Fluctuation theorems are fundamental results in nonequilibrium thermodynamics beyond the linear response regime. Among these, the paradigmatic Tasaki-Crooks fluctuation theorem relates the statistics of the works done in a forward out-of-equilibrium quantum process and in a corresponding backward one. In particular, the initial states of the two processes are thermal states and thus incoherent in the energy basis. Here we aim to investigate the role of initial quantum coherence in work fluctuation theorems, by considering a quasiprobability distribution of work. To do this, we formulate and examine the implications of a detailed fluctuation theorem, which reproduces the Tasaki-Crooks fluctuation theorem in the absence of initial quantum coherence.

We present elliptic-rogue wave solutions for integrable nonlinear soliton equations in rational form by elliptic functions. Unlike solutions generated on the plane wave background, these solutions depict rogue waves emerging on elliptic function backgrounds. By refining the modified squared wave function method in tandem with the Darboux-Bäcklund transformation, we establish a quantitative correspondence between elliptic-rogue waves and the modulational instability. This connection reveals that the modulational instability of elliptic function solutions triggers rational-form solutions displaying elliptic-rogue waves, whereas the modulational stability of elliptic function solutions results in the rational-form solutions exhibiting the elliptic solitons or elliptic breathers. Moreover, this approach enables the derivation of higher-order elliptic-rogue waves, offering a versatile framework for constructing elliptic-rogue waves and exploring modulational stability in other integrable equations.

Analyzing the long-term behavior of hyperchaotic systems poses formidable challenges in the field of nonlinear science. This paper proposes a data-driven model called the delayed self-feedback echo state network (self-ESN) specifically designed for the evolution behavior of hyperchaotic systems. Self-ESN incorporates a delayed self-feedback term into the dynamic equation of a reservoir to reflect the finite transmission speed of neuron signals. Delayed self-feedback establishes a connection between the current and previous $m$ time steps of the reservoir state and provides an effective means to capture the dynamic characteristics of the system, thereby significantly improving memory performance. In addition, the concept of local echo state property (ESP) is introduced to relax the conventional ESP condition, and theoretical analysis is conducted on guiding the selection of feedback delay and gain to ensure the local ESP. The judicious selection of feedback gain and delay in self-ESN improves prediction accuracy and overcomes the challenges associated with obtaining optimal parameters of the reservoir in conventional ESN models. Numerical experiments are conducted to assess the long-term prediction capabilities of the self-ESN across various scenarios, including a 4D hyperchaotic system, a hyperchaotic network, and an infinite-dimensional delayed chaotic system. The experiments involve reconstructing bifurcation diagrams, predicting the chaotic synchronization, examining spatiotemporal evolution patterns, and uncovering the hidden attractors. The results underscore the capability of the proposed self-ESN as a strategy for long-term prediction and analysis of the complex systems.

We investigated, both analytically and numerically, the dynamics of a noiseless overdamped active particle in a square lattice of planar counter-rotating convection rolls. Below a first threshold of the self-propulsion speed, a fraction of the simulated particle's trajectories spatially diffuse around the convection rolls, whereas the remaining trajectories remain trapped inside the injection roll. We detected two chaotic diffusion regimes: (i) below a second, higher threshold of the self-propulsion speed, the particle performs a random motion characterized by asymptotic normal diffusion. Long superdiffusive transients were observed for vanishing small self-propulsion speeds. (ii) above that threshold, the particle follows chaotic running trajectories with speed and orientation close to those of the self-propulsion vector at injection and its dynamics is superdiffusive. Chaotic diffusion disappears in the ballistic limit of extremely large self-propulsion speeds.

