How the human brain processes information during different cognitive tasks is one of the greatest questions in contemporary neuroscience. Understanding the statistical properties of brain signals during specific activities is one promising way to address this question. Here we analyze freely available data from implanted electrocorticography (ECoG) in five human subjects during two different cognitive tasks in the light of information theory quantifiers ideas. We employ a symbolic information approach to determine the probability distribution function associated with the time series from different cortical areas. Then we utilize these probabilities to calculate the associated Shannon entropy and a statistical complexity measure based on the disequilibrium between the actual time series and one with a uniform probability distribution function. We show that an Euclidian distance in the complexity-entropy plane and an asymmetry index for complexity are useful for comparing the two conditions. We show that our method can distinguish visual search epochs from blank screen intervals in different electrodes and patients. By using a multiscale approach and embedding time delays to downsample the data, we find important timescales in which the relevant information is being processed. We also determine cortical regions and time intervals along the 2-s-long trials that present more pronounced differences between the two cognitive tasks. Finally, we show that the method is useful to distinguish cognitive processes using brain activity on a trial-by-trial basis.

We introduce a model for sputter cone formation that includes only the angular dependence of the sputter yield and a fourth-order smoothing effect like surface diffusion. In one dimension, a sputter cone is a particular kind of shock wave that is known as an undercompressive shock. Simulations of our model show that a wide variety of initial conditions lead to the formation of sputter cones and that the opening angle of the cones does not depend on the detailed form of the initial condition. In two dimensions, a sputter cone is a higher-dimensional analog of an undercompressive shock. For two particularly simple choices of parameters, a sputter cone is a four-sided pyramid with rounded edges that is produced by the superposition of two orthogonal, one-dimensional undercompressive shocks.

Spiking neural networks play an important role in brainlike neuromorphic computations and in studying working mechanisms of neural circuits. One drawback of training a large-scale spiking neural network is that updating all weights is quite expensive. Furthermore, after training, all information related to the computational task is hidden into the weight matrix, prohibiting us from a transparent understanding of circuit mechanisms. Therefore, in this work, we address these challenges by proposing a spiking mode-based training protocol, where the recurrent weight matrix is explained as a Hopfield-like multiplication of three matrices: input modes, output modes, and a score matrix. The first advantage is that the weight is interpreted by input and output modes and their associated scores characterizing the importance of each decomposition term. The number of modes is thus adjustable, allowing more degrees of freedom for modeling the experimental data. This significantly reduces the training cost because of significantly reduced space complexity for learning. Training spiking networks is thus carried out in the mode-score space. The second advantage is that one can project the high-dimensional neural activity (filtered spike train) in the state space onto the mode space which is typically of a low dimension, e.g., a few modes are sufficient to capture the shape of the underlying neural manifolds. We successfully apply our framework in two computational tasks—digit classification and selective sensory integration tasks. Our method thus accelerates the training of spiking neural networks by a Hopfield-like decomposition, and moreover this training leads to low-dimensional attractor structures of high-dimensional neural dynamics.

We employ a lattice Boltzmann method to compute the acoustic radiation force produced by standing waves on a compressible object for the density matched case. Instead of simulating the fluid mechanics equations directly, the proposed method uses a lattice Boltzmann model that reproduces the wave equation, together with a kernel interpolation scheme, to compute the first-order perturbations of the pressure and velocity fields on the object's surface and, from them, the acoustic radiation force. The procedure reproduces with excellent accuracy the theoretical expressions by Gor'kov and Wei for the sphere as the 3D case and an infinitely long cylinder as the 2D case, respectively, even with a modest number of lattice Boltzmann cells. The proposed method shows to be a promising tool for simulating phenomena where the acoustic radiation force plays a relevant role, like acoustic tweezers or the acoustic manipulation of microswimmers, with applications in medicine and engineering.

We study charge fluctuations in single-file dynamics with general charge measures. The exact finite-time distribution of charge fluctuations is obtained in terms of a dressing transformation acting on the finite-time distribution of particle fluctuations. The transformation is mapped to a simple substitution rule for corresponding full-counting statistics. By taking the asymptotics of the dressing transformation, we analyze typical and large scale charge fluctuations. Typical charge fluctuations in equilibrium states with vanishing mean charge are anomalous, while large charge fluctuations undergo first and second order dynamical phase transitions out of equilibrium.

