The difference $\mathrm{\Delta }F$ between free energies has applications in biology, chemistry, and pharmacology. The value of $\mathrm{\Delta }F$ can be estimated from experiments or simulations, via fluctuation theorems developed in statistical mechanics. Calculating the error in a $\mathrm{\Delta }F$ estimate is difficult. Worse, atypical trials dominate estimates. How many trials one should perform was estimated roughly by Jarzynski [Phys. Rev. E 73, 046105 (2006)]. We enhance the approximation with the following information-theoretic strategies. We quantify “dominance” with a tolerance parameter chosen by the experimenter or simulator. We bound the number of trials one should expect to perform, using the order-$\infty$ Rényi entropy. The bound can be estimated if one implements the “good practice” of bidirectionality, known to improve estimates of $\mathrm{\Delta }F$. Estimating $\mathrm{\Delta }F$ from this number of trials leads to an error that we bound approximately. Numerical experiments on a weakly interacting dilute classical gas support our analytical calculations.

For current fluctuations in nonequilibrium steady states of Markovian processes, we derive four different universal bounds valid beyond the Gaussian regime. Different variants of these bounds apply to either the entropy change or any individual current, e.g., the rate of substrate consumption in a chemical reaction or the electron current in an electronic device. The bounds vary with respect to their degree of universality and tightness. A universal parabolic bound on the generating function of an arbitrary current depends solely on the average entropy production. A second, stronger bound requires knowledge both of the thermodynamic forces that drive the system and of the topology of the network of states. These two bounds are conjectures based on extensive numerics. An exponential bound that depends only on the average entropy production and the average number of transitions per time is rigorously proved. This bound has no obvious relation to the parabolic bound but it is typically tighter further away from equilibrium. An asymptotic bound that depends on the specific transition rates and becomes tight for large fluctuations is also derived. This bound allows for the prediction of the asymptotic growth of the generating function. Even though our results are restricted to networks with a finite number of states, we show that the parabolic bound is also valid for three paradigmatic examples of driven diffusive systems for which the generating function can be calculated using the additivity principle. Our bounds provide a general class of constraints for nonequilibrium systems.

We propose the improved ergodicity and mixing estimators to identify nonergodic dynamics from a single particle trajectory. The estimators are based on the time-averaged characteristic function of the increments and can thus capture additional information on the process as compared to the conventional time-averaged mean-square displacement. The estimators are first investigated and validated for several models of anomalous diffusion, such as ergodic fractional Brownian motion and diffusion on percolating clusters, and nonergodic continuous-time random walks and scaled Brownian motion. The estimators are then applied to two sets of earlier published trajectories of mRNA molecules inside live Escherichia coli cells and of Kv2.1 potassium channels in the plasma membrane. These statistical tests did not reveal nonergodic features in the former set, while some trajectories of the latter set could be classified as nonergodic. Time averages along such trajectories are thus not representative and may be strongly misleading. Since the estimators do not rely on ensemble averages, the nonergodic features can be revealed separately for each trajectory, providing a more flexible and reliable analysis of single-particle tracking experiments in microbiology.

We study fluctuation properties of embedded random matrix ensembles of noninteracting particles. For ensemble of two noninteracting particle systems, we find that unlike the spectra of classical random matrices, correlation functions are nonstationary. In the locally stationary region of spectra, we study the number variance and the spacing distributions. The spacing distributions follow the Poisson statistics, which is a key behavior of uncorrelated spectra. The number variance varies linearly as in the Poisson case for short correlation lengths but a kind of regularization occurs for large correlation lengths, and the number variance approaches saturation values. These results are known in the study of integrable systems but are being demonstrated for the first time in random matrix theory. We conjecture that the interacting particle cases, which exhibit the characteristics of classical random matrices for short correlation lengths, will also show saturation effects for large correlation lengths.

Following a previous paper [Phys. Rev. E 88, 052907 (2013)], we study in detail the mechanism of aging transition in globally and diffusively coupled excitable and oscillatory units. Here two of the three models taken up in the earlier work are used, each composed of a large number of units with their bifurcation parameters forming a uniform distribution. The control parameters are the coupling strength and the average of the bifurcation parameters. The present work is mostly devoted to a region of the phase diagram near the aging transition boundary with the coupling strength greater than its critical value for the onset of bistability and hysteresis. The bifurcation structure of each system at the aging transition boundary is investigated theoretically as well as numerically. Moreover, we show that critical scaling laws of order parameters $S$ and $M$ used in the previous paper are different depending on which region of the coupling strength to be chosen.

