Inspired by the recent experimental progress in the time-driven phase transition in quantum chaos, we investigate comprehensively the energy diffusion of a kicked rotor in the presence of phase modulation. In the classical case, we found that there always exists anomalous diffusion as long as the phase is modulated periodically and changes by 0 or $\pi$ from kick to kick. On the contrary, for quasiperiodic and random phase modulation, anomalous diffusion is suppressed. On the other hand, in the quantum case, there exist only ballistic energy diffusion and dynamical localization in the standard and periodically shifted cases, while random phase modulation destroys the quantum coherence and totally suppresses the dynamical localization. Furthermore, the quasiperiodic phase modulation is an intermediate phase between the standard case and the random one. In both the classical and quantum cases, quasiperiodic phase modulation is inequivalent to random phase modulation at large kicking times ($>{10}^3$), thus caution has to be taken when dealing with these two kinds of phase modulation in experiments.

The well-known Vicsek model describes the dynamics of a flock of self-propelled particles (SPPs). Surprisingly, there is no direct measure of the chaotic behavior of such systems. Here we discuss the dynamical phase transition present in Vicsek systems in light of the largest Lyapunov exponent (LLE), which is numerically computed by following the dynamical evolution in tangent space for up to two million SPPs. As discontinuities in the neighbor weighting factor hinder the computations, we propose a smooth form of the Vicsek model. We find a chaotic regime for the collective behavior of the SPPs based on the LLE. The dependence of LLE with the applied noise, used as a control parameter, changes sensibly in the vicinity of the well-known transition points of the Vicsek model.

We study the dynamics of clustering in systems containing active particles that are immersed in an explicit solvent. For this, we have adopted a hybrid simulation method, consisting of molecular dynamics and multiparticle collision dynamics. In our model, the overlap-avoiding passive interaction of an active particle with another active particle or a solvent particle has been taken care of via variants of the Lennard-Jones potential. Dynamic interactions among the active particles have been incorporated via a Vicsek-like alignment rule in self-propulsion that facilitates clustering. We quantify the effects of activity and importance of hydrodynamics on the dynamics of clustering via variations of relevant system parameters. Results are obtained for low overall density of active particles, for which the state point is close to the vapor branch of the coexistence curve, and thus the morphology consists of disconnected clusters. In such a situation, the mechanism of growth switches among particle diffusion, diffusive coalescence, and ballistic aggregation, depending upon the presence or absence of active and hydrodynamic interactions providing different kinds of mobilities to the clusters. Corresponding growth laws have been quantified and discussed in the context of appropriate theoretical pictures. Our results suggest that multiparticle collision dynamics is an effective method for the investigation of hydrodynamic phenomena in phase-separating active matter systems.

Quantifying the ways in which local particle rearrangements contribute to macroscopic plasticity is one of the fundamental pursuits of granular mechanics and soft matter physics. Here we examine local rearrangements that occur naturally during the deformation of three samples of 3D granular materials subjected to distinct boundary conditions by employing in situ x-ray measurements of particle-resolved structure and stress. We focus on five distinct rearrangement measures, their statistics, interrelationships, contributions to macroscopic deformation, repeatability, and dependence on local structure and stress. Our most significant findings are that local rearrangements (1) are correlated on a scale of three to four particle diameters, (2) exhibit volumetric strain-shear strain and nonaffine displacement-rotation coupling, (3) exhibit correlations that suggest either rearrangement repeatability or that rearrangements span multiple steps of incremental sample strain, and (4) show little dependence on local stress but correlate with quantities describing local structure, such as porosity. Our results are presented in the context of relevant plasticity theories and are consistent with recent findings suggesting that local structure may play at least as important of a role as local stress in determining the nature of local rearrangements.

The counterintuitive phenomenon—that an initially hotter water freezes faster than initially cooler water—is named the “Mpemba effect.” Although it has been known for centuries, the underlying mechanism remains unclear. Recently, the Mpemba effect rekindled the interest of researchers since several studies identified that it might occur in some Markovian systems, and a general statistical-physical Mpemba effect framework was correspondingly proposed. In our previous study [Z.-Y. Yang and J.-X. Hou, Phys. Rev. E 101, 052106 (2020)], we observed the non-Markovian Mpemba effect in a mean-field system (MFS), where the Mpemba effect originates from the back-reaction of the thermal reservoir. Naturally, the phase transition time is the key to the occurrence of the Mpemba effect, which, however, has not been quantitatively described. Following the direction of previous work, this study rigorously derives the phase transition time under different conditions, and quantitatively describes the mechanism of the non-Markovian Mpemba effect in a MFS. In addition, the validation of our theory was further verified via the microcanonical Monte Carlo simulation. An accurate description of the underlying mechanism of our proposed MFS facilitates the generalization of the Mpemba effect framework in statistical physics and may benefit in answering the riddle of the century, the original Mpemba effect in water.