We study the Oslo model, a paradigm for absorbing-phase transition, on a one-dimensional ring of $L$ sites with a fixed global density $\overline{\rho }$; we consider the system strictly above critical density ${\rho }_c$. Notably, microscopic dynamics conserve both mass and center of mass (CoM), but lack time-reversal symmetry. We show that, despite having highly constrained dynamics due to CoM conservation, the system exhibits diffusive relaxation away from criticality and superdiffusive relaxation near criticality. Furthermore, the CoM conservation severely restricts particle movement, causing the mobility—a transport coefficient analogous to the conductivity for charged particles—to vanish exactly. Indeed, the steady-state temporal growth of current fluctuation is qualitatively different from that observed in diffusive systems with a single conservation law. Remarkably, far from criticality where the relative density $\mathrm{\Delta }=\overline{\rho }-{\rho }_c\gg {\rho }_c$, the second cumulant, or the variance, ${\langle {\mathcal{Q}}_i^2(T,\mathrm{\Delta })\rangle }_c$, of current ${\mathcal{Q}}_i$ across the $i\mathrm{th}$ bond up to time $T$ in the steady-state saturates as ${\langle {\mathcal{Q}}_i^2\rangle }_c\simeq {\mathrm{\Sigma }}_Q^2\left(\mathrm{\Delta }\right)-\mathrm{const}{T}^{-1/2}$; near criticality, it grows subdiffusively as ${\langle {\mathcal{Q}}_i^2\rangle }_c\sim T^{\alpha }$, with $0<\alpha <1/2$, and eventually saturates to ${\mathrm{\Sigma }}_Q^2\left(\mathrm{\Delta }\right)$. Interestingly, the asymptotic current fluctuation ${\mathrm{\Sigma }}_Q^2\left(\mathrm{\Delta }\right)$ is a nonmonotonic function of $\mathrm{\Delta }$: It diverges as ${\mathrm{\Sigma }}_Q^2\left(\mathrm{\Delta }\right)\sim {\mathrm{\Delta }}^2$ for $\mathrm{\Delta }\gg {\rho }_c$ and ${\mathrm{\Sigma }}_Q^2\left(\mathrm{\Delta }\right)\sim {\mathrm{\Delta }}^{-\delta }$, with $\delta >0$, for $\mathrm{\Delta }\to 0^{+}$. Using a mass-conservation principle, we exactly determine the exponents $\delta =2(1-1/{\nu }_{\perp })/{\nu }_{\perp }$ and $\alpha =\delta /z{\nu }_{\perp }$ via the correlation-length and dynamic exponents, ${\nu }_{\perp }$ and $z$, respectively. Finally, we show that in the steady state the self-diffusion coefficient ${\mathcal{D}}_s\left(\overline{\rho }\right)$ of tagged particles is connected to activity through the relation ${\mathcal{D}}_s\left(\overline{\rho }\right)=a\left(\overline{\rho }\right)/\overline{\rho }$.

Studying the structure of systems in nonequilibrium steady states necessitates tools that quantify population shifts and associated deformations of equilibrium free-energy landscapes under persistent currents. Within the framework of stochastic thermodynamics, we establish a variant of the Kawasaki–Crooks equality that relates nonequilibrium free-energy corrections in overdamped Langevin systems to heat dissipation statistics along time-reversed relaxation trajectories computable with molecular simulation. Using stochastic control theory, we arrive at a general variational approach to evaluate the Kawasaki–Crooks equality and use it to estimate distribution functions of order parameters in specific models of driven and active matter, attaining substantial improvement in accuracy over simple perturbative methods.

We define the heat capacity for steady periodically driven systems and as an example we compute it for dissipative two-level systems where the energy gap is time-modulated. There, as a function of ambient temperature, the Schottky peak remains the dominant feature. Yet, in contrast with equilibrium, the quasistatic thermal response of a nonequilibrium system also reveals kinetic information present in the transition rates; e.g., the heat capacity depends on the time-symmetric reactivities and changes by the presence of a kinetic barrier. It still vanishes though at absolute zero, in accord with an extended Nernst heat postulate, but at a different rate from the equilibrium case. More generally, we discuss the dependence on driving frequency and amplitude.

