Many natural and engineered systems display oscillations that are characterized by multiple timescales. Typically, such systems are described as slow-fast systems, where the slow dynamics result from a hyperbolic slow manifold that guides the movement of the system's trajectories. Recently, we have provided an alternative description in which the slow timescale results from Lyapunov-unstable transient dynamics of connected dynamical ghosts that form a closed orbit termed ghost cycle. Here, we investigate the response properties of both types of systems to external forcing. Using the classical Van der Pol oscillator and modified versions of this model that correspond to a one-ghost and a two-ghost cycle, respectively, we find significant differences in the responses of slow-fast systems and ghost cycles, including increased entrainment regions of the latter. Nonautonomous model analysis reveals that the differences stem from a continuous remodeling of the attractor landscape of the ghost cycle models, enabled by being organized close to saddle-node on invariant cycle bifurcations, in contrast to a qualitatively unaltered attractor landscape of the slow-fast system. We further demonstrate that the observed features occur in various systems with ghost cycles regardless of the exact mathematical model formulation leading to those ghost cycles, making them likely to apply to many other models with ghost cycles across different disciplines and contexts. We thus propose that systems containing ghost cycles display increased flexibility and responsiveness to continuous environmental changes.

The observation of the Fermi-Pasta-Ulam-Tsingou (FPUT) paradox, namely the lack of equipartition in the evolution of a normal mode in a nonlinear chain on unexpectedly long times, is arguably the most famous numerical experiment in the history of physics. Seventy years after the original publication, most studies in FPUT chains still focus on long wavelength initial states similar to the original paper. It is shown here that all characteristic features of the FPUT paradox are rendered even more striking if modes with short(er) wavelengths are evolved instead. Since not every normal mode leads to equipartition, we also provide a simple technique to predict which modes, and in what perturbation order, are excited starting from an initial mode (root) in $\alpha$-FPUT chains. The excitation sequences associated with a root are then numerically shown to spread energy at different speeds, leading to prethermalization regimes that become longer as a function of mode excitation number. This effect is visible in observables such as mode energies and spectral entropies and, surprisingly, also in the time evolution of invariant quantities such as Lyapunov times and Kolmogorov-Sinai entropies. Our findings generalize the original FPUT experiment, provide an original look at the paradox's source, and enrich the vast literature dedicated to studying equipartition in classical many-body systems.

We consider a kinetic model of opinion dynamics known as the Biswas-Chatterjee-Sen model with a modular interaction structure. The system consists of two groups of agents that feature more frequent interactions within each group and rarer interactions between agents of different groups. We use the mean-field analytical approximation to determine that aside from previously known ordered and disordered states, a new antisymmetric ordered state is stable, where each group has an opposite dominant opinion. The limits of system interaction strength and noise for the stability of such a state are determined, with a discontinuous transition from an antisymmetric to a symmetric state happening if thresholds are exceeded. The results of numerical agent-based simulations confirm our analytical predictions and show that the critical values of noise and interaction strength are predicted with good accuracy.

Cell cultures exhibit rich and complex behaviors driven by dynamic metabolic interactions among cells. In this work, we present a model that captures these interactions through a framework inspired by statistical mechanics. Using Monte Carlo simulations, we explore the equilibrium and dynamical properties of a population of cells arranged in a two-dimensional lattice, where each cell is characterized by fluxes of three reactions: glucose consumption $\left(g\right)$, respiration $\left(r\right)$, and waste production/absorption $\left(w\right)$. The system minimizes an energy function influenced by competitive $(J_g>0)$ and cooperative $(J_w<0)$ couplings between cells. Our results reveal three distinct phases: a competitive phase dominated by glucose competition, a cooperative phase marked by ordered waste exchange, and a disordered phase with local-scale cooperation. By incorporating evolutionary dynamics, we demonstrate how initially noninteracting cells can develop effective metabolic interactions, leading to heterogeneous cultures sustained by cross feeding. These findings are further supported by analytical solutions derived using mean-field approximations. The model provides insights into how environmental constraints and stochastic fluctuations shape community structures, offering a versatile approach to study several emergent phenomena in biological systems.

