The occurrence of spontaneous bursts of uncontrolled electrical activity between neurons can disrupt normal brain function and lead to epileptic seizures. Despite extensive research, the mechanisms underlying seizure onset remain unclear. This study investigates the onset of seizures from the perspective of nonequilibrium statistical physics. By analyzing the probability flux within the framework of the nonequilibrium potential-flux landscape, we establish a connection between seizure dynamics and nonequilibrium. Our findings demonstrate that the degree of nonequilibrium is sensitive to the onset of epileptic seizures. This result offers an alternative perspective on assessing seizure onset in epilepsy.

The notion of mean temperature is crucial for a number of fields, including climate science, fluid dynamics, and biophysics. However, so far its correct thermodynamic foundation is lacking or even believed to be impossible. A physically correct definition should not be based on mathematical notions of the means (e.g., the mean geometric or mean arithmetic), because they are not unique, and they ignore the fact that temperature is an ordinal level variable. We offer a thermodynamic definition of the mean temperature that is based upon the following two assumptions. First, the correct definition should necessarily involve equilibration processes in the initially nonequilibrium system. Among such processes, reversible equilibration and fully irreversible equilibration are the two extreme cases. Second, within the thermodynamic approach we assume that the mean temperature is determined mostly by energy and entropy. Together with the dimensional analysis, the two assumptions lead to a definition of the mean temperature that is determined up to a weight factor that can be fixed to $1/2$ due to the maximum ignorance principle. The mean temperature for ideal and (van der Waals) nonideal gases with temperature-independent heat capacity is given by a general and compact formula that (besides the initial temperatures) only depends on the heat capacities and concentration of gases. Our method works for any nonequilibrium initial state, not only two-temperature states.

Recently, measurement-based quantum thermal machines have drawn more attention in the field of quantum thermodynamics. However, the previous results on quantum Otto heat engines were either limited to special unital and nonunital channels in the bath stages, or a specific driving protocol at the work strokes and assuming the cycle being time-reversal symmetric, i.e., $V^{†}=U$ (or $V=U)$. In this paper, we consider a single spin-1/2 quantum Otto heat engine, by first replacing one of the heat baths by an arbitrary unital channel, and then we give the exact analytical expression of the characteristic function from which all the cumulants of heat and work emerge. We prove that under the effect of monitoring, ${\nu }_2>{\nu }_1$ is a necessary condition for positive work, either for a symmetric or asymmetric-driven Otto cycle. Furthermore, going beyond the average we show that the ratio of the fluctuations of work and heat is lower and upper-bounded when the system is working as a heat engine. However, differently from the previous results in the literature, we consider the third and fourth cumulants as well. It is shown that the ratio of the third (fourth) cumulants of work and heat is not upper-bounded by unity nor lower-bounded by the third (fourth) power of the efficiency, as is the case for the ratio of fluctuations. Finally, we consider applying a specific unital map that plays the role of a heat bath in a coherently superposed manner, and we show the role of the initial coherence of the control qubit on efficiency, on the average work and its relative fluctuations.

The emergence of collective oscillations and synchronization is a widespread phenomenon in complex systems. While widely studied in the setting of dynamical systems, this phenomenon is not well understood in the context of out-of-equilibrium phase transitions in many-body systems. Here we consider three classical lattice models, namely the Ising, the Blume-Capel, and the Potts models, provided with a feedback among the order and control parameters. With the help of the linear response theory we derive low-dimensional nonlinear dynamical systems for mean-field cases. These dynamical systems quantitatively reproduce many-body stochastic simulations. In general, we find that the usual equilibrium phase transitions are taken over by more complex bifurcations where nonlinear collective self-oscillations emerge, a behavior that we illustrate by the feedback Landau theory. For the case of the Ising model, we obtain that the bifurcation that takes over the critical point is nontrivial in finite dimensions. Namely, we provide numerical evidence that in two dimensions the most probable value of a cycle's amplitude follows the Onsager law for slow feedback. We illustrate multistability for the case of discontinuously emerging oscillations in the Blume-Capel model, whose tricritical point is substituted by the Bautin bifurcation. For the Potts model with $q=3$ colors we highlight the appearance of two mirror stable limit cycles at a bifurcation line and characterize the onset of chaotic oscillations that emerge at low temperature through either the Feigenbaum cascade of period doubling or the Afraimovich-Shilnikov scenario of a torus destruction. We also demonstrate that entropy production singularities as a function of the temperature correspond to qualitative change in the spectrum of Lyapunov exponents. Our results show that mean-field collective behavior can be described by the bifurcation theory of low-dimensional dynamical systems, which paves the way for the definition of universality classes of collective oscillations.