Biological and psychological processes have been conceptualized as emerging from intricate multiplicative interactions among component processes across various spatial and temporal scales. Among the statistical models employed to approximate these intricate nonlinear interactions across scales, one prominent framework is that of cascades. Despite decades of empirical work using multifractal formalisms, several fundamental questions persist concerning the proper interpretations of multifractal evidence of nonlinear cross-scale interactivity. Does multifractal spectrum width depend on multiplicative interactions, constituent noise processes participating in those interactions, or both? We conducted numerical simulations of cascade time series featuring component noise processes characterizing a range of nonlinear temporal correlations: nonlinearly multifractal, linearly multifractal (obtained via the iterative amplitude adjusted wavelet transform of nonlinearly multifractal), phase-randomized linearity (obtained via the iterative amplitude adjustment Fourier transform of nonlinearly multifractal), and phase and amplitude randomized (obtained via shuffling of nonlinearly multifractal). Our findings show that the multiplicative interactions coordinate with the nonlinear temporal correlations of noise components to dictate emergent multifractal properties. Multiplicative cascades with stronger nonlinear temporal correlations make multifractal spectra more asymmetric with wider left sides. However, when considering multifractal spectral differences between the original and surrogate time series, even multiplicative cascades produce multifractality greater than in surrogate time series, even with linearized multifractal noise components. In contrast, additivity among component processes leads to a linear outcome. These findings provide a robust framework for generating multifractal expectations for biological and psychological models in which cascade dynamics flow from one part of an organism to another.

We study the cascading failures in a system of two interdependent networks whose internetwork supply links are directional. We will show that, by utilizing generating function formalism, the cascading process can be modeled by a set of recursive relations. Most importantly, the functions involved in these relations are solely dependent upon the choice of the degree distribution of ingoing links. Simulation results in the limit of very large networks based on different choices of degree distributions for outgoing links, e.g., Kronecker delta, Poisson and Pareto, are indeed identical and are in excellent agreement with the theory. However, for Pareto distribution with the shape parameter $1<\alpha <2$, the convergence is slow. In general, directional networks can be more vulnerable or less vulnerable than their bidirectional counterparts. For three special settings of interdependent networks, we analytically compare their vulnerability. For practical applications it is important to predict if a system responds to the size of the initial attack continuously or if there is catastrophic collapse of the system if the attack exceeds a specific transition size. We analytically show that systems with lower average degrees are more resilient against this abrupt transition. We also establish an equivalence of this transition with the liquid-gas transition in statistical mechanics. In the last section, we derive the set of recursive relation to describe the cascading process where the initial attack is not restricted to a single network.

Protein-mediated interactions are ubiquitous in the cellular environment, and particularly in the nucleus, where they are responsible for the structuring of chromatin. We show through molecular-dynamics simulations of a polymer surrounded by binders that the strength of the binder-polymer interaction separates an equilibrium from a nonequilibrium regime. In the equilibrium regime, the system can be efficiently described by an effective model in which the binders are traced out. Even in this case, the polymers display features that are different from those of a standard homopolymer interacting with two-body interactions. We then extend the effective model to deal with the case where binders cannot be regarded as in equilibrium and a new phenomenology appears, including local blobs in the polymer. An effective description of this system can be useful in elucidating the fundamental mechanisms that govern chromatin structuring in particular and indirect interactions in general.

The self-organization of cells into complex tissues relies on a tight coordination of cell behavior. Identifying the cellular processes driving tissue growth is key to understanding the emergence of tissue forms and devising targeted therapies for aberrant growth, such as in cancer. Inferring the mode of tissue growth, whether it is driven by cells on the surface or by cells in the bulk, is possible in cell culture experiments but difficult in most tissues in living organisms (in vivo). Genetic tracing experiments, where a subset of cells is labeled with inheritable markers, have become important experimental tools to study cell fate in vivo. Here we show that the mode of tissue growth is reflected in the size distribution of the progeny of marked cells. To this end, we derive the clone size distributions using analytical calculations in the limit of negligible cell migration and cell death, and we test our predictions with an agent-based stochastic sampling technique. We show that for surface-driven growth the clone size distribution takes a characteristic power-law form with an exponent determined by fluctuations of the tissue surface. Our results propose a possible way of determining the mode of tissue growth from genetic tracing experiments.