We study the full distribution of $A={\int }_0^T{x}^n\left(t\right)dt, n=1,2,\cdots$, where $x\left(t\right)$ is an Ornstein-Uhlenbeck process. We find that for $n>2$ the long-time ($T\to \infty$) scaling form of the distribution is of the anomalous form $P(A;T)\sim e^{-T^{\mu }{f}_n(\mathrm{\Delta }A/T^{\nu })}$ where $\mathrm{\Delta }A$ is the difference between $A$ and its mean value, and the anomalous exponents are $\mu =2/(2n-2)$ and $\nu =n/(2n-2)$. The rate function $f_n\left(y\right)$, which we calculate exactly, exhibits a first-order dynamical phase transition which separates between a homogeneous phase that describes the Gaussian distribution of typical fluctuations, and a “condensed” phase that describes the tails of the distribution. We also calculate the most likely realizations of $\mathcal{A}\left(t\right)={\int }_0^t{x}^n\left(s\right)ds$ and the distribution of $x\left(t\right)$ at an intermediate time $t$ conditioned on a given value of $A$. Extensions and implications to other continuous-time systems are discussed.

We consider an open (Brownian) classical harmonic oscillator in contact with a non-Markovian thermal bath and described by the generalized Langevin equation. When the bath's spectrum has a finite upper cutoff frequency, the oscillator may have ergodic and nonergodic configurations. In ergodic configurations (when they exist, they correspond to lower oscillator frequencies) the oscillator demonstrates conventional relaxation to thermal equilibrium with the bath. In nonergodic configurations (which correspond to higher oscillator frequencies) the oscillator in general does not thermalize but relaxes to periodically correlated (cyclostationary) states whose statistics vary periodically in time. For a specific dissipation kernel in the Langevin equation, we evaluate explicitly relevant relaxation functions, which describe the evolution of mean values and time correlations. When the oscillator frequency is switched from a lower value to higher one, the oscillator may show parametric ergodic to nonergodic transitions with equilibrium initial and cyclostationary final states. These transitions are shown to resemble phase transitions of the second kind.

We study species abundance in the empirical plant-pollinator mutualistic networks exhibiting broad degree distributions, with uniform intragroup competition assumed, by the Lotka-Volterra equation. The stability of a fixed point is found to be identified by the signs of its nonzero components and those of its neighboring fixed points. Taking the annealed approximation, we derive the nonzero components to be formulated in terms of degrees and the rescaled interaction strengths, which lead us to find different stable fixed points depending on parameters, and we obtain the phase diagram. The selective extinction phase finds small-degree species extinct and effective interaction reduced, maintaining stability and hindering the onset of instability. The nonzero minimum species abundances from different empirical networks show data collapse when rescaled as predicted theoretically.

Social interactions may affect the update of individuals' opinions. The existing models such as the majority-vote (MV) model have been extensively studied in different static networks. However, in reality, social networks change over time and individuals interact dynamically. In this work, we study the behavior of the MV model on temporal networks to analyze the effects of temporality on opinion dynamics. In social networks, people are able to both actively send connections and passively receive connections, which leads to different effects on individuals' opinions. In order to compare the impact of different patterns of interactions on opinion dynamics, we simplify them into two processes, that is, the single directed (SD) process and the undirected (UD) process. The former only allows each individual to adopt an opinion by following the majority of actively interactive neighbors, while the latter allows each individual to flip opinion by following the majority of both actively interactive and passively interactive neighbors. By borrowing the activity-driven time-varying network with attractiveness (ADA model), the two opinion update processes, i.e., the SD and the UD processes, are related with the network evolution. With the mean-field approach, we derive the critical noise threshold for each process, which is also verified by numerical simulations. Compared with the SD process, the UD process reaches a larger consensus level below the same critical noise. Finally, we also verify the main results in real networks.

