Estimating free-energy differences using nonequilibrium work relations, such as the Jarzynski equality, is hindered by poor convergence when work fluctuations are large. For systems governed by overdamped Langevin dynamics, we propose the counterintuitive approach of adding noise in order to increase the precision of such calculations. By introducing additional stochastic fluctuations to the system and rescaling its potential energy accordingly, we leave the thermodynamics of the system unchanged while increasing its relaxation rate. For a given time-dependent protocol this modification reduces the dissipated reduced work, leading to more accurate free-energy estimates. The method is designed to be used in experiment, and we illustrate its operation using computer simulations applied to two model systems. However, the regime of applicability of this strategy is likely limited, because it requires control of the system's potential energy in a way that is feasible in only a few experimental settings.

Achieving uniform, stable, and reliable erosion of electrode materials is crucial for enhancing the performance and lifespan of vacuum-arc devices. This study investigates the rotation and erosion characteristics of cathode spots on Cu and Ti cathodes with various applied magnetic fields. The results indicate that with the discharge current changes, cathode spots evolve from a single spot to multiple spots and then back to a single spot. Without an applied magnetic field, Ti cathode spots exhibit a large-scale random walk, while Cu cathode spots show a concentrated distribution. With an applied magnetic field, cathode spots of both materials undergo directional rotation. The velocity of the Ti cathode spots is higher than that of Cu, and spot velocity increases with the increase of magnetic flux density. When the radial magnetic field is enhanced to 70 mT, the rotational velocity of the cathode spots actually decreases with the increase of the peak current. The increase of applied magnetic field leads to a significant decrease in the total erosion rate and macroparticle loss, accompanied by an increase in the average ion charge state. The application of an applied magnetic field can effectively regulate the rotation of cathode spots, allowing both Cu and Ti cathode spots to rotate for more than one full circle. Scanning electron microscopy observations indicate that the dimensions of the erosion craters on the cathode surfaces are significantly reduced, leading to a substantial improvement in the uniformity of erosion.

Grain boundaries (GBs), crucial to polycrystalline materials, have been extensively studied in conventional periodic structures with rotational and translational symmetries. However, the characteristics of GBs in quasicrystals (QCs), which lack translational symmetry, remain mysterious. This study investigates the atomic configurations and formation mechanisms of GBs in two-dimensional decagonal QCs using phase-field crystal simulations. Atomic characterizations reveal that QC GBs comprise various defects, including basic and combined defects, as well as phasonic defects. The population densities of these defects increase with GB misorientation. Interestingly, the spacing of initial seeds, not causing structural changes in crystal GBs, affects defect distribution in QC GBs. The formation mechanism of QC GBs involves two stages: lattice collision and atom local rearrangement. Lattice collision occurs when two growing grains meet, inevitably leading to intergranular defects. Subsequently, atom local rearrangements—including multiatom motions around intergranular defects and phasonic flips of individual atom—act as repairs to mitigate distortions caused by lattice collisions. Phasonic flips not only reduce the number of defects but also maintain the long-range quasiperiodicity of QCs. This work elucidates the characteristics of QC GBs and their formation mechanisms, offering insights into the similarities and differences between GBs in crystals and QCs.

When analyzing experimental or simulation time-series data, the question arises whether it is possible to tell from the mere observation of the time-dependent trajectory of a one-dimensional observable whether the system is in equilibrium or not. We here consider the nonequilibrium version of the generalized Langevin equation for a Gaussian non-Markovian observable and show that (i) the multipoint joint distribution solely depends on the two-point correlation function and that (ii) for any nonequilibrium process an equilibrium process with uniquely determined parameters can be found that produces the same two-point correlation function. Since the multipoint joint distribution completely characterizes the dynamics of an observable, we conclude that the nonequilibrium character of a system, in contrast to its non-Markovianity, cannot be read off from the one-dimensional trajectory of a Gaussian observable. These findings are relevant for human cancer and algae cells, whose single-cell velocity distributions have been found to be Gaussian within the data accuracy.

The question of how classical thermodynamic laws emerge from the underlying quantum substrate lies at the foundations of physics. Here we examine the validity of the ideal gas law (IGL) for a single quantum particle confined within a two-dimensional cavity. By interpreting the quantum wave function as a probability density analogous to that of an ideal gas, we employ the energy equipartition principle to define the temperature of the quantum state. For the mean pressure we take two definitions, one straightforwardly based on the radiation pressure concept and the other taking advantage of a quasi-orthogonality relation valid for billiard eigenstates. We analyze systems with regular dynamics—the circular and rectangular billiards—and compare them with the classically chaotic Bunimovich stadium. We find that the IGL for the first definition of pressure holds exactly in isotropic systems (as the circular case), while for anisotropic geometries, quantum eigenfunctions generally conform to the IGL only on average, exhibiting meaningful deviations. These deviations are diminished in the presence of chaotic dynamics and for coherent states. This observation is consistent with the eigenstate thermalization hypothesis (ETH). Notably, the second definition of pressure allows for a good matching with the IGL.

