We consider the nonlinear-cost random-walk model in discrete time introduced in Phys. Rev. Lett. 130, 237102 (2023), where a fee is charged for each jump of the walker. The nonlinear cost function is such that slow or short jumps incur a flat fee, while for fast or long jumps the cost is proportional to the distance covered. In this paper we compute analytically the average and variance of the distance covered in $n$ steps when the total budget $C$ is fixed, as well as the statistics of the number of long or short jumps in a trajectory of length $n$, for the exponential jump distribution. These observables exhibit a very rich and nonmonotonic scaling behavior as a function of the variable $C/n$, which is traced back to the makeup of a typical trajectory in terms of long or short jumps, and the resulting entropy thereof. As a by-product, we compute the asymptotic behavior of ratios of Kummer hypergeometric functions when both the first and last arguments are large. All our analytical results are corroborated by numerical simulations.

Chimera states in nonidentical oscillators have received extensive attention in recent years. Previous studies have demonstrated that chimera states can exist in a ring of nonlocally coupled bicomponent oscillators even in the presence of strong parameter heterogeneity. In this study, we investigate spiral wave chimeras in two-dimensional nonlocally coupled bicomponent oscillators where oscillators are randomly divided into two groups, with identical oscillators in the same group. Using phase oscillators and FitzHugh-Nagumo oscillators as examples, we numerically demonstrate that each group of oscillators supports its own spiral wave chimera and two spiral wave chimeras coexist with each other. We find that there exist three heterogeneity regimes: the synchronous regime at weak heterogeneity, the asynchronous regime at strong heterogeneity, and the transition regime in between. In the synchronous regime, spiral wave chimeras supported by different groups are synchronized with each other by sharing a same rotating frequency and a same incoherent core. In the asynchronous regime, the two spiral wave chimeras rotate at different frequencies and their incoherent cores are far away from each other. These phenomena are also observed in a nonrandom distribution of the two group oscillators and the continuum limit of infinitely many phase oscillators. The transition from synchronous to asynchronous spiral wave chimeras depends on the component oscillators. Specifically, it is a discontinuous transition for phase oscillators but a continuous one for FitzHugh-Nagumo oscillators. We also find that, in the asynchronous regime, increasing heterogeneity leads irregularly meandering spiral wave chimeras to rigidly rotating ones.

We investigate the information-theoretical limits of inference tasks in epidemic spreading on graphs in the thermodynamic limit. The typical inference tasks consist in computing observables of the posterior distribution of the epidemic model given observations taken from a ground-truth (sometimes called planted) random trajectory. We can identify two main sources of quenched disorder: the graph ensemble and the planted trajectory. The epidemic dynamics however induces nontrivial long-range correlations among individuals' states on the latter. This results in nonlocal correlated quenched disorder which unfortunately is typically hard to handle. To overcome this difficulty, we divide the dynamical process into two sets of variables: a set of stochastic independent variables (representing transmission delays), plus a set of correlated variables (the infection times) that depend deterministically on the first. Treating the former as quenched variables and the latter as dynamic ones, computing disorder average becomes feasible by means of the replica-symmetric cavity method. We give theoretical predictions on the posterior probability distribution of the trajectory of each individual, conditioned to observations on the state of individuals at given times, focusing on the susceptible infectious (SI) model. In the Bayes-optimal condition, i.e., when true dynamic parameters are known, the inference task is expected to fall in the replica-symmetric regime. We indeed provide predictions for the information theoretic limits of various inference tasks, in form of phase diagrams. We also identify a region, in the Bayes-optimal setting, with strong hints of replica-symmetry breaking. When true parameters are unknown, we show how a maximum-likelihood procedure is able to recover them with mostly unaffected performance.