We study methylation dynamics of the chemoreceptors as an Escherichia coli cell moves around in a spatially varying chemoattractant environment. We consider attractant concentration with strong and weak spatial gradient. During the uphill and downhill motion of the cell along the gradient, we measure the temporal variation of average methylation level of the receptor clusters. Our numerical simulations we show that the methylation dynamics depends sensitively on the size of the receptor clusters and also on the strength of the gradient. At short times after the beginning of a run, the methylation dynamics is mainly controlled by short runs which are generally associated with high receptor activity. This results in demethylation at short times. But for intermediate or large times, long runs play an important role and depending on receptor cooperativity or gradient strength, the qualitative variation of methylation can be completely different in this time regime. For weak gradient, both for uphill and downhill runs, after the initial demethylation, we find methylation level increases steadily with time for all cluster sizes. Similar qualitative behavior is observed for strong gradient during uphill runs as well. However, the methylation dynamics for downhill runs in strong gradient show highly nontrivial dependence on the receptor cluster size. We explain this behavior as a result of interplay between the sensing and adaptation modules of the signaling network.

The conformational and dynamical properties of active Brownian polymers embedded in a fluid depend on the nature of the driving mechanism, e.g., self-propulsion or external actuation of the monomers. Implementations of self-propelled and actuated active Brownian polymers in a multiparticle collision (MPC) dynamics fluid are presented, which capture the distinct differences between the two driving mechanisms. The active force-free nature of self-propelled monomers requires adaptations of the MPC simulation scheme, with its streaming and collision steps, where the monomer self-propulsion velocity has to be omitted in the collision step. Comparison of MPC simulation results for active polymers in dilute solution with results of Brownian dynamics simulations accounting for hydrodynamics via the Rotne-Prager-Yamakawa tensor confirm the suitability of the implementation. The polymer conformational and dynamical properties are analyzed by the static and dynamic structure factor, and the scaling behavior of the latter with respect to the wave number and time dependence are discussed. The dynamic structure factor displays various activity-induced temporal regimes, depending on the considered wave number, which reflect the persistent diffusive motion of the whole polymer at small wave numbers, and the activity-enhanced internal dynamics at large wave numbers. The obtained simulation results are compared with theoretical predictions.

We study microscopic engines that use a single active particle as their “working medium.” Part of the energy required to drive the directed motion of the particle can be recovered as work, even at a constant temperature. A wide class of synthetic active particles can be captured by schematically accounting for the chemical degrees of freedom that power the directed motion without having to resolve the exact microscopic mechanism. We derive analytical results for the quasistatic thermodynamic efficiency, i.e., the fraction of available chemical energy that can be recovered as mechanical work. While this efficiency is vanishingly small for colloidal particles, it increases as the dissipation is increased beyond the linear-response regime and goes through a maximum at large propulsion speeds. Our results demonstrate that driving beyond the linear-response regime has nontrivial consequences for the efficiency of active engines.

In this paper we analyze the asymptotic behavior of Lévy walks with rests. Applying recent results in the field of functional convergence of continuous-time random walks we find the corresponding limiting processes. Depending on the parameters of the model, we show that in the limit we can obtain standard Lévy walk or the process describing competition between subdiffusion and Lévy flights. Some other more complicated limit forms are also possible to obtain. Finally we present some numerical results, which confirm our findings.

Classical equilibrium thermodynamics provides, in a general way, upper Carnot bounds for the performance of energy converters. Nevertheless, to suggest lower bounds is a much more subtle issue, especially when they are related to a definition of convenience. Here, this issue is investigated in a unified way for heat engines, refrigerators, and heat pumps. First, irreversibilities are weighted in the context of heat reservoir stability for irreversible engines by using the thermodynamic distance between minimum energy and maximum entropy steady states. Some stability coefficients can be related to a majorization process and the obtention of Pareto fronts, linking stability and optimization by means of efficiency and entropy due to correlations between system and reservoirs. Second, these findings are interpreted in a very simple context. A region where the heat device is efficient is defined in a general scheme and, below this zone, the heat device is inefficient in the sense that irreversibilities somehow dominate its behavior. These findings allow for a clearer understanding of the role played by some well-known figures of merit in the scope of finite-time and -size optimization. Comparison with experimental results is provided.