In this paper, we propose a complex short-pulse equation of both focusing and defocusing types, which governs the propagation of ultrashort pulses in nonlinear optical fibers. It can be viewed as an analog of the nonlinear Schrödinger (NLS) equation in the ultrashort-pulse regime. Furthermore, we construct the multi-dark-soliton solution for the defocusing complex short-pulse equation through the Darboux transformation and reciprocal (hodograph) transformation. One- and two-dark-soliton solutions are given explicitly, whose properties and dynamics are analyzed and illustrated.

Based on a recent exact differential equation, the time dependence of the SIS prevalence, the average fraction of infected nodes, in any graph is first studied and then upper and lower bounded by an explicit analytic function of time. That new approximate “tanh formula” obeys a Riccati differential equation and bears resemblance to the classical expression in epidemiology of Kermack and McKendrick [Proc. R. Soc. London A 115, 700 (1927)] but enhanced with graph specific properties, such as the algebraic connectivity, the second smallest eigenvalue of the Laplacian of the graph. We further revisit the challenge of finding tight upper bounds for the SIS (and SIR) epidemic threshold for all graphs. We propose two new upper bounds and show the importance of the variance of the number of infected nodes. Finally, a formula for the epidemic threshold in the cycle (or ring graph) is presented.

As a simplified model of a liquid nanostripe adsorbed on a chemically structured substrate surface, a two-dimensional Ising system with two boundaries at which surface fields act is studied. At the upper boundary, the surface field is uniformly negative, while at the lower boundary (a distance $L$ apart), the surface field is negative only outside a range of extension $b$, where a positive surface stabilizes a droplet of the phase with positive magnetization for temperatures $T$ exceeding the critical temperature $T_w$ of the wetting transition of this model. We investigate the local order parameter profiles across the droplet, both in the directions parallel and perpendicular to the substrate, varying both $b$ and $T$. Also, precursor effects to droplet formation as $T$ approaches $T_w$ from below are studied. In accord with theoretical predictions, for $T>T_w$ the droplet is found to have the shape of a semiellipse, where the width (distance of the interface from the substrate) scale is proportional to $b$ ($b^{1/2}$). So, the area of the droplet is proportional to $b^{3/2}$, and the temperature dependence of the corresponding prefactor, which also involves the interfacial stiffness, is studied.

We report on the kinetic Boltzmann approach adapted for simulations of highly ionized matter created from a solid by its x-ray irradiation. X rays can excite inner-shell electrons, which leads to the creation of deeply lying core holes. Their relaxation, especially in heavier elements, can take complicated paths, leading to a large number of active configurations. Their number can be so large that solving the set of respective evolution equations becomes computationally inefficient and another modeling approach should be used instead. To circumvent this complexity, the commonly used continuum models employ a superconfiguration scheme. Here, we propose an alternative approach which still uses “true” atomic configurations but limits their number by restricting the sample relaxation to the predominant relaxation paths. We test its reliability, performing respective calculations for a bulk material consisting of light atoms and comparing the results with a full calculation including all relaxation paths. Prospective application for heavy elements is discussed.

Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of $\alpha$-uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechanical analyses reveal for $\alpha =2$ that the LP optimal solution is typically equal to that given by the IP below the critical average degree $c=e$ in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result $c=1$ and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with $\alpha \ge 3$, minimum vertex covers on $\alpha$-uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree $c=e/(\alpha -1)$ where the replica symmetry is broken.

The Brownian force model is a mean-field model for local velocities during avalanches in elastic interfaces of internal space dimension $d$, driven in a random medium. It is exactly solvable via a nonlinear differential equation. We study avalanches following a kick, i.e., a step in the driving force. We first recall the calculation of the distributions of the global size (total swept area) and of the local jump size for an arbitrary kick amplitude. We extend this calculation to the joint density of local and global sizes within a single avalanche in the limit of an infinitesimal kick. When the interface is driven by a single point, we find new exponents ${\tau }_0=5/3$ and $\tau =7/4$, depending on whether the force or the displacement is imposed. We show that the extension of a “single avalanche” along one internal direction (i.e., the total length in $d=1$) is finite, and we calculate its distribution following either a local or a global kick. In all cases, it exhibits a divergence $P\left(\ell \right)\sim {\ell }^{-3}$ at small $\ell$. Most of our results are tested in a numerical simulation in dimension $d=1$.