Stress-strain constitutive relations in solids with an internal angular degree of freedom can be modeled using Cosserat (also called micropolar) elasticity. In this paper, we explore Cosserat materials that include chiral active components and hence odd elasticity. We calculate static elastic properties and show that the static response to rotational stresses leads to strains that depend on both Cosserat and odd elasticity. We compute the dispersion relations in odd Cosserat materials in the overdamped regime and find the presence of exceptional points. These exceptional points create a sharp boundary between a Cosserat-dominated regime of complete wave attenuation and an odd-elasticity-dominated regime of propagating waves. We conclude by showing the effect of Cosserat and odd-elasticity terms on the polarization of Rayleigh surface waves.

Following on recent experimental characterization of the transport properties of stealthy hyperuniform media for electromagnetic and acoustic waves, we report here measurements at ultrasonic frequencies of the multiple scattering of waves by 2D hyperuniform distributions of steel rods immersed in water. The transparency, for which the effective attenuation of the medium is canceled, is first evidenced by measuring the transmission of a plane wave propagating in a highly correlated and relatively dense medium. It is shown that a band gap occurs in the vicinity of the first Bragg frequency. The isotropy of both transparency and band gap are also evidenced for the case of waves generated by a point source in differently ordered and circular-shaped distributions. In other words, we thus obtain a representation of the Green's function. Our results demonstrate the huge potential of hyperuniform, as well as highly correlated, media for the design of functional materials.

We study the $q$-state Potts model for $q$ and the space dimension $d$ arbitrary real numbers using the derivative expansion of the nonperturbative renormalization group at its leading order, the local potential approximation (LPA and ${\mathrm{LPA}}^{\prime }$). We determine the curve $q_c\left(d\right)$ separating the first $[q>q_c\left(d\right)]$ and second $[q<q_c\left(d\right)]$ -order phase transition regions for $2.8<d\le 4$. At small $\epsilon =4-d$ and $\delta =q-2$ the calculation is performed in a double expansion in these parameters, and we find $q_c\left(d\right)=2+a{\epsilon }^2$ with $a\simeq 0.1$. For finite values of $\epsilon$ and $\delta$, we obtain this curve by integrating the LPA and ${\mathrm{LPA}}^{\prime }$ flow equations. We find that $q_c(d=3)=2.11\left(7\right)$, which confirms that the transition is of first order in $d=3$ for the three-state Potts model.

We experimentally explore the magnetization dynamics of thin ferromagnetic Co films with uniaxial in-plane anisotropy near the dynamic phase transition (DPT) and, in particular, we study the temporal characteristics of anomalous metamagnetic fluctuations that occur in its vicinity, and for which no thermodynamic equivalent exists. For this purpose, we measure the real-time evolution of magnetization trajectories in the relevant dynamic phase space, conduct a Fourier analysis of these experimental results and compare it to a model, in which the fluctuating metamagnetic behavior occurs in a purely random manner, following individual state probability distributions. We find excellent quantitative agreement in between our experimental results and the random state model, clearly indicating that multiperiod time-correlations of magnetic states are not relevant in our DPT system, not even for the occurrence of the anomalous metamagnetic fluctuations that are nonetheless associated with nonperiodic magnetic state evolutions.

During recent decades active particles have attracted an incipient attention as they have been observed in a broad class of scenarios, ranging from bacterial suspension in living systems to artificial swimmers in nonequilibirum systems. The main feature of these particles is that they are able to gain kinetic energy from the environment, which is widely modeled by a stochastic process due to both (Gaussian) white and Ornstein-Uhlenbeck noises. In the present work, we study the nonlinear dynamics of the forced, time-delayed Duffing oscillator subject to these noises, paying special attention to their impact upon the maximum oscillations amplitude and characteristic frequency of the steady state for different values of the time delay and the driving force. Overall, our results indicate that the role of the time delay is substantially modified with respect to the situation without noise. For instance, we show that the oscillations amplitude grows with increasing noise strength when the time delay acts as a damping term in absence of noise, whereas the trajectories eventually become aperiodic when the oscillations are sustained by the time delay. In short, the interplay among the noises, forcing, and time delay gives rise to a rich dynamics: a regular and periodic motion is destroyed or restored owing to the competition between the noise and the driving force depending on time delay values, whereas an erratic motion insensitive to the driving force emerges when the time delay makes the motion aperiodic. Interestingly, we also show that, for a sufficient noise strength and forcing amplitude, an approximately periodic interwell motion is promoted by means of stochastic resonance.

