conservation. We show that, in the absence of fluctuations, such systems generically form a “time cholesteric,” in which the velocity of the entire system rotates uniformly at a fixed frequency $b$. Fluctuations about this state belong to the universality class of $(2+1)$-dimensional Kardar-Parisi-Zhang (KPZ) equation, which implies short-ranged orientational order in the hydrodynamic limit. We then show that, in the limit of weak chirality, the hydrodynamics of a system with reasonable size is expected to be governed by the linear regime of the KPZ equation, exhibiting quasi-long-ranged orientational order. Our predictions for the velocity and number density correlations are testable in both simulations and experiments.

Temperature-Induced Quantum Migration (TIQM) is a macroscopic quantum phenomenon that fundamentally reshapes the local thermodynamics of confined systems. While previously explored in Maxwell-Boltzmann and Bose gases, we here extend the TIQM framework to noninteracting Fermi gases confined in anisometric rectangular domains. These domains are characterized by $D_I$, representing the number of dimensions that remain unconfined. We derive the local heat capacity and demonstrate that the standard temperature derivative of local energy yields unphysical negative regions, a discrepancy resolved by the TIQM correction. We show that quantum degeneracy in Fermi gases generally suppresses the TIQM contribution to global heat capacity compared to other statistics, yet it drives a distinct redistribution of local heat capacity. Notably, for the most constrained case ($D_I=0$), a Schottky-type anomaly emerges at low densities, which is progressively “washed out” by increasing dimensionality ($D_I=1,2$). Based on an idealized noninteracting model, our calculations suggest that a measurable (22%) enhancement in the local-to-global electronic heat capacity ratio could emerge at approximately 84 nm from the longitudinal boundaries of a $12\times 12\times 5600$ ${\mathrm{nm}}^3$ bismuth nanowire at 30 K, offering a potential experimental signature for TIQM. These results complete a systematic trilogy of studies across all fundamental quantum statistics, establishing TIQM as a necessary correction for the local thermodynamics of nanoscale devices.

We consider populations evolving according to natural selection, mutation, and recombination and assume that the genomes of all or a representative selection of individuals are known. We pose the problem of whether it is possible to infer fitness parameters and genotype fitness order from such data. We tested this hypothesis in simulated populations. We delineate parameter ranges where this is possible and other ranges where it is not. Our work provides a framework for determining when fitness inference is feasible from population-wide, whole-genome, time-stratified data and highlights settings where it is not. We give a brief survey of biological model organisms and human pathogens that fit into this framework.

It is well known that the spectral form factor (SFF) of a possibly degenerate many-body Hamiltonian can be identified with a planar random walk taking steps of unequal length. In this paper we push this identification further and propose to study the chaotic content of a Hamiltonian $H$ via its associated random walk seen as a fractal, using the tools of fractal geometry. In particular, we conjecture that for chaotic Hamiltonians the Hausdorff dimension of the frontier of the corresponding random walk approaches the universal value $d_F=4/3$—the same value obtained when the random walk describes a Wiener process. Our numerical simulations for nonintegrable models confirm this expectation while for quasifree integrable models we obtain a value $d_F=1$. Additionally, we numerically show that “Bethe-Ansatz walkers” fall into a category similar to the nonintegrable walkers. To motivate this conjecture we consider many-body Hamiltonians with degenerate but rationally independent eigenvalues. We prove that if the degeneracies satisfy certain Lyapunov conditions, the random walk becomes a Wiener process, $d_F=4/3$, and the distribution of the SFF becomes Gaussian. This is the familiar Gaussian approximation for the SFF which we show to be violated at very low temperature. We also compute the moments of the SFF exactly under milder hypotheses thus solving the classical problem of determining the moments of a random walker taking steps of unequal lengths. Finally, we consider quasifree Fermionic models with possibly degenerate but rationally independent one-particle spectra. We show that in this case the distribution of the SFF becomes lognormal and also give the exact form of the moments under milder hypotheses.