Closely related to the laws of thermodynamics, the detection and quantification of disequilibria are crucial in unraveling the complexities of nature, particularly those beneath observable layers. Theoretical developments in nonequilibrium thermodynamics employ coarse-graining methods to consider a diversity of partial information scenarios that mimic experimental limitations, allowing the inference of properties such as the entropy production rate. A ubiquitous but rather unexplored scenario involves observing events that can possibly arise from many transitions in the underlying Markov process–which we dub multifilar events–as in the cases of exchanges measured at particle reservoirs, hidden Markov models, mixed chemical and mechanical transformations in biological function, composite systems, and more. We relax one of the main assumptions in a previously developed framework, based on first-passage problems, to assess the non-Markovian statistics of multifilar events. By using the asymmetry of event distributions and their waiting times, we put forward model-free tools to detect nonequilibrium behavior and estimate entropy production, while discussing their suitability for different classes of systems and regimes where they provide no new information, evidence of nonequilibrium, a lower bound for entropy production, or even its exact value. The results are illustrated in reference models through analytics and numerics.

This paper focuses on the coefficient of performance (COP) at maximum ${\chi }^R$ figure of merit for a Brownian Carnot-like refrigerator, within the context of the low-dissipation approach. Our proposal is based on the Langevin equation for a Brownian particle bounded to a harmonic potential trap, which can perform Carnot-like cycles at finite time. The theoretical approach is related to the equilibrium ensemble average of ${\langle x^2\rangle }_{\mathrm{eq}}$ which plays the role of a statelike equation, $x$ being the Brownian particle position. This statelike equation comes from the macroscopic version of the corresponding Langevin equation for a Brownian particle. We show that under quasistatic conditions the COP has the same expression as the macroscopic Carnot refrigerator, while for irreversible cycles at finite time and under symmetric dissipation the optimal COP is the counterpart of Curzon-Ahlborn efficiency as also obtained for irreversible macroscopic refrigerators.

Extracting meaningful information from signals has always been a challenge. Due to the influence of environmental noise, collected signals often exhibit nonlinear characteristics, rendering traditional metrics inadequate in capturing the dynamic properties and complex structures of signals. To address this challenge, this study proposes an innovative metric for quantifying signal complexity—dispersion network-transition entropy (DNTE), which integrates the concepts of complex networks and information entropy. Specifically, we assign single cumulative distribution function values to network nodes and utilize Markov chains to represent links, transforming nonlinear signals into weighted directed complex networks. Subsequently, we assess the importance of network nodes and links, and employ the mathematical expression of information entropy to calculate the DNTE value, quantifying the complexity of the original signal. Next, through extensive experiments on simulated chaotic models and real underwater acoustic signals, we confirm the outstanding performance of DNTE. The results indicate that, compared to Lempel-Ziv complexity, permutation entropy, and dispersion entropy, DNTE not only more accurately reflects changes in signal complexity but also exhibits higher computational efficiency. Importantly, DNTE demonstrates optimal performance in distinguishing different categories of chaotic models, ships, and modulation signals, showcasing its significant potential in extracting effective information from signals.

Decisions are often made by heterogeneous groups of individuals, each with distinct initial biases and access to information of different quality. We show that in groups of independent agents who accumulate evidence the first to decide are those with the strongest initial biases. Their decisions align with their initial bias, regardless of the underlying truth. In contrast, agents who decide last make decisions as if they were initially unbiased and hence make better choices. We obtain asymptotic expressions in the large population limit quantifying how agents' initial inclinations shape early decisions. Our analysis shows how bias, information quality, and decision order interact in nontrivial ways to determine the reliability of decisions in a group.

Recently, it has been shown that purely anti-aligning interaction between active particles may induce a finite wavelength instability. The formed patterns display intricate spatiotemporal dynamics, suggesting the presence of chaos. Here, we propose a quasi-one-dimensional simplification of the particle interaction model. This simplified model allows us to deduce amplitude equations that describe the collective motion of the active entities. We show that these equations exhibit chaotic orbits. Furthermore, via direct numerical simulations of the particle's system, we discuss the pertinence of these amplitude equations approach for describing the particle's self-coordinated motions.