The surface-directed spinodal decomposition of a binary liquid confined inside a cylindrical pore is investigated using molecular dynamics simulations. One component of the liquid wets the pore surface while the other remains neutral. A variety of wetting conditions are studied. For the partial wetting case, after an initial period of phase separation, the domains organize themselves into pluglike structures and the system enters into a metastable state. Therefore, a complete phase separation is never achieved. Analysis of domain growth and the structure factor suggests a one-dimensional growth dynamics for the partial wetting case. As the wetting interaction is increased beyond a critical value, a transition from the pluglike to tubelike domain formation is observed, which corresponds to the full wetting morphology. Thus, a complete phase separation is achieved as the wetting species moves towards the pore surface and forms layers enclosing the nonwetting species residing around the axis of the cylinder. The coarsening dynamics of both the species are studied separately. The wetting species is found to follow a two-dimensional domain growth dynamics with a growth exponent $1/2$ in the viscous hydrodynamic regime. This was substantiated by the Porod tail of the structure factor. On the other hand, the domain grows linearly with time for the nonwetting species. This suggests that the nonwetting species behaves akin to a three-dimensional bulk system. An appropriate reasoning is presented to justify the given observations.

Understanding the transport properties of microorganisms and self-propelled particles in porous media has important implications for human health as well as microbial ecology. In free space, most microswimmers perform diffusive random walks as a result of the interplay of self-propulsion and orientation decorrelation mechanisms such as run-and-tumble dynamics or rotational diffusion. In an unstructured porous medium, collisions with the microstructure result in a decrease in the effective spatial diffusivity of the particles from its free-space value. Here, we analyze this problem for a simple model system consisting of noninteracting point particles performing run-and-tumble dynamics through a two-dimensional disordered medium composed of a random distribution of circular obstacles, in the absence of Brownian diffusion or hydrodynamic interactions. The particles are assumed to collide with the obstacles as hard spheres and subsequently slide on the obstacle surface with no frictional resistance while maintaining their orientation, until they either escape or tumble. We show that the variations in the long-time diffusivity can be described by a universal dimensionless hindrance function $f(\varphi ,\mathrm{Pe})$ of the obstacle area fraction $\varphi$ and Péclet number $\mathrm{Pe}$, or ratio of the swimmer run length to the obstacle size. We analytically derive an asymptotic expression for the hindrance function valid for dilute media ($\mathrm{Pe}\varphi \ll 1$), and its extension to denser media is obtained using stochastic simulations. As we explain, the model is also easily generalized to describe dispersion in three dimensions.

The triggering of avalanches is investigated using discrete element simulations for a process of random extraction of spheres. A monolayer, formed by identical spheres in a hexagonal configuration, is placed on a tilted plane surrounded by a small fence that sustains the spheres, mimicking the disposal of fruits in the market. Then, a random continuous extraction process of spheres is imposed until the collapse. For this simple numerical experiment, a phase diagram was obtained to visualize the occurrence of avalanches triggered by vacancies as a function of the tilting angle, system size, and friction coefficient. More importantly, a subzone was found where we can predict the critical number of extractions until the avalanche takes place. The prediction is made from an evolution model of the average coordination number based on statistical considerations. The theoretical prediction also gives a constant critical void fraction of spheres, which implies the system collapses at a critical packing fraction.

Active fluids such as bacterial swarms, self-propelled colloids, and cell tissues can all display complex spatiotemporal vortices that are reminiscent of inertial turbulence. This emergent behavior, despite the overdamped nature of these systems, is the hallmark of active turbulence. In this Letter, using a generalized hydrodynamic model, we present a study of the persistence problem in active turbulence. We report that the persistence time of passive tracers inside the coherent vortices follows a Weibull probability density whose shape and scale are decided by the strength of activity—contrary to inertial turbulence that displays power-law statistics in this region. In the turbulent background, the persistence time is exponentially distributed that is remindful of inertial turbulence. Finally we show that the driver of persistence inside the coherent vortices is the temporal decorrelation of the topological field, whereas it is the vortex turnover time in the turbulent background.