Spiral waves are a type of typical pattern in open reaction-diffusion systems far from thermodynamic equilibrium. The study of spiral waves has attracted great interest because of its nonlinear characteristics and extensive applications. However, the study of spiral waves has been confined to continuous-time systems, while spiral waves in discrete-time systems have been rarely reported. In recent years, discrete-time models have been widely studied in ecology because of their appropriateness to systems with nonoverlapping generations and other factors. Therefore, spiral waves in discrete-time systems need to be studied. Here, we investigated a novel type of spiral wave called a composite spiral wave in a discrete-time predator-pest model, and we revealed the formation mechanism. To explain the observed phenomena, we defined and quantified a move state effect of multiperiod states caused by the coupling of adjacent stable multiperiod orbits, which is strictly consistent with the numerical results. The other move state effect is caused by an unstable focus, which is the state of the local points at the spiral center. The combined effect of these two influences can lead to rich dynamical behaviors of spiral waves, and the specific structure of the composite spiral waves is the result of the competition of the two effects in opposite directions. Our findings shed light on the dynamics of spiral waves in discrete-time systems, and they may guide the prediction and control of pests in deciduous forests.

Using the supersymmetric method of random matrix theory within the Heidelberg approach framework we provide statistical description of stationary intensity sampled in locations inside an open wave-chaotic cavity, assuming that the time-reversal invariance inside the cavity is fully broken. In particular, we show that when incoming waves are fed via a finite number $M$ of open channels the probability density $\mathcal{P}\left(I\right)$ for the single-point intensity $I$ decays as a power law for large intensities: $\mathcal{P}\left(I\right)\sim I^{-(M+2)}$, provided there is no internal losses. This behavior is in marked difference with the Rayleigh law $\mathcal{P}\left(I\right)\sim exp(-I/\overline{I})$, which turns out to be valid only in the limit $M\to \infty$. We also find the joint probability density of intensities $I_1,...,I_L$ in $L>1$ observation points, and then we extract the corresponding statistics for the maximal intensity in the observation pattern. For $L\to \infty$ the resulting limiting extreme value statistics (EVS) turns out to be different from the classical EVS distributions.

We investigate the dynamical evolution of Stuart-Landau oscillators globally coupled through conjugate or dissimilar variables on simplicial complexes. We report a first-order explosive phase transition from an oscillatory state to oscillation death, with higher-order (2-simplex triadic) interactions, as opposed to the second-order transition with only pairwise (1-simplex) interactions. Moreover, the system displays four distinct homogeneous steady states in the presence of triadic interactions, in contrast to the two homogeneous steady states observed with dyadic interactions. We calculate the backward transition point analytically, confirming the numerical results and providing the origin of the dynamical states in the transition region. The results are robust against the application of noise. The study will be useful in understanding complex systems, such as ecological and epidemiological, having higher-order interactions and coupling through conjugate variables.

A meaningful topic that needs to be explored in the field of nonlinear waves is whether a neural network can reveal the phase transition of different types of waves and novel dynamical properties. In this paper, a physics-informed neural network (PINN) with parameters is used to explore the phase transition and time-varying dynamics of nonlinear waves of the $(2+1)$-dimensional Boussinesq equation describing the propagation of gravity waves on the surface of water. We embed the physical parameters into the neural network for this purpose. Via such algorithm, we find the exact boundary of the phase transition that distinguishes the periodic lump chain and transformed wave, and the inexact boundaries of the phase transition for various transformed waves are detected through PINNs with phase domain decomposition. In particular, based only on the simple soliton solution, we discover types of nonlinear waves as well as their interesting time-varying properties for the $(2+1)$-dimensional Boussinesq equation. We further investigate the stability by adding noise to the initial data. Finally, we perform the parameters discovery of the equation in the case of data with and without noise, respectively. Our paper introduces deep learning into the study of the phase transition of nonlinear waves and paves the way for intelligent explorations of the unknown properties of waves by means of the PINN technique with a simple solution and small data set.