The convective and absolute instabilities in electrohydrodynamic-Poiseuille mixed convection for viscoelastic fluids with the Oldroyd-B model are examined. In the absence of Poiseuille flow, based on the stationary and oscillatory characteristics at the onset of convection, we distinguish weakly and strongly elastic fluid, dominated by viscosity effects and elasticity effects, respectively. Their borderline of the two effects in terms of the critical electric Weissenberg $W_{\mathrm{ec}}$ satisfies the relation $W_{\mathrm{ec}}=a/\left(1-\beta \right)+b$ where β is viscosity ratio, and the parameters $a$ and $b$ depend on dimensionless ion mobility. In the presence of Poiseuille flow, with an increase in shear strength, the convective and absolute instability thresholds increase in both weakly and strongly elastic fluids, and the jump of phase speed and saddle point shift are observed at low polymer concentration with sufficient elasticity, causing the faster transverse rolls (TRs) to propagate downstream. However, at the high polymer concentration of large $W_{\mathrm{e}}$, instead of downstream moving TRs, the upstream moving TRs can be the most unstable at the onset of absolute instability. Kinetic energy budget analysis reveals that with an increase in shear strength and elasticity, the suppressive effect of polymeric stresses on instability is enhanced in viscosity effects-dominated flow, while it is reduced in elasticity effects-dominated flow. Besides, the energy transfer from the wall-normal gradient of the perturbed electric field to the wall-normal gradient of the perturbed wall-normal velocity under the effect of the wall-normal gradient of the base electric field becomes the most destabilizing factor in the very strongly elastic fluids.

We propose and demonstrate numerically a fast classical annealing scheme for the Sherrington-Kirkpatrick (SK) spin glass model, employing the Suzuki-Kubo mean-field Ising dynamics (supplemented by a modified Thouless-Anderson-Palmer reaction field). The resultant dynamics, starting from any arbitrary paramagnetic phase (with local magnetizations $m_i=\pm 1$, for the $i\mathrm{th}$ spin, and the global magnetization $m=0$), takes the system quickly to an appropriate state with small local values of magnetization ($m_i$) commensurate with the (frustrated) interactions. As the temperature decreases with the annealing, the configuration practically remains (in an effective adiabatic way) close to a low-energy configuration as the magnitudes of $m_i$'s and the spin glass order parameter $q$ grow to unity. While the configuration reached by the procedure is not the ground state, for an $N$-spin SK model (with $N$ up to 10 000), the deviation in the energy per spin $E_N^0-E^0$ found by the annealing procedure scales as $N^{-2/3}$, with $E^0=-0.7629\pm 0.0002$, suggesting that in the thermodynamic limit the energy per spin of the low-energy configurations converges to the ground state of the SK model (analytical estimate being $E^0=-0.7631667265\cdots$), fluctuation ${\sigma }_N$ in $E_N^0$ decreases as $\sim N^{-3/4}$, and the annealing time ${\tau }_N\sim N$, making this protocol highly efficient in estimating the ground state energy of the SK model.

We introduce a numerical method to sample the distributions of charge, heat, and entropy production in open quantum systems coupled strongly to macroscopic reservoirs, with both temporal and energy resolution and beyond the linear-response regime. Our method exploits the mesoscopic-leads formulation, where macroscopic reservoirs are modeled by a finite collection of modes that are continuously damped toward thermal equilibrium by an appropriate Gorini-Kossakowski-Sudarshan-Lindblad master equation. Focussing on noninteracting fermionic systems, we access the time-resolved full counting statistics through a trajectory unraveling of the master equation. We show that the integral fluctuation theorems for the total entropy production, as well as the martingale and uncertainty entropy production, hold. Furthermore, we investigate the fluctuations of the dissipated heat in finite-time information erasure. Conceptually, our approach extends the continuous-time trajectory description of quantum stochastic thermodynamics beyond the regime of weak system-environment coupling.