Electrohydrodynamic phenomena in liquid crystals constitute an old but still very active research area. The reason is that these phenomena play the key role in various applications of liquid crystals and due to the general interest of the physical community in out-of-equilibrium systems. Nematic liquid crystals (NLCs) are ideally representative for such investigations. Our article aims to study theoretically the linear NLCs dynamics. We include into consideration orientation elastic energy, hydrodynamic motion, external alternating electric field, electric conductivity, and flexoelectric polarization. We analyze the linear stability of the NLC film, determining dynamics of perturbations with respect to the homogeneous initial state of the NLC. For the purpose we compute eigenvalues of the evolution matrix for a period of the external alternating electric field. These eigenvalues determine the amplification factors for the modes during the period. The instability occurs when the principal eigenvalue of the evolution matrix becomes unity by its absolute value. The condition determines the threshold (critical field) for the instability of the uniform state. It turns out that one might expect various types of the instability, only partially known and investigated in the literature. Particularly, we find that the flexoelectric instability may lead to two-dimensionally space-modulated patterns exhibiting time oscillations. This type of the structures was somehow overlooked in the previous works. We formulate conditions needed for the scenario to be realized. We hope that the results of our work will open the door to a broad range of further studies. Of especial importance would be a comprehensive understanding of the role of various material parameters and nonlinear effects which is a key step for the rational design of NLCs exhibiting the predicted in this publication multidimensional oscillating in time patterns.

A comprehensive dynamic analysis of the dielectric relaxation-time data across a broad temperature range for both isotropic and nematic phases has been conducted on the CBO3O.Py liquid crystal dimer, the shorter chain-length compound within the highly nonsymmetric pyrene-based series of liquid crystal dimers (CBOnO.Py, with $n$ ranging from 3 to 11). It was known from another previous study that in the nematic phase, three different relaxation processes contribute to the complex dielectric permittivity depending on the orientation of the alignment axis with respect to the probing electric field direction. The temperature-derivative analysis of the relaxation-time data using different analytic functions reveals that the critical-like description, through the dynamic scaling model, best portrays the relaxation-time data in the nematic phase as the system approaches the glass transition. A single glass transition temperature is obtained which is consistent with thermal stimulated depolarization currents experimental determinations published elsewhere. From temperature-dependent steepness index m(T), the activation-critical model is also considered as a more general analytic function from which the dynamic scaling model is a terminal approximation. Additionally, the critical-like parametrization provides insight into obtaining a universal description of the temperature-dependent steepness index m(T), for all liquid crystal compounds belonging to symmetry-selected glass formers, such as rodlike liquid crystal monomers.

This work investigates the interaction between gas channels in a vertical Hele-Shaw cell when air is injected simultaneously from two points at a constant flow rate. Unlike single-injection experiments, this dual-point system induces the formation of numerous bubbles, thereby intensifying the interactions between air channels. We use an image analysis technique for tracking motion in the granular bed to define a flow density parameter throughout the cell. The vertical accumulation of this parameter ($n_z$) reveals two specific heights, one marking a finger-to-fracture transition and another indicating the average interaction height of the air channels. Conversely, its horizontal accumulation ($n_x$) assesses the extent of overlap in the fluidized zones created by each airflow. Notably, the analysis indicates that the optimum distribution of the three phases in the system is more closely related to the interaction's variability than its intensity. This finding is significant for industrial applications such as air sparging and catalytic reactors.