In our effort to tackle the problem of letting nontrivial interactions, thermodynamic equilibrium, and full synchronicity coexist, and in the hope of reviving interest in cellular automata as promising tools for the quantitative, large-scale investigation of multiparticle systems, we built a fully synchronous cellular automaton rule for the simulation of occupancy-based lattice systems with multistate cells and neighboring interactions. The core of this rule, which constitutes an actual synchronous sampling scheme, is a negotiation stage; it produces cell occupancy distributions in very good agreement with their sequential Monte Carlo counterparts, and it satisfies a cellwise detailed balance principle thanks to the use of “mixed” intermediate states that allow for the computation of locally averaged acceptance probabilities. We took a square lattice (but the rule itself is not bound by dimensionality) as a basis for comparison with sequential Monte Carlo for showing that this synchronous rule leads to quasiequilibrium; the fulfillment of cellwise detailed balance is shown through results obtained for a small one-dimensional system, where the transition matrix could be computed exactly.

We present a statistical mechanical description of randomly packed spherical particles, where the average coordination number is treated as a macroscopic thermodynamic variable. The overall packing entropy is shown to have two contributions: geometric, reflecting statistical weights of individual configurations, and topological, which corresponds to the number of topologically distinct states. Both of them are computed in the thermodynamic limit for isostatic and weakly underconstrained packings in 2D and 3D. The theory generalizes concepts of granular and glassy configurational entropies for the case of nonjammed systems. It is directly applicable to sticky colloids and predicts an asymptotic phase behavior of sticky spheres in the limit of strong binding.

The time series recordings of typical songs of songbirds exhibit highly complex and structured behavior, which is characteristic of their species and stage of development, and need to be analyzed by methods that can uncover their correlation structure. Here we analyze a typical song of a canary using Hurst exponents and multifractal analysis, which uncovers the correlation structure of typical song segments. These are then compared with the corresponding quantities from shuffled data, which destroys the temporal correlations and iterative amplitude-adjusted Fourier transform (IAAFT) data. It is seen that temporal correlations are responsible for the multifractal behavior seen in the data and that two-point correlations, which are preserved by the transform, are important in the high-fluctuation regime. Higher-order correlations and intersyllabic gaps dominate the behavior of the low-fluctuation regime. These observations are supported by the simplicial characterization of the corresponding time series networks. Complexity measures are also used to analyze the amplitude envelope time series. These indicate that intersyllabic gaps contribute a significant fraction to the complexity of the birdsong. Our method provides a detailed characterization of the data, which can enable the comparison of real and synthetic birdsong and comparisons across stages of development and species. A brief comparison with the song of the zebra finch supports this.

Linear stability of synchronized states in networks of delay-coupled oscillators depends on the type of interaction, the network, and oscillator properties. For inert oscillator response, found ubiquitously from biology to engineering, states with time-dependent frequencies can arise. These generate side bands in the frequency spectrum or lead to chaotic dynamics. The time delay introduces multistability of synchronized states and an exponential term in the characteristic equation. Stability analysis using the resulting transcendental characteristic equation is a difficult task and is usually carried out numerically. We derive criteria and conditions that enable fast and robust analytical linear stability analysis based on the system parameters. These apply to arbitrary network topologies, identical oscillators, and delays.

We study the collective behavior of swarmalators, generalizations of phase oscillators that both sync and swarm, confined to move on a one-dimensional (1D) ring. This simple model captures the essence of movement in two or three dimensions, but has the benefit of being solvable: most of the collective states and their bifurcations can be specified exactly. The model also captures the behavior of real-world swarmalators which swarm in quasi-1D rings such as bordertaxic vinegar eels and sperm.

As opposed to most previous works focusing on random walks on deterministic tree networks, in this paper, we pay more attention on random growth tree networks. Specifically, we propose two distinct types of random growth tree networks $\mathcal{T}(1;t,p)$ and $\mathcal{T}(2;t,p)$ where $t$ represents time step and $p$ is a probability parameter $(0\le p\le 1)$. Tree $\mathcal{T}(1;t,p)$ is iteratively built in a fractal manner; however, $\mathcal{T}(2;t,p)$ is generated using a nonfractal operation. Then we study random walks on tree network $\mathcal{T}(i;t,p)$ $(i=1,2)$ and derive the analytical solution to mean first-passage time $\langle {\mathcal{F}}_{\mathcal{T}(i;t,p)}\rangle$. The results suggest that two growth ways have remarkably different influence on parameters $\langle {\mathcal{F}}_{\mathcal{T}(i;t,p)}\rangle$. More precisely, the fractal-growth manner makes topological structure of tree network more loose than the nonfractal one and thus increases drastically mean first-passage time in the large graph limit. Finally, we extensively conduct experimental simulations, and the results demonstrate that computer simulations are in strong agreement with the theoretical analysis.