The exploration of the intrinsic mechanisms underlying synchronization has long held pervasive significance within the scientific community, as it offers profound insights for understanding the macroscopic self-organized dynamics on top of complex systems. Here, we investigate the generalized Kuramoto model incorporating the mixed higher-order interactions. In particular, we mathematically argue that, in the mean-field representation, the coupling scheme is equivalent to the biharmonic coupling, wherein the coupling function of phase oscillators goes beyond the setting of the single-Fourier modes. Importantly, we ascertain that the interplay between the pairwise single-harmonic coupling and the nonpairwise biharmonic coupling is responsible for the occurrence of a number of fascinating synchronized states, as well as extensive multistability and diverse phase transitions. We establish a general framework for comprehending the underlying mechanisms of the emergent phenomena involved, and our work, thus, provides profound insights for shaping the collective behaviors observed in the complex networks encoded with higher-order topologies.

Recent investigations have discovered the potential of high-dimensional nonlinear systems for predicting nontemporal and temporal tasks. The prediction is demonstrated here for an asymmetrical seventh-degree polynomial and time series of variables in Rössler system by using spin-torque nano oscillator (STNO) as a reservoir corresponding to the nontemporal and temporal tasks, respectively. For training, the inputs are supplied through the bifurcation parameters, (i) magnitude of the alternating current (AC) passed through the STNO and (ii) the frequency with which the AC is applied. The computed values of root-mean-square error affirms that the STNO is a good candidate for the role of reservoir in reservoir computing. Further the output is predicted close to the target even in the presence of noise. The performance of the reservoir is investigated against the hyperparameters for both the nontemporal and temporal tasks. The performance of the reservoir is quite robust in the presence of thermal noise and the accuracy is maintained even at higher temperatures.

This paper investigates the simulation and analysis of collective self-propelled motion in the presence of a leader, a phenomenon commonly observed in natural and artificial systems, such as bird flocks or robotic swarms. Using a dynamic approach based on the Langevin equation, the study models interactions between particles and a leader through elastic restoring forces and incorporates stochastic noise to simulate random fluctuations. These forces ensure group cohesion, avoid collisions, and mimic real-world conditions where unpredictability plays a significant role. The simulation starts with particles randomly distributed in a two-dimensional space. As the leader moves at a constant velocity, particles adjust their positions and velocities to follow it. The results demonstrate a two-phase evolution: an initial rapid clustering around the leader due to strong elastic forces, followed by a gradual alignment of particle velocities to match the leader. The velocity profile, represented by a linear increase followed by an exponential decay, captures the transition from disorder to order. Key parameters such as the spring constant $k_1$, which governs the leader-particle interaction, and the diffusion coefficient $D$, which regulates stochastic noise, are shown to significantly influence the system dynamics. High interaction strength accelerates synchronization and stabilizes the group, while weaker interactions lead to slower clustering and potential dispersion. Phase diagrams and susceptibility analyses confirm that the leader's role is critical in initiating and maintaining collective behavior. This study highlights the emergence of coordinated motion in a leader-follower context, offering insights into biological systems and inspiring applications in swarm robotics, where efficient and cohesive movement is essential.

The two-state Togashi-Kaneko model demonstrates how, at finite system sizes, autocatalysis can lead to noise-induced bistability between the cellular concentrations of different molecular species. Here, we show that, in the biologically relevant scenario of species-dependent export rates, the nascent stochastic switching between molecular species also drives a concomitant switching between periods of growth or decay in the total population size. We demonstrate this behavior using stochastic simulations, as well as the numerical integration of a Fokker-Planck equation that approximates the finite system-size limit. By combining Piecewise Deterministic Markov and linear-noise approximations, we further find analytic expressions for the stationary distributions of the different molecular species when stochastic switching is faster than the dynamics in the total population size. We envisage that other models in the voter class—including spin systems, flocking, and opinion dynamics—may also exhibit aperiodic growth and decay in population size, as well as be amenable to similar techniques.

System analysis depends critically on the identification of the connections—especially the causal relationships—that exist between the components of the system. In particular, the causal relationships connecting neurons in brains, whose activities are typically observed as spike trains (a type of point process), need to be elucidated. Although various causality detection methods have been developed for time series signals, an effective causality detection method for spike trains has not been developed yet. To this end, we propose a causality detection method for spike trains based on the theory of nonlinear dynamical systems. We use the mutual prediction accuracy of the interspike intervals of spike trains for causality detection. Furthermore, we test the prediction accuracy obtained by the proposed method using the method of surrogate data from nonlinear dynamical systems theory. Numerical experiments revealed that the proposed method provides accurate causality detection for a small number of neural spike trains generated by the mathematical model.