The tribology between surfaces can have a profound impact on the response of a mechanical system, such as how granular particles are driven to flow. In this work, we perform experiments that time resolve the tangential and normal components of the force between two semicylindrical polydimethylsiloxane samples immersed in fluid, as they slide against each other in a range of controlled speeds. The time-averaged friction force shows a nonmonotonic dependence on the sliding speed over four decades, which is consistent with the paradigmatic Stribeck diagram and three dynamical regimes associated with it. Our specially designed fixed-depth setup allows us to study the fluctuation of force that exhibits strong stick-slip patterns in one of the regimes. Data from repetitive experiments reveal that both the “onset speed” for the stick-slip patterns and its spatial location along the sample change gradually during the course of our experiments, indicating changes on the sample surfaces. In addition, we conduct counterpart experiments by using spherical samples rubbing against each other, to make a direct connection of the interparticle tribology to the granular flow reported in our previous work [J.-C. Tsai et al., Phys. Rev. Lett. 126, 128001 (2021)].

Circles of a single size can pack together densely in a hexagonal lattice, but adding in size variety disrupts the order of those packings. We conduct simulations which generate dense random packings of circles with specified size distributions and measure the area fraction in each case. While the size distributions can be arbitrary, we find that for a wide range of size distributions the random close-packing area fraction ${\varphi }_{\mathrm{rcp}}$ under this general protocol is determined to high accuracy by the polydispersity and skewness of the size distribution. At low skewness, all packings tend to a minimum packing fraction ${\varphi }_0\approx 0.840$ independent of polydispersity. In the limit of high skewness, ${\varphi }_{\mathrm{rcp}}$ becomes independent of skewness, asymptoting to a polydispersity-dependent limit. We show how these results can be predicted from the behavior of bidisperse or bi-Gaussian circle size distributions.

In turbulent free shear flows such as jets and wakes, and also in turbulent boundary layers, the turbulent region is bounded by a region of irrotational flow where the magnitude of the potential velocity fluctuations can be very high. This is particularly true close to the turbulent-nonturbulent interface layer (TNTI) that separates the regions of turbulent (rotational) and nonturbulent (irrotational) fluid motion in these flows. Previous works have shown that for distances from the TNTI $x_2$ much bigger than the integral scale $L$ in the nearby turbulent region ($x_2\gg L$), the variance of the velocity fluctuations $\langle u_i^2\rangle$ ($i=1,2,3$) depends on the shape of the kinetic energy spectrum in the infrared region $E\left(k\right)\sim k^n$ [O. M. Phillips, Proc. Camb. Phil. Soc. 51, 220 (1955); Xavier et al., J. Fluid Mech. 918, A3 (2021)]. Using rapid distortion theory, we derive the generalized scaling laws for the potential velocity fluctuations, at distances sufficiently far from the TNTI layer, for any value of $n$. While the cases $n=4$ (Batchelor turbulence) and $n=2$ (Saffman turbulence) have been previously derived, with $\langle u_i^2\rangle \sim x_2^{-4}$ and $\langle u_i^2\rangle \sim x_2^{-3}$, for $n=4$ and $n=2$, respectively [O. M. Phillips, Proc. Camb. Phil. Soc. 51, 220 (1955); Xavier et al., J. Fluid Mech. 918, A3 (2021).], we extend these results by including any other value of $n$. In particular, we obtain $\langle u_i^2\rangle \sim x_2^{-2}$ and $\langle u_i^2\rangle \sim x_2^{-4}$, for $n=1$ and $n\ge 5$, respectively, while $n=3$ yields $\langle u_i^2\rangle \sim x_2^{-4}ln\left(x_2\right)$. These theoretical results are confirmed by direct numerical simulations of turbulent fronts evolving into an irrotational flow region in the absence of mean shear.