Hysteresis, a widespread occurrence in both natural and artificial systems, is typically discussed under the quasistatic limit. However, studying the hysteresis behavior of complex systems in real world is highly challenging due to the involvement of nonequilibrium processes. In this work, we report that a stochastic model based on competing firms in a market, which exhibits a first-order phase transition, may also show hysteresis effects when subjected to a disturbance applied at a finite rate. We find that the cause of such phenomena is the incomplete relaxation, which continuously delays the system's responding dynamics. The strength of hysteresis effects can be measured by the ratio of characteristic timescales of relaxation and disturbance. This study provides an additional perspective for understanding hysteresis behavior and offers assistance in studying how complex systems respond to environmental changes.

We study particle transport in a class of open channels of finite length, made of identical cells of connected open polygonal billiards with parallel boundaries. In these systems, the mean square displacement (MSD) grows in time faster than linearly. We show that, irrespective of the geometry of these channels, the distribution of the first return times decays algebraically with two different exponents, separated by a crossover region determined by the MSD. We find that the distribution of first return times satisfies a simple scaling form. In turn, the transmission coefficient—defined as the fraction of trajectories that, starting at the cell at the origin, escape the channel through the other boundary—decays algebraically with the size of the system and, as a signature of nonrecurrent transport, sometimes slower. From these two processes, we derive a locking relation among the scaling exponents for the asymptotic behavior of the MSD, the times of first return to the origin, and the way transmission decays with the system size, showing that these three processes are interdependent. The locking relation holds for diffusive processes as well as for fractional Brownian motion with an arbitrary Hurst exponent. We argue that the locking relation may be valid for many other transport processes, Markovian or not, with finite MSD.

The effects of "diffusing diffusivity” (DD), a stochastically time-varying diffusion coefficient, are explored within the frameworks of three different forms of fractional Brownian motion (FBM): (i) the Langevin equation driven by fractional Gaussian noise (LE-FBM), (ii) the Weyl integral representation introduced by Mandelbrot and van Ness (MN-FBM), and (iii) the Riemann-Liouville fractional integral representation (RL-FBM) introduced by Lévy. The statistical properties of the three FBM-generalized DD models are examined, including the mean-squared displacement (MSD), mean-squared increment (MSI), autocovariance function (ACVF) of increments, and the probability density function (PDF). Despite the long-believed equivalence of MN-FBM and LE-FBM, their corresponding FBM-DD models exhibit distinct behavior in terms of MSD and MSI. In the MN-FBM-DD model, the statistical characteristics directly reflect an effective diffusivity equal to its mean value. In contrast, in LE-FBM-DD, correlations in the random diffusivity give rise to an unexpected crossover behavior in both MSD and MSI. We also find that the MSI and ACVF are nonstationary in RL-FBM-DD but stationary in the other two DD models. All DD models display a crossover from a short-time non-Gaussian PDF to a long-time Gaussian PDF. Our findings offer guidance for experimentalists in selecting appropriate FBM-generalized models to describe viscoelastic yet non-Gaussian dynamics in bio- and soft-matter systems with heterogeneous environments.

When driving a disordered elastic manifold through quenched disorder, the pinning forces exerted on the center of mass are fluctuating, with mean $f_{\mathrm{c}}=-\overline{F_w}$ and variance $\mathrm{\Delta }\left(w\right)={\overline{F_w{F}_0}}^c$, where $w$ is the externally imposed control parameter for the preferred position of the center of mass. $\mathrm{\Delta }\left(w\right)$ was obtained via the functional renormalization group in the limit of vanishing temperature $T\to 0$, and vanishing driving velocity $v\to 0$. There are two fixed points, and deformations thereof, which are well understood: The depinning fixed point ($T\to 0$ before $v\to 0$) rounded at $v>0$, and the zero-temperature equilibrium fixed point ($v\to 0$ before $T\to 0$) rounded at $T>0$. Here we consider the whole parameter space of driving velocity $v>0$ and temperature $T>0$, and quantify numerically the crossover between these two fixed points.