We study scattering of waves by impurities in strongly precompressed granular chains. We explore the linear scattering of plane waves and identify a closed-form expression for the reflection and transmission coefficients for the scattering of the waves from both a single impurity and a double impurity. For single-impurity chains, we show that, within the transmission band of the host granular chain, high-frequency waves are strongly attenuated (such that the transmission coefficient vanishes as the wavenumber $k\to \pm \pi$), whereas low-frequency waves are well-transmitted through the impurity. For double-impurity chains, we identify a resonance—enabling full transmission at a particular frequency—in a manner that is analogous to the Ramsauer–Townsend (RT) resonance from quantum physics. We also demonstrate that one can tune the frequency of the RT resonance to any value in the pass band of the host chain. We corroborate our theoretical predictions both numerically and experimentally, and we directly observe almost complete transmission for frequencies close to the RT resonance frequency. Finally, we show how this RT resonance can lead to the existence of reflectionless modes in granular chains (including disordered ones) with multiple double impurities.

Understanding human mobility in cyberspace becomes increasingly important in this information era. While human mobility, memory-dependent and subdiffusive, is well understood in Euclidean space, it remains elusive in random heterogeneous networks like the World Wide Web. Here we study the diffusion characteristics of self-attracting walks, in which a walker is more likely to move to the locations visited previously than to unvisited ones, on scale-free networks. Under strong attraction, the number of distinct visited nodes grows linearly in time with larger coefficients in more heterogeneous networks. More interestingly, crossovers to sublinear growths occur in strongly heterogeneous networks. To understand these phenomena, we investigate the characteristic volumes and topology of the cluster of visited nodes and find that the reinforced attraction to hubs results in expediting exploration first but delaying later, as characterized by the scaling exponents that we derive. Our findings and analysis method can be useful for understanding various diffusion processes mediated by human.

The naming game has become an archetype for linguistic evolution and mathematical social behavioral analysis. In the model presented here, there are $N$ individuals and $K$ words. Our contribution is developing a robust method that handles the case when $K=O\left(N\right)$. The initial condition plays a crucial role in the ordering of the system. We find that the system with high Shannon entropy has a higher consensus time and a lower critical fraction of zealots compared to low-entropy states. We also show that the critical number of committed agents decreases with the number of opinions and grows with the community size for each word. These results complement earlier conclusions that diversity of opinion is essential for evolution; without it, the system stagnates in the status quo [S. A. Marvel et al., Phys. Rev. Lett. 109, 118702 (2012)]. In contrast, our results suggest that committed minorities can more easily conquer highly diverse systems, showing them to be inherently unstable.

Brain cognitive functions arise through the coordinated activity of several brain regions, which actually form complex dynamical systems operating at multiple frequencies. These systems often consist of interacting subsystems, whose characterization is of importance for a complete understanding of the brain interaction processes. To address this issue, we present a technique, namely the bispectral pairwise interacting source analysis (biPISA), for analyzing systems of cross-frequency interacting brain sources when multichannel electroencephalographic (EEG) or magnetoencephalographic (MEG) data are available. Specifically, the biPISA makes it possible to identify one or many subsystems of cross-frequency interacting sources by decomposing the antisymmetric components of the cross-bispectra between EEG or MEG signals, based on the assumption that interactions are pairwise. Thanks to the properties of the antisymmetric components of the cross-bispectra, biPISA is also robust to spurious interactions arising from mixing artifacts, i.e., volume conduction or field spread, which always affect EEG or MEG functional connectivity estimates. This method is an extension of the pairwise interacting source analysis (PISA), which was originally introduced for investigating interactions at the same frequency, to the study of cross-frequency interactions. The effectiveness of this approach is demonstrated in simulations for up to three interacting source pairs and for real MEG recordings of spontaneous brain activity. Simulations show that the performances of biPISA in estimating the phase difference between the interacting sources are affected by the increasing level of noise rather than by the number of the interacting subsystems. The analysis of real MEG data reveals an interaction between two pairs of sources of central mu and beta rhythms, localizing in the proximity of the left and right central sulci.