We present a data-driven reduced-order modeling of the space-charge dynamics for electromagnetic particle-in-cell (EMPIC) plasma simulations based on dynamic mode decomposition (DMD). The dynamics of the charged particles in kinetic plasma simulations such as EMPIC is manifested through the plasma current density defined along the edges of the spatial mesh. We showcase the efficacy of DMD in modeling the time evolution of current density through a low-dimensional feature space. Not only do such DMD-based predictive reduced-order models help accelerate EMPIC simulations, they also have the potential to facilitate investigative analysis and control applications. We demonstrate the proposed DMD-EMPIC scheme for reduced-order modeling of current density and speedup in EMPIC simulations involving electron beam under the influence of magnetic field, virtual cathode oscillations, and backward wave oscillator.

Nonequilibrium fluctuation relation lies at the heart of the quantum thermodynamics. Many previous studies have demonstrated that the heat exchange between a quantum system and a thermal bath initially prepared in their own Gibbs states at different temperatures obeys the famous Jarzynski-Wójcik fluctuation theorem. However, this conclusion is obtained under the assumption of Born-Markovian approximation. In this paper, going beyond the Born-Markovian limitation, we investigate the statistics of quantum heat in an exactly non-Markovian relaxation process described by the well-known Caldeira-Leggett model. It is revealed that the Jarzynski-Wójcik fluctuation theorem breaks down in the strongly non-Markovian regime. Moreover, we find the steady-state quantum heat within the non-Markovian framework can be widely tunable by using the quantum reservoir-engineering technique. These results are sharply contrary to the common Born-Markovian predictions. Our results presented in this paper may update the understanding of the quantum thermodynamics in strongly coupled and low-temperature systems. Moreover, the controllable heat may have some potential applications in improving the performance of a quantum heat engine.

Polymer physics models suggest that chromatin spontaneously folds into loop networks with transcription units (TUs), such as enhancers and promoters, as anchors. Here we use combinatoric arguments to enumerate the emergent chromatin loop networks, both in the case where TUs are labeled and where they are unlabeled. We then combine these mathematical results with those of computer simulations aimed at finding the inter-TU energy required to form a target loop network. We show that different topologies are vastly different in terms of both their combinatorial weight and energy of formation. We explain the latter result qualitatively by computing the topological weight of a given network—i.e., its partition function in statistical mechanics language—in the approximation where excluded volume interactions are neglected. Our results show that networks featuring local loops are statistically more likely with respect to networks including more nonlocal contacts. We suggest our classification of loop networks, together with our estimate of the combinatorial and topological weight of each network, will be relevant to catalog three-dimensional structures of chromatin fibers around eukaryotic genes, and to estimate their relative frequency in both simulations and experiments.

Shock-ignition effect in indirect-drive thermonuclear target is demonstrated on the base of numerical simulations. Thermonuclear gain (in relation to laser pulse energy) of a shock-ignited indirect-drive thermonuclear capsule is obtained, which is 22.5 times higher than that at a traditional spark ignition of the capsule with the same DT-fuel mass, wherein the shock-ignition laser pulse energy is 1.5 times less than the energy of a laser pulse at traditional spark ignition. To implement the shock-ignition effect in indirect-drive target, a rapid increase in radiation temperature is required over several hundred picoseconds at the final stage of thermonuclear capsule implosion. The ability of such a rapid response of radiation temperature to variation in the intensity of an x-ray-producing laser pulse is the main factor in the uncertainty of the degree of manifestation of the shock-ignition effect in an indirect-drive target. This circumstance, first of all, requires experimental study.

In this work, the recent lattice Boltzmann (LB) model with self-tuning equation of state (EOS) [Huang et al., Phys. Rev. E 99, 023303 (2019)] is extended to three dimensions for the simulation of multiphase flows, which is based on the standard three-dimensional 27-velocity lattice and multiple-relaxation-time collision operator. To achieve the self-tuning EOS, the equilibrium moment is devised by introducing a built-in variable, and the collision matrix is improved by introducing some velocity-dependent nondiagonal elements. Meanwhile, the additional cubic terms of velocity in recovering the Newtonian viscous stress are eliminated to enhance the numerical accuracy. For modeling multiphase flows, an attractive pairwise interaction force is introduced to mimic the long-range molecular interaction, and a consistent scheme is proposed to compensate for the ${\varepsilon }^3\text{-order}$ discrete lattice effect. Thermodynamic consistency in a strict sense is established for the multiphase LB model with self-tuning EOS, and the wetting condition is also treated in a thermodynamically consistent manner. As a result, the contact angle, surface tension, and interface thickness can be independently adjusted in the present theoretical framework. Numerical tests are first performed to validate the multiphase LB model with self-tuning EOS and the theoretical analyses of bulk and surface thermodynamics. The collision of equal-sized droplets is then simulated to demonstrate the applicability and effectiveness of the present LB model for multiphase flows.