We revisit force evaluation methodologies on rigid solid particles suspended in a viscous fluid that is simulated via the lattice Boltzmann method (LBM). We point out the noncommutativity of streaming and collision operators in the force evaluation procedure due to the presence of a solid boundary, and provide a theoretical explanation for this observation. Based on this analysis, we propose a discrete force calculation scheme with enhanced accuracy. The proposed scheme is essentially a discrete version of the Reynolds transport theorem (RTT) in the context of a lattice Boltzmann formulation. Besides maintaining satisfactory levels of reliability and accuracy, the method also handles force evaluation on complex geometries in a simple and transparent way. We run benchmark simulations for flow past cylinder and NACA0012 airfoil (for Reynolds numbers ranging from ${10}^2$ to $0.5\times {10}^6$) and show that the current approach significantly reduces the grid size requirement for accurate force evaluation.

We study a system of equal-size circular disks, each with an asymmetrically placed pivot at a fixed distance from the center. The pivots are fixed at the vertices of a regular triangular lattice. The disks can rotate freely about the pivots, with the constraint that no disks can overlap with each other. Our Monte Carlo simulations show that the one-point probability distribution of orientations has multiple cusplike singularities. We determine the exact positions and qualitative behavior of these singularities. In addition to these geometrical singularities, we also find that the system shows order-disorder transitions, with a disordered phase at large lattice spacings, a phase with spontaneously broken orientational lattice symmetry at small lattice spacings, and an intervening Berezinskii-Kosterlitz-Thouless phase in between.

Urban transport systems are gaining in importance, as an increasing share of the global population lives in cities and mobility-based carbon emissions must be reduced to mitigate climate change and improve air quality and citizens' health. As a result, public transport systems are prone to congestion, raising the question of how to optimize them to cope with this challenge. In this paper, we analyze the optimal design of urban transport networks to minimize the average travel time in monocentric as well as in polycentric cities. We suggest an elementary model for congestion and introduce a numerical method to determine the optimal shape among a set of predefined geometries considering different models for the behavior of individual travelers. We map out the optimal shape of fundamental network geometries with a focus on the impact of congestion.

The analysis of systemic risk often revolves around examining various measures utilized by practitioners and policymakers. These measures typically focus on assessing the extent to which external events can impact a financial system, without delving into the nature of the initial shock. In contrast, our approach takes a symmetrical standpoint and introduces a set of measures centered on the quantity of external shock that the system can absorb before experiencing deterioration. To achieve this, we employ a linearized version of DebtRank, which facilitates a clear depiction of the onset of financial distress, thereby enabling accurate estimation of systemic risk. Through the utilization of spectral graph theory, we explicitly compute localized and uniform exogenous shocks, elucidating their behavior. Additionally, we expand the analysis to encompass heterogeneous shocks, necessitating computation via Monte Carlo simulations. We firmly believe that our approach is both comprehensive and intuitive, enabling a standardized assessment of failure risk in financial systems.

Acoustic emission (AE) is a powerful experimental method for studying discrete and impulsive events termed avalanches that occur in a wide variety of materials and physical phenomena. A particular challenge is the detection of small-scale avalanches, whose associated acoustic signals are at the noise level of the experimental setup. The conventional detection approach is based on setting a threshold significantly larger than this level, ignoring “false” events with low AE amplitudes that originate from noise. At the same time, this approach overlooks small-scale events that might be true and impedes the investigation of avalanches occurring at the nanoscale, constituting the natural response of many nanoparticles and nanostructured materials. In this work, we develop a data-driven method that allows the detection of small-scale AE events, which is based on two propositions. The first includes a modification of the experimental conditions by setting a lower threshold compared to the conventional threshold, such that an abundance of small-scale events with low amplitudes are considered. Second, instead of analyzing several conventional scalar features (e.g., amplitude, duration, energy), we consider the entire waveform of each AE event and obtain an informative representation using dynamic mode decomposition. We apply the developed method to AE signals measured during the compression of platinum nanoparticles and demonstrate a significant enhancement of the detection range toward small-scale events that are below the conventional threshold.

Acoustofluidic systems often employ prefabricated acoustic scatterers that perturb the imposed acoustic field to realize the acoustophoresis of immersed microparticles. We present a numerical study to investigate the time-averaged streaming and radiation force fields around a scatterer. Based on the streaming and radiation force field, we obtain the trajectories of the immersed microparticles with varying sizes and identify a critical transition size at which the motion of immersed microparticles in the vicinity of a prefabricated scatterer shifts from being streaming dominated to radiation dominated. We consider a range of acoustic frequencies to reveal that the critical transition size decreases with increasing frequency; this result explains the choice of acoustic frequencies in previously reported experimental studies. We also examine the impact of scatterer material and fluid properties on the streaming and radiation force fields, as well as on the critical transition size. Our results demonstrate that the critical transition size decreases with an increase in acoustic contrast factor: a nondimensional quantity that depends on material properties of the scatterer and the fluid. Our results provide a pathway to realize radiation force based manipulation of small particles by increasing the acoustic contrast factor of the scatterer, lowering the kinematic viscosity of the fluid, and increasing the acoustic frequency.