The investigation of nonequilibrium thermodynamics in quantum many-body systems underscores the importance of quantum work, which differs from its classical counterpart due to its statistical nature. Recent studies have shown that quantum work can serve as an effective indicator of quantum phase transitions in systems subjected to sudden quenches. However, the potential of quantum work to identify thermal phase transitions remains largely unexplored. In this paper, we examine several types of thermal phase transitions in a sudden-quench hard-core boson model, including Ising, three-state Potts, and Berezinskii-Kosterlitz-Thouless transitions. Through finite-size scaling analysis, we conclude that work statistics can also characterize the critical behaviors of thermal phase transitions in generic many-body systems. This study lays the groundwork for broader applications of work statistics in analyzing critical phenomena across diverse settings.

Long-time global cooperation is required to reduce ${\mathrm{CO}}_2$ emissions towards controlling climate change, one of the most paradigmatic examples of a risky common. The problem has been often modeled, theoretically, employing the so-called Collective Risk Dilemma (CRD), a threshold public goods game in the presence of risk, which has been shown to play a crucial role. Up to now, however, the long delays that mediate (i) political decisions and their implementation, (ii) implementations and their effective emissions reduction, and (iii) emissions reduction and risk assessment, have been largely ignored. Here we investigate how these multiple delays affect overall cooperation, by analyzing the evolutionary game dynamics of a recently developed variant of the CRD model where the dynamical feedback between risk and cooperation is incorporated. We show how the consideration of multiple, incremental delays may lead to scenarios that range from the conventional wisdom of straight delay-intrinsic destabilization of otherwise stable fixed points, to scenarios in which additional delays may limit the impact of delay-intrinsic destabilization. We trace these different outcomes back to the scaling relation between risk feedback and cooperation and discuss under which conditions multiple delay effects may actually foster global cooperation.

In the field of DNA nanotechnology, it is common wisdom that charge transport occurs through the $\pi$ stacked bases of double-stranded DNA. However, recent experimental findings by Zhuravel et al. [Nat. Nanotechnol. 15, 836 (2020)] suggest that electronic transport happens through the backbone channels instead of $\pi \text{−}\pi$ interaction of the nitrogen bases. This experimental insight calls for a detailed investigation. In keeping with this, we examine charge transport properties of three characteristic double-stranded DNA sequences (periodic GC, periodic AT, and random ATGC sequences) within a tight-binding framework where backbones form the main conduction channels. Using techniques based on the Green's function method, we inspect the single-particle density of states and localization properties of DNA in the presence of discontinuities (“nicks”) along the backbone channels. We also investigate the effect of these nicks on current-voltage response using the Landauer-Büttiker formalism for a two-terminal geometry where the source electrode is attached to one backbone strand and the drain to the other. We observe that the periodic DNA sequence of GC bases is metallic in nature, while the periodic AT sequence and the random ATGC sequence are insulating. Further, the effects of nicks on the transport properties of the periodic GC sequence is interesting: while a single nick on the upper backbone does not affect electronic transport, the addition of a second nick on the lower backbone causes the current to vanish altogether. This is found to be robust against changes in the positions of the nicks, as well as the alternation of the source and drain electrodes. Analysis of the position dependence of the probability distribution of the zero-energy electronic wave function leads us to conclude that the insulation mechanism arises from a quantum interference of the electronic wave function from the two nicks.

Nonequilibrium plasma has attracted significant attention owing to its excellent physical properties, which are highly valued by the industrial community. However, determining the electron temperature in nonequilibrium plasmas proves challenging unless the energy distribution function is approximated as an ideal Maxwell-Boltzmann distribution, where the slope of the Boltzmann plot is directly related to temperature based on traditional Boltzmann-Gibbs statistics. To overcome this problem, Tsallis and Rényi entropies are applied to nonequilibrium systems using nonextensive Tsallis and extensive Rényi statistics, respectively. Here, the temperature is determined through a power-law distribution derived from the entropy maximization principle, which accounts for the influence of previously neglected high-energy electrons. However, because the resulting distribution function requires a self-consistent function that cannot be solved analytically, a self-consistent iterative scheme is proposed to calculate the temperature. Consequently, the electron temperature is uniquely determined in nonequilibrium plasmas, satisfying the entropy maximization principle. This study may open additional avenues for understanding plasma properties using an additional parameter $q$ expanding the meaning of temperature $T$.