Inertial particles are often observed to be trapped, temporarily or permanently, by recirculation cells which are ubiquitous in natural or industrial flows. In the limit of small particle inertia, determining the conditions of trapping is a challenging task, as it requires a large number of numerical simulations or experiments to test various particle sizes or densities. Here, we investigate this phenomenon analytically and numerically in the case of heavy particles (e.g., aerosols) at low Reynolds number, to derive a trapping criterion that can be used both in analytical and numerical velocity fields. The resulting criterion allows one to predict the characteristics of trapped particles as soon as single-phase simulations of the flow are performed. Our analysis is valid for two-dimensional particle-laden flows in the vertical plane, in the limit where the particle inertia, the free-fall terminal velocity, and the flow unsteadiness can be treated as perturbations. The weak unsteadiness of the flow generally induces a chaotic tangle near heteroclinic or homoclinic cycles if any, leading to the apparent diffusion of fluid elements through the boundary of the cell. The critical particle Stokes number ${\text{St}}_c$ below which aerosols also enter and exit the cell in a complex manner has been derived analytically, in terms of the flow characteristics. It involves the nondimensional curvature-weighted integral of the squared velocity of the steady fluid flow along the dividing streamline of the recirculation cell. When the flow is unsteady and $\text{St}>{\text{St}}_c$, a regular motion takes place due to gravity and centrifugal effects, like in the steady case. Particles driven towards the interior of the cell are trapped permanently. In contrast, when the flow is unsteady and $\text{St}<{\text{St}}_c$, particles wander in a chaotic manner in the vicinity of the border of the cell, and can escape the cell.

The effect of a transient magnetic field on right-hand circularly polarized (RHCP) laser light propagation in overcritical-density plasma is investigated. When the electron gyrofrequency is larger than the wave frequency, RHCP light can propagate along the external magnetic field in an overcritical density plasma without resonance or cutoff. However, when the magnetic field falls to below the cyclotron resonance point, the propagating laser pulse will be truncated and the local plasma electrons resonantly heated. Particle-in-cell simulation shows that when applied to a thin slab, the process can produce intense two-cycle light pulses as well as long-lasting self-magnetic fields.

In order to mimic the Brownian particle in liquid, molecular dynamics calculations of dilute solutions of spherical fullerene molecules with various sizes in liquid Ar were performed. To establish the scaling equation for self-diffusion coefficient, $D$, of the fullerenes, the dependence of $D$ was examined on the mass ratio of solute to solvent and on the energy-parameter ratio used in the Lennard-Jones potentials. The dependence on the energy-parameter ratio remains up to ${\mathrm{C}}_{540}$, whereas $D$ rapidly becomes independent of the mass ratio with increasing mass of the solute. The product of the scaling equations obtained for the $D$ of the solute and for shear viscosity, ${\eta }_{\mathrm{sv}}$, for the solvent gives a relation which replaces the Stokes-Einstein relation based on the hydrodynamics. The present expression does not need both the boundary conditions and the hydrodynamic particle size, but instead the energy-parameter ratio, packing fraction of solvent, and bare size of solute. From the viewpoint of the tackiness at the boundary, the cage correlation function around the diffusing particle was examined; it was found that the decay time of the function depends mainly on the the energy-parameter ratio. Therefore, the energy-parameter ratio accounts for the main part of both the boundary conditions and the hydrodynamic particle size in the Stokes equation, which have so far been ill-defined in any molecular theories.

The paradigm of extracting work from an isolated quantum system through a cyclic Hamiltonian process is a topic of immense research interest. The optimal work extracted under such a process is termed ergotropy [Europhys. Lett. 67, 565 (2004)]. Here, in a multiparty scenario, we consider only a class of such cyclic processes that can be implemented locally, giving rise to the concept of local ergotropy. Eventually, the presence of quantum correlations results in a nonvanishing thermodynamic quantity called an ergotropic gap, measured by the difference between global and local ergotropy. However, the converse does not hold in general, i.e., its nonzero value does not necessarily imply the presence of quantum correlations. For arbitrary multiparty states, we quantify this gap. We also evaluate the difference between maximum global and local extractable work for arbitrary states when the system is no longer isolated but put in contact with a bath of the same local temperature.

Thermal transport through liquid-solid interfaces plays an important role in many chemical and biological processes, and better understanding of liquid-solid energy transfer is expected to enable improving the efficiency of thermally driven applications. We determine the spectral distribution of thermal current at liquid-solid interfaces from nonequilibrium molecular dynamics, delivering a detailed picture of the contributions of different vibrational modes to liquid-solid energy transfer. Our results show that surface modes located at the Brillouin zone edge and polarized along the liquid-solid surface normal play a crucial role in liquid-solid energy transfer. Strong liquid-solid adhesion allows also for the coupling of in-plane polarized modes in the solid with the liquid, enhancing the heat-transfer rate and enabling efficient energy transfer up to the cutoff frequency of the solid. Our results provide fundamental understanding of the energy-transfer mechanisms in liquid-solid systems and enable detailed investigations of energy transfer between, e.g., water and organic molecules.