We study the hydrodynamic drag force exerted on a sphere in a static anisotropic porous medium. This problem is analyzed using the Brinkman-Debye-Bueche equations with an axisymmetric shielding (or permeability) tensor. Using the exact Green's functions for this model fluid within a single-layer boundary element formulation, we numerically compute the friction tensor for a translating sphere subjected to stick boundary conditions. Furthermore, we derive approximate analytical expressions for small anisotropy using the Lorentz reciprocal theorem. By benchmarking this result against the numerical solutions, we find that a linear approximation is valid in a broad parameter regime. Our results are important for studying self-diffusion in general anisotropic porous media, but can also be applied to small tracers in nematic fluids composed of disk- or rodlike crowders.

We investigate the generation of kilotesla-level magnetic fields in laser-irradiated hollow conical targets through particle-in-cell simulations. This configuration proves effective in producing magnetic fields tens of kiloteslas in strength that persist on a picosecond timescale. Moreover, the hollow conical shape provides an azimuthal structure to the magnetic fields within its interior, leading to large magnetized regions in a confined geometry, even under relatively modest laser intensities. The time evolution of the magnetic field is captured by an effective $\mathit{RL}$ circuit model, in which the current loop—consisting of the driven forward hot electrons and the return currents along the walls—discharges inductively after the laser stops driving the current. The high magnetic field regions shrink closer to the wall through this magnetic energy decay as the magnetic pressure shrinks. These findings provide valuable possibilities for future experimental studies—based on the capability of confining and collimating particles—and have potential applications in areas such as laboratory astrophysics, fast ignition, and particle acceleration.

Two layers of dry granular particles of different density are initially superimposed in an unstable configuration, the layer of dense particles above. This layering is set in motion, numerically by tilting the gravity in discrete element method simulations with periodic boundary conditions and experimentally by opening a confinement gate at the bottom of an inclined channel. In both cases, a Rayleigh-Taylor-like instability (RTI) is rapidly observed and plumes from the lower layer of light particles emerge at the free surface. Owing to the downslope mean flow and shear, these plumes organize themselves in a pattern of alternated bands of dense and light particles. Dense particles segregate toward the surface due to their larger size compared to lighter ones. This continuous transport at the free surface feeds the bands of dense particles and sustains longitudinal rolls underneath these bands. The granular RTI shares similarities with viscous fluid RTI, showing a wavelength proportional to flow thickness, a perturbation that grows exponentially and a growth rate increasing with density ratio. The two layers are miscible, yet, unlike fluids, two additional processes come into play, sedimentation that favors diffusion and size segregation that acts as an antidiffusion process. Both combine to control the extent of the diffusion zone at the interface between layers.

The experimental results on molecular diffusion in supercritical methane in a wide pressure range reported by [U. Ranieri et al., Nat. Commun. 15, 4142 (2024)] are compared with the theoretical expectations based on the Lennard-Jones model. In the low-pressure low-density limit, the kinetic approach within the Chapman-Enskog approximation is shown to be adequate. At higher pressures and densities, the freezing density scaling approach becomes appropriate. In this approach, the properly reduced transport coefficients along isotherms appear as quasi-universal functions of the density divided by the density at the freezing point. We analyze the transition from gaslike to liquidlike dynamical behavior from the perspective of the Stokes-Einstein-Sutherland relation linking self-diffusion and shear viscosity coefficients. This analysis locates the dynamical crossover close to the transition from gas- to liquidlike molecular diffusion in methane, which is observed experimentally. We emphasize the importance of distinguishing between two separate transitions: the intersection of gaslike and liquidlike asymptotes of transport-related properties and the onset of the rigid-fluid regime. These transitions occur at significantly different locations on the phase diagram, which explains the conflicting criteria often used to define the gas-to-liquid-like dynamical crossover and the Frenkel line. In addition, our results offer a practical and predictive framework for estimating the transport properties of supercritical methane in pressure and temperature regimes where experimental data are currently unavailable.