Breakdown in Argon at nanoscale interelectrode gaps is studied to highlight the deviation from Paschen's law prediction. The discharge occurs between gold-plated electrodes in a setup similar to a planar configuration. A fast cutoff system allows the measurement of up to one hundred breakdowns for each experimental condition. A statistical study is then conducted on the probability distribution of breakdown voltages. The presence of two peaks in the breakdown distribution shows a competition between two different elementary discharge processes. One of it always occurs around a field value of $7.7\times {10}^8\mathrm{V}/\mathrm{m}$ and does not seem to be affected by the pressure: this is the field emission breakdown mechanism. The other pressure-dependent mechanism is present only when the electrode gap is sufficiently large: this is the Townsend avalanche breakdown mechanism. The statistical method introduced in this work allows for a better interpretation of the processes involved in breakdown in submicrometer interelectrode spaces.

We show that combining the ideas of anticipatory synchronization and machine learning enables real-time prediction of chaotic time series without prior knowledge of the system model. A next-generation reservoir computing approach is used to develop slave system models for anticipatory synchronization with scalar chaotic time series. The multidimensional state space is reconstructed using time-delay embedding coordinates. The developed models satisfy the requirement of the negativeness of the largest transversal Lyapunov exponent, which is necessary for the stability of the anticipatory synchronization mode. The prediction time of one slave system constructed in this way is equal to the embedding delay time. We increase the prediction time by implementing a chain of serially connected slave systems. The prediction performance using anticipatory synchronization and machine learning is demonstrated for scalar chaotic time series obtained from Rössler and Lorenz systems, as well as for experimental time series of an electronic chaos oscillator and a theoretical time series generated by a large heterogeneous network of quadratic integrate-and-fire neurons.

Spiral waves are common self-organized spatiotemporal patterns in nature and experimental systems, playing a particularly crucial role in cardiac tissues and neuronal networks. Traditional spiral waves in period-2 domains typically exhibit defect lines, which can significantly influence spiral wave dynamics and have attracted considerable attention in recent years. The regulation of line defects in spiral waves holds significant implications in various domains, including cardiology and neuroscience. Here, we utilize periodic forcing to eliminate line defects in the traditional period-doubled spiral waves, resulting in a different form of the period-doubled spiral wave, named the restless spiral wave. The disappearance of line defects restores spiral waves to a simple helical structure but does not reinstate their rotational symmetry. The waves in the restless spiral wave are coherent at a certain moment but exhibit periodic oscillations during propagation. Analysis indicates that the disappearance of line defects occurs at the expense of the breaking of symmetry in the distribution of local point states in phase space. This method overcomes the limitations of traditional defect line-dependent control strategies, providing a different approach to controlling arrhythmias in cardiac tissue and studying wave dynamics in neuroscience.

Scale invariance is a ubiquitous observation in the dynamics of large distributed complex systems. The computation of its scaling exponents, which provide clues on its origin, is often hampered by the limited available sampling data, making an appropriate mathematical description a challenge. This work investigates the behavior of correlation functions in fractal systems under conditions of severe subsampling. Analytical and numerical results reveal a striking robustness: the correlation functions continue to capture the expected scaling exponents despite substantial data reduction. This behavior is demonstrated numerically for the random 2D Cantor set and the Sierpinski gasket, both consistent with exact analytical predictions. Similar robustness is observed in 1D time series both synthetic and experimental, as well as in high resolution images of a neuronal structure. Overall, these findings are broadly relevant for the structural characterization of biological systems under realistic sampling constraints.