This study formulates a two-dimensional self-consistent kinetic model for numerical simulations a hollow-cathode glow discharge. This model includes a solution of the spatially inhomogeneous Boltzmann kinetic equation for electrons, taking into account both energy and two spatial variables: the longitudinal and radial coordinates. The model also incorporates fluid balance equations for the densities of heavy particles (ions and metastable excited atoms) and the Poisson equation for finding the electric field. It is shown based on the calculations results that extended regions of electron energy distribution function (EEDF) inversion can be realized both inside and outside the hollow cathode. An approximate analytical model is developed which explains the obtained results and allows scaling the results for varying external conditions. Thus, this study clarifies the formation mechanisms of EEDF and makes it possible to develop recommendations for the further experimental detection of an inverse EEDF.

Recent stellarator reactor designs demonstrate mostly outward turbulent particle transport, which, without advanced fueling technology, inhibits the formation of density gradients needed for confinement. We introduce “SQuID-$\tau$,” a self-fueling quasi-isodynamic stellarator capable of sustaining density peaking through inward particle transport caused by turbulence. Temperature and density profile predictions based on high-fidelity gyrokinetic simulations demonstrate enhanced performance, significantly relaxing constraints on the size and magnetic field strength for reactor designs.

We investigate the kinetics of particle aggregation within the framework of the Smoluchowski coagulation equation, extending it to account for electrostatic interactions among charged clusters. Using a stochastic Monte Carlo implementation, we examine how different charge distributions and net system charge affect cluster growth dynamics. Electrostatic interactions are incorporated directly into the classical Brownian collision kernel, yielding charge-dependent modifications of the collision rates that may either enhance or suppress aggregation depending on the signs and magnitudes of the interacting charges. Our simulations reveal distinct regimes of growth: At intermediate times, charge heterogeneity accelerates or delays aggregation depending on the initial underlying charge distribution, while at long times the system tends toward quasistationary states whose properties depend on the net charge. Comparisons between Gaussian and Cauchy-Lorentz initial charge statistics highlight the role of heavy-tailed distributions in promoting faster cluster growth. These findings contribute to a unified understanding of coagulation kinetics in charged particulate systems, with potential implications for aerosol and astrophysical coagulation processes, volcanic ash aggregation, and clustering in industrial fluidized granular beds.

Despite substantial advances in mitigating turbulent heat losses, including those achieved in the stable quasi-isodynamic design family [J. Plasma Phys. 89, 905890504 (2023); PRX Energy 3, 023010 (2024)], particle confinement remains a principal performance bottleneck in modern quasi-isodynamic stellarators, a challenge not fully addressed in previous optimization efforts. Using gyrokinetic simulations within the gene-Tango framework, we identify suppressed inward thermodiffusion, caused by unfavorable magnetic geometry, as the primary cause. To overcome this limitation, we design a new configuration with a reduced mirror ratio, which enhances the contribution of passing electrons to the inward particle flux. This facilitates the formation of strongly peaked density profiles, suppresses turbulence, and leads to a substantial improvement in confinement. Our optimized configuration achieves nearly a twofold increase in energy confinement compared to Stellaris, highlighting the crucial role of optimizing particle transport in next-generation stellarator designs.

We present two derivations of an entropy-related function known as diversity in terms of entropy functionals. In the first case, we express diversity as an exponential of the difference between two forms of Shannon entropy. In the second case, the Jensen-Shannon divergence, an entropic function, only depends on diversity. Then, in the second part of this work, we apply diversity and Shannon entropy to a system in equilibrium (Ising model) and also to an out-of-equilibrium system (seismic region in Alaska). It turns out that diversity gives sharper responses at the critical points and more texture in the general trends.

The drag force on planar structures of arbitrary shape is derived in free molecular flow using gas kinetic theory. The theory is formulated by considering the anisotropic intermolecular potential between the particle and gas molecules, in the limits of specular and diffuse scatterings. The drag force theory formulated by Dahneke [J. Aerosol Sci. 4, 147 (1973)] for disklike bodies in free-molecular flow is shown to be a special case of the theory derived herein. The Einstein-Smoluchowski relationship is generalized with anisotropic drag to structures of arbitrary shape. Binary diffusion coefficients of planar molecules (benzene, naphthalene, phenanthrene, pyrene, coronene, and ovalene) in nitrogen are calculated using gas kinetic theory. The diffusion coefficients are in close agreement with available experimental data and with molecular dynamics simulations.