In equilibrium, the Mermin-Wagner theorem prohibits the continuous symmetry breaking for all dimensions $d\le 2$. In this work, we discuss that this limitation can be circumvented in nonequilibrium systems driven by the spatiotemporally long-range anticorrelated noise. We first compute the lower and upper critical dimensions of the $\mathrm{O}\left(n\right)$ model driven by the spatiotemporally correlated noise by means of the dimensional analysis. Next we consider the spherical model, which corresponds to the large-$n$ limit of the $\mathrm{O}\left(n\right)$ model and allows us to compute the critical dimensions and critical exponents, analytically. Both results suggest that the critical dimensions increase when the noise is positively correlated in space and time and decrease when anticorrelated. We also report that the spherical model with the correlated noise shows the hyperuniformity and giant number fluctuation even well above the critical point.

Recent studies have revealed the significant influence of finite resistivity on high-energy-density plasmas, contrary to the previous findings of Jukes [J. Fluid Mech. 16, 177 (1963)]. This paper reexamines Jukes' theory in the context of magneto-Rayleigh-Taylor instability in magnetohydrodynamics with finite resistivity represented by $\eta$. The inadequacy of Jukes' approach due to an erroneous boundary condition is demonstrated, and it is shown that although the theory provides some physical insights, it fails to capture crucial features. The dispersion relation proposed in this study highlights that larger growth rates tend to diffuse the magnetic field rapidly, negating its suppressive effect. Moreover, the Atwood number has a significant influence on the growth-rate curves' shape, which differs from those of viscous or elastic flows and ideal magnetohydrodynamics. Additionally, long wavelengths grow proportionally to ${\eta }^{1/3}$, while $\alpha$ indicating growth rates behaves classically when the magnetic field is entirely diffused.

We present a scalable machine learning (ML) framework for predicting intensive properties and particularly classifying phases of Ising models. Scalability and transferability are central to the unprecedented computational efficiency of ML methods. In general, linear-scaling computation can be achieved through the divide-and-conquer approach, and the locality of physical properties is key to partitioning the system into subdomains that can be solved separately. Based on the locality assumption, ML model is developed for the prediction of intensive properties of a finite-size block. Predictions of large-scale systems can then be obtained by averaging results of the ML model from randomly sampled blocks of the system. We show that the applicability of this approach depends on whether the block-size of the ML model is greater than the characteristic length scale of the system. In particular, in the case of phase identification across a critical point, the accuracy of the ML prediction is limited by the diverging correlation length. We obtain an intriguing scaling relation between the prediction accuracy and the ratio of ML block size over the spin-spin correlation length. Implications for practical applications are also discussed. While the two-dimensional Ising model is used to demonstrate the proposed approach, the ML framework can be generalized to other many-body or condensed-matter systems.

In some nonequilibrium systems, the distribution of entropy production $p\left(\mathrm{\Sigma }\right)$ satisfies the detailed fluctuation theorem (DFT) $p\left(\mathrm{\Sigma }\right)/p(-\mathrm{\Sigma })=exp\left(\mathrm{\Sigma }\right)$. When the distribution $p\left(\mathrm{\Sigma }\right)$ shows a time dependence, the celebrated Cramér-Rao (CR) bound asserts that the mean entropy production rate is upper bounded in terms of the variance of $\mathrm{\Sigma }$ and the Fisher information with respect to time. In this paper we employ the DFT to derive an upper bound for the mean entropy production rate that improves the CR bound. We show that this new bound serves as an accurate approximation for the entropy production rate in the heat exchange problem mediated by a weakly coupled bosonic mode. The bound is saturated for the same setup when mediated by a weakly coupled qubit.