We study the performance of a quantum Otto heat engine with two spins coupled by a Heisenberg interaction, taking into account not only the mean values of work and efficiency but also their fluctuations. We first show that, for this system, the output work and its fluctuations are directly related to the magnetization and magnetic susceptibility of the system at equilibrium with either heat bath. We analyze the regions where the work extraction can be done with low relative fluctuation for a given range of temperatures, while still achieving an efficiency higher than that of a single spin system heat engine. In particular, we find that, due to the presence of “idle” levels, an increase in the interspin coupling can either increase or decrease fluctuations, depending on the other parameters. In all cases, however, we find that the relative fluctuations in work or efficiency remain large, implying that this microscopic engine is not very reliable as a source of work.

The fidelity is widely used to detect quantum phase transitions, which is characterized by either a sharp change of fidelity or the divergence of fidelity susceptibility in the thermodynamical limit when the phase-driving parameter is across the transition point. In this work, we unveil that the occurrence of exact zeros of fidelity in finite-size systems can be applied to detect quantum phase transitions. In general, the fidelity $\mathcal{F}(\gamma ,\tilde{\gamma })$ always approaches zero in the thermodynamical limit, due to the Anderson orthogonality catastrophe, no matter whether the parameters of two ground states ($\gamma$ and $\tilde{\gamma }$) are in the same phase or different phases, and this makes it difficult to distinguish whether an exact zero of fidelity exists by finite-size analysis. To overcome the influence of orthogonality catastrophe, we study finite-size systems with twist boundary conditions, which can be introduced by applying a magnetic flux, and demonstrate that exact zeros of fidelity can be always accessed by tuning the magnetic flux when $\gamma$ and $\tilde{\gamma }$ belong to different phases. On the other hand, no exact zero of fidelity can be observed if $\gamma$ and $\tilde{\gamma }$ are in the same phase. We demonstrate the applicability of our theoretical scheme by studying concrete examples, including the Su-Schrieffer-Heeger model, Creutz model, and Haldane model. Our work provides a practicable way to detect quantum phase transitions via the calculation of fidelity of finite-size systems.

By combining the nonconserved spin-flip dynamics driving ferromagnetic ordering with the conserved Kawasaki-exchange dynamics driving phase segregation, we perform Monte Carlo simulations of the nearest-neighbor Ising model. This kind of mixed dynamics is found in a system consisting of a binary mixture of isomers, simultaneously undergoing a segregation and an interconversion reaction among themselves. Here, we study such a system following a quench from the high-temperature homogeneous phase to a temperature below the demixing transition. We monitor the growth of domains of both the winner; the isomer, which survives as the majority; and the loser, the isomer that perishes. Our results show a strong interplay of the two dynamics at early times, leading to a growth of the average domain size of both the winner and loser as $\sim t^{1/7}$, slower than a purely phase-segregating system. At later times, eventually the dynamics becomes reaction dominated and the winner exhibits a $\sim t^{1/2}$ growth, expected for a system with purely nonconserved dynamics. On the other hand, the loser at first show a faster growth, albeit, slower than the winner, and then starts to decay before it almost vanishes. Further, we estimate the time ${\tau }_s$ marking the crossover from the early-time slow growth to the late-time reaction-dominated faster growth. As a function of the reaction probability $p_r$, we observe a power-law scaling ${\tau }_s\sim p_r^{-x}$, where $x\approx 1.05$, irrespective of the temperature. For a fixed value of $p_r$ too, ${\tau }_s$ appears to be independent of the temperature.