We apply statistical analysis to search for processes responsible for turbulence in physical systems. In our previous studies, we have shown that solar wind turbulence in the inertial range of large magnetohydrodynamic scales exhibits Markov properties. We have recently extended this approach on much smaller kinetic scales. Here we are testing for the Markovian character of stochastic processes in a kinetic regime based on magnetic field and velocity fluctuations in the solar wind, measured onboard the Magnetospheric Multiscale (MMS) mission: behind the bow shock, inside the magnetosheath, and near the magnetopause. We have verified that the Chapman-Kolmogorov necessary conditions for Markov processes is satisfied for local transfer of energy between the magnetic and velocity fields also on kinetic scales. We have confirmed that for magnetic fluctuations, the first Kramers-Moyal coefficient is linear, while the second term is quadratic, corresponding to drift and diffusion processes in the resulting Fokker-Planck equation. It means that magnetic self-similar turbulence is described by generalized Ornstein-Uhlenbeck processes. We show that for the magnetic case, the Fokker-Planck equation leads to the probability density functions of the kappa distributions, which exhibit global universal scale invariance with a linear scaling and lack of intermittency. On the contrary, for velocity fluctuations, higher order Kramers-Moyal coefficients should be taken into account and hence scale invariance is not observed. However, the nonextensity parameter in Tsallis entropy provides a robust measure of the departure of the system from equilibrium. The obtained results are important for a better understanding of the physical mechanism governing turbulent systems in space and laboratory.

In geometrically frustrated assemblies local intersubunit misfits propagate to intra-assembly strain gradients, giving rise to anomalous self-limiting assembly thermodynamics. Here we use theory and coarse-grained simulation to study a recently developed class of “curvamer” particles, flexible shell-like particles that exhibit self-limiting assembly due to the build up of curvature deformation in cohesive stacks. To address a generic, yet poorly understood aspect of frustrated assembly, we introduce a model of curvamer assembly that incorporates both intraparticle shape deformation as well as compliance of interparticle cohesive gaps, an effect we can attribute to a finite range of attraction between particles. We show that the ratio of intraparticle (bending elasticity) to interparticle stiffness not only controls the regimes of self-limitation but also the nature of frustration propagation through curvamer stacks. We find a transition from uniformly bound, curvature-focusing stacks at small size to gap opened, uniformly curved stacks at large size is controlled by a dimensionless measure of inter- versus intracurvamer stiffness. The finite range of interparticle attraction determines the range of cohesion in stacks that are self-limiting, a prediction which is in strong agreement with numerical studies of our coarse-grained colloidal model. These predictions provide critical guidance for experimental realizations of frustrated particle systems designed to exhibit self-limitation at especially large multiparticle scales.

We demonstrate the efficient injection of a pulsed positron beam into a magnetic dipole trap and investigate the ensuing particle dynamics in the inhomogeneous electric and magnetic fields. Bunches of $\sim {10}^5{e}^{+}$ were transferred from a buffer-gas trap into the field of a permanent magnet using a lossless $\mathrm{E}\times \mathrm{B}$ drift technique. The $\mathrm{\Delta }t\approx 0.2\mu \mathrm{s}$ pulses were short compared to the toroidal rotation period, ${\tau }_d\approx 16\mu \mathrm{s}$, and $e^{+}$ confinement time, ${\tau }_c\approx 0.6$ s. The redistribution dynamics were studied by measuring the delayed $\gamma$-ray emission as the trap was emptied. This work extends the record for the number of low-energy positrons held in a dipole trap by two orders of magnitude and represents a significant advance toward the confinement of an electron-positron pair plasma.

We consider a $d$-dimensional correlated percolation problem of sites not visited by a random walk on a hypercubic lattice $L^d$ for $d=3$, 4, and 5. The length of the random walk is $\mathcal{N}=u{L}^d$. Close to the critical value $u=u_c$, many geometrical properties of the problem can be described as powers (critical exponents) of $u_c-u$, such as $\beta$, which controls the strength of the spanning cluster, and $\gamma$, which characterizes the behavior of the mean finite cluster size $S$. We show that at $u_c$ the ratio between the mean mass of the largest cluster $M_1$ and the mass of the second largest cluster $M_2$ is independent of $L$ and can be used to find $u_c$. We calculate $\beta$ from the $L$ dependence of $M_1$ and $M_2$, and $\gamma$ from the finite size scaling of $S$. The resulting exponent $\beta$ remains close to 1 in all dimensions. The exponent $\gamma$ decreases from $\approx 3.9$ in $d=3$ to $\approx 1.9$ in $d=4$ and $\approx 1.3$ in $d=5$ towards $\gamma =1$ expected in $d=6$, which is close to $\gamma =4/(d-2)$.