The selection of parameters in the contact law for interparticle interactions affects the results of simulations of flowing granular materials. The present study aims to understand the effect of the ratio of tangential to normal spring stiffness coefficient ($\kappa$) on interparticle contact behavior in terms of the rotational coefficient of restitution determined using data obtained from multiparticle simulations. The effect of $\kappa$ on the profiles of the micro- and macroscopic properties of particles in a vibrofluidized bed is also investigated. The discrete element method (DEM) is used to simulate a vertically vibrated fluidized bed using the open-source software LAMMPS. The interparticle and wall-particle contact forces are determined using the linear spring dashpot (LSD) model. The distribution of the mean co-ordination number, force during the contact, contact regimes, and rotational coefficient of restitution are determined from the data obtained from simulations. It is observed that $\kappa$ plays a significant role in the distribution of interparticle contacts between different regimes and, thereby, the velocity distribution and profiles of statistically averaged properties of the vibrofluidized particles. Our results show that for particles with surface friction coefficient $\mu >0.1$, the commonly used value $\kappa =\frac{2}{7}$ results in quantitatively different results from those obtained using $0.67\le \kappa <1$, a range consistent with the realistic values of Poisson ratios for simple materials.

In this study, we present an experimental work on bubble nucleation and growth using a model system comprised of viscoelastic polyvinyl butyral confined in a Hele-Shaw cell geometry that is decompressed at elevated temperatures. The appearance and growth of bubbles are connected to the temperature-induced shift in chemical equilibrium experienced simultaneously by two gases present in the bulk. The latter becomes simultaneously oversaturated with water vapor and slightly undersaturated in air. Our bubbles grow with various shapes and sizes depending on the initial morphology of the nucleus or the presence of neighboring bubbles. For large nuclei, bubbles grow anisotropically because of contact line pinning. The likelihood of nucleation is related to the amount of water dissolved in the bulk and the imposed temperature. Counterintuitively, the number of nuclei whence a bubble can grow is inversely correlated with said temperature. In an analogy with champagne, we show that nucleation can either be natural, at trapped fibers or dust particles, or artificial, at crenels we purposefully made in the glass surface. Our results indicate that the growth rate of bubbles can be impacted by the nucleation mechanism.

We study a generalized Kardar-Parisi-Zhang (KPZ) equation [Jana et al., Phys. Rev. E 109, L032104 (2024)] that sets the paradigm for universality in roughening of growing nonequilibrium surfaces without any conservation laws but with competing local and nonlocal nonlinear effects. This equation in two dimensions exhibits two distinct strong coupling regimes: a rough phase and a crumpled phase, in addition to a weak coupling phase. The conformation fluctuations of such a rough surface are given by nonuniversal scaling exponents, with orientational long-range order and positional short-range order, whereas the crumpled phase has positional and orientational short-range order.

We derive the master equations for the Susceptible-Infected (SI) model on general hypernetworks with $N$-body interactions. We solve these equations exactly for infinite $d$-regular hypernetworks, and obtain an explicit solution for the expected infection level as a function of time. The solution shows that the epidemic spreads out to the entire population as $t\to \infty$ if and only if the initial infection level exceeds a positive threshold value. This phase transition is a high-order interaction effect, which is absent with pairwise interactions.

It is known that the long-range quantum entanglement exhibited in free fermion systems is sufficient to “thermalize” a small subsystem in that the subsystem reduced density matrix computed from a typical excited eigenstate of the combined system is approximately thermal. Remarkably, fermions without any interactions are thus thought to satisfy the eigenstate thermalization hypothesis. We explore this hypothesis when the fermion subsystem is only minimally coupled to a quantum reservoir (in the form of another fermion system) through a quantum point contact (QPC). The entanglement entropy of two free fermion systems connected by one or more QPCs is examined at finite energy and in the ground state. When the combined system is in a typical excited state, it is shown that the entanglement entropy of a subsystem connected by a small number of QPCs is subextensive, scaling as the linear size of the subsystem ($L_A$). For sufficiently low energies ($E$) and small subsystems, it is demonstrated numerically that the entanglement entropy $S_A\sim L_{A}E$, what one would expect for the thermodynamics of a one-dimensional system. In this limit, we suggest that the entropy carried by each additional QPC is quantized using the one-dimensional finite size and temperature conformal scaling: $\mathrm{\Delta }{S}_A=\alpha log(1/E)sinh\left(L_{A}E\right)$. The subextensive entropy in the case of a small number of QPCs should be contrasted with the expectation for both classical, ergodic systems and quantum chaotic systems, wherein a restricted geometry might affect the equilibrium relaxation times but not the equilibrium properties themselves, such as extensive entropy and heat capacity.

We present a two-player game in a chaotic dynamical system where players have opposing objectives regarding the system's behavior. The game is analyzed using a methodology from the field of chaos control known as partial control. Our aim is to introduce the utility of this methodology in the scope of game theory. These algorithms enable players to devise winning strategies even when they lack complete information about their opponent's actions. To illustrate the approach, we apply it to a chaotic system—the logistic map. In this scenario, one player aims to maintain the system's trajectory within a transient chaotic region, while the opposing player seeks to expel the trajectory from this region. The methodology identifies the set of initial conditions that guarantee victory for each player, referred to as the winning sets, along with the corresponding strategies required to achieve their respective objectives.