Integral equation theories (IETs) based on the Ornstein-Zernike (OZ) relation can be used as an analytical tool to predict structural and thermodynamic properties and phase behavior of fluids with low numerical cost. However, there are no studies of the IETs for the dipolar density interaction potential in two-dimensional systems, a relevant interdomain interaction in lipid monolayers with phase coexistence. This repulsive interaction arises due to the excess dipole density of the domains, which are aligned perpendicular to the interface. This work studies the performance of three closures of the OZ equation for this novel system: Rogers-Young (RY), modified hypernetted chain (MHNC), and variational modified hypernetted chain (VMHNC). For the last two closures the bridge function of a reference system is required, with the hard disk being the most convenient reference system. Given that in two dimensions there is no analytical expressions for the hard disk correlation functions, two different approximations are proposed: one based on the Percus-Yevick (PY) approximation, and the other based on an extension of the hard spheres Verlet-Weis-Henderson-Grundke (LB) parametrization. The accuracy of the five approaches is evaluated by comparison of the pair correlation function and the structure factor with Monte Carlo simulation data. The results show that RY closure is satisfactory only for low-structured regimes. MHNC and VMHNC closures perform globally well, and there are no significant differences between them. However, the reference system in some cases affects their performance; when the pair correlation function serves as the measure, the LB-based closures quantitatively outperform the PY ones. From the point of view of its applicability, LB-based closures do not have a solution for all studied interaction strength parameters, and, in general, PY-based closures are numerically preferable.

We study stochastic motion under a nonlinear frictional force that levels off with increasing velocity. Specifically, our frictional force is of the so-called Coulomb-tanh type. At small speed, it increases approximately linearly with velocity, while at large speed, it approaches a constant magnitude, similarly to solid (dry, Coulomb) friction. In one spatial dimension, a formal analogy between the associated Fokker-Planck equation and the Schrödinger equation for a quantum mechanical oscillator in a nonharmonic Pöschl-Teller potential is revealed. Then, the stationary velocity statistics can be treated analytically. From such analytical considerations, we determine associated diffusion coefficients, which we confirm by agent-based simulations. Moreover, from such simulations and from numerically solving the associated Fokker-Planck equation, we find that the spatial distribution function, starting from an initial Gaussian shape, develops tails that appear exponential at intermediate timescales. At small magnitudes of stochastic driving, the velocity distribution resembles the case of linear friction, while at large magnitudes, it rather approaches the case of solid (dry, Coulomb) friction. The same is true for diffusion coefficients. In a certain sense thus interpolating between the two extreme cases of linear friction and solid (dry, Coulomb) friction, our approach should be useful to describe several cases of practical relevance. For instance, a reduced increase in friction with increasing relative speed is typical of shear-thinning behavior. Therefore, driven motion in shear-thinning environments is one specific example to which our description may be applied.

Quantifying irreversibility of a system using finite information constitutes a major challenge in stochastic thermodynamics. We introduce an observable that measures the time-reversal asymmetry between two states after a given time lag. Our central result is a bound on the time-reversal asymmetry in terms of the total cycle affinity driving the system out of equilibrium. This result leads to further thermodynamic bounds on the asymmetry of directed fluxes, on the asymmetry of finite-time cross-correlations, and on the cycle affinity of coarse-grained dynamics.

We obtain the exact ground-state energy of the quasi-one-dimensional restricted $\pm J$ Ising spin glass in a uniform magnetic field using the transfer matrix method. Magnetic field dependence allows us to derive the magnetization as a function of concentration and magnetic field. It turns out that, in the limit of zero field, the magnetization tends to a nonzero value with a singular dependence on the magnetic field. We derive the explicit form of the singularity in thermodynamic quantities such as energy $E\simeq E_0+m_{0}h+E_1{e}^{-h_0/h}$, which is an essential singularity known as Griffiths singularity. We confirm our analytical results using the numerical approach based on iterative equations for energy.