Possible existence of chaotic oscillations in ion dynamics in the sheath and presheath regions of a dusty plasma, induced by externally driven dust-charge fluctuation, is presented in this work. In a complex plasma, dust charge fluctuation occurs continuously with time due to the variation of electron and ion currents flowing into the dust particles. In most of the works related to dust-charge fluctuation, theoretically it is assumed that the average dust-charge fluctuation follows the plasma perturbation, while in reality, the dust-charge fluctuation is a semirandom phenomenon, fluctuating about some average value. The very cause of dust-charge fluctuation in a dusty plasma also points to the fact that these fluctuations can be driven externally by changing electron and ion currents to the dust particles. With the help of a hybrid-particle in cell-Monte Carlo collision $\left(h\text{−}\mathrm{PIC}\text{−}\mathrm{MCC}\right)$ code in this work, we use the plasma sheath as a candidate for driving the dust-charge fluctuation by periodically exposing the sheath-side wall to UV radiation, causing photoemission of electrons, which in turn drive the dust-charge fluctuation. We show that this driven dust-charge fluctuation can induce a chaotic response in the ion dynamics in the sheath and the presheath regions.

We propose an invasion model where domains grow up to their convex hulls and merge when they overlap. This model can be seen as a continuum and isotropic counterpart of bootstrap percolation models. From numerical investigations of the model starting with randomly deposited overlapping disks on a plane, we find an invasion transition that occurs via macroscopic avalanches. The disk concentration threshold and the width of the transition are found to decrease as the system size is increased. Our results are consistent with a vanishing threshold in the limit of infinitely large system sizes. However, this limit could not be investigated by simulations. For finite initial concentrations of disks, the cluster size distribution presents a power-law tail characterized by an exponent that varies approximately linearly with the initial concentration of disks. These results at finite initial concentration open novel directions for the understanding of the transition in systems of finite size. Furthermore, we find that the domain area distribution has oscillations with discontinuities. In addition, the deviation from circularity of large domains is constant. Finally, we compare our results to experimental observations on de-adhesion of graphene induced by the intercalation of nanoparticles.

We study the one-dimensional Bak-Sneppen model for the evolution of species in an ecosystem. Of particular interest are the temporal fluctuations in fitness variables. We numerically compute the power spectral density and apply the finite-size scaling method to get data collapse. A clear signature of $1/f^{\alpha }$ noise with $\alpha \approx 1.2$ (long-time correlations) emerges for both local and global (or average) fitness noises. The limiting value of the spectral exponent, 0 or 2, corresponds to no interaction or a random neighbor version of the model, respectively. The local power spectra are spatially uncorrelated and also show an additional scaling, $\sim 1/L$, in the frequency regime $L^{-\lambda }\ll f\ll 1/2$, where $L$ is the linear extent of the system.

One major objective of controlling classical chaotic dynamical systems is exploiting the system's extreme sensitivity to initial conditions in order to arrive at a predetermined target state. In a recent Letter [Phys. Rev. Lett. 130, 020201 (2023)], a generalization of this targeting method to quantum systems was demonstrated using successive unitary transformations that counter the natural spreading of a quantum state. In this paper further details are given and an important quite general extension is established. In particular, an alternate approach to constructing the coherent control dynamics is given, which introduces a time-dependent, locally stable control Hamiltonian that continues to use the chaotic heteroclinic orbits previously introduced, but without the need of countering quantum state spreading. Implementing that extension for the quantum kicked rotor generates a much simpler approximate control technique than discussed in the Letter, which is a little less accurate, but far more easily realizable in experiments. The simpler method's error can still be made to vanish as $\hslash \to 0$.

We present an updated version of a general-purpose collective coordinate model that aims to fully map out the dynamics of a single scalar field in $1+1$ dimensions. This is achieved by a procedure that we call a mechanization, in which we reduce the infinite number of degrees of freedom down to a finite and controllable number by chopping the field into flat segments connected via joints. In this paper we introduce two new ingredients to our procedure. The first is a manifestly Bogomol'nyi-Prasad-Sommerfeld (BPS) mechanization in which BPS mechanical kinks saturate the same bound on energy as their field-theoretic progenitors. The second is allowing the joints to switch, leading to an extended concept of the effective Lagrangian, through which we describe direct collisions of mechanical kinks and antikinks.