In this work we investigate a finite-time quantum Otto-like heat engine with a single-qubit working substance, distinguished from the standard Otto cycle by introducing a unitary operation before the cold isochore. This operation suppresses the slowest decaying mode of the open-system dynamics and broadens the spectral gap, thereby inducing an exponential to accelerate the subsequent thermalization process toward stationarity. We derive analytic expressions for the work, heat, and efficiency, and perform numerical simulations comparing the standard Otto engine, the shortcut to adiabatic engine, and our proposed Otto-like engine. Our analysis demonstrates that with an appropriate parameter selection, the additional unitary operation can significantly boost the system's power and efficiency. Finally, using the unified optimization criterion $\mathrm{\Phi }$, we further show that the modified cycle consistently outperforms both the conventional cycle and the shortcut to adiabatic protocol.

We study the role of fluctuations in particle systems modeled by Dean-Kawasaki-type equations, which describe the evolution of particle densities in systems with Brownian motion. By comparing microscopic simulations, stochastic partial differential equations, and their deterministic counterparts, we analyze four models of increasing complexity. Our results identify macroscopic quantities that can be altered by the conserved multiplicative noise that typically appears in the Dean-Kawasaki-type description. We find that this noise enhances front propagation speed in systems with density-dependent diffusivity, accelerates the onset of pattern formation in particle systems with nonlocal interactions, and reduces hysteresis in systems interacting via repulsive forces. In some cases, it accelerates transitions or induces structures absent in deterministic models. These findings illustrate that (conservative) fluctuations can have constructive and nontrivial effects, emphasizing the importance of stochastic modeling in understanding collective particle dynamics.

The Dicke model, renowned for its superradiant quantum phase transition, also exhibits a transition from regular to chaotic dynamics. In this work we provide a systematic, comparative study of static and dynamical indicators of chaos for the closed and open Dicke models. In the closed Dicke model, we find that indicators of chaos sensitive to long-range correlations in the energy spectrum, such as the spectral form factor, can deviate from the Poissonian predictions and show a dip-ramp-plateau feature even in the regular region of the Dicke model unless very large values of the spin size are chosen. Thus, care is needed in using such indicators of chaos in general. In the open Dicke model with cavity damping, we find that the dissipative spectral form factor emerges as a robust diagnostic displaying a quadratic dip-ramp-plateau behavior in agreement with the Ginibre Unitary Ensemble (GinUE) in the superradiant regime. Moreover, by examining the spectral properties of the Liouvillian, we provide indirect evidence for the concurrence of the dissipative superradiant quantum phase transition and the change in Liouvillian eigenvalue statistics from 2D Poissonian to GinUE behavior.

The classical Kuramoto oscillator typically involves a single scalar state variable representing the phase of each oscillator. In contrast, swarmalators, an extension of the framework of Kuramoto oscillators, incorporate two coupled variables per unit: one describing spatial position and the other representing phase or orientation. Depending on the application, these state variables may differ in their nature and interpretation. However, many natural systems involve interactions among three or more coupled state variables, raising the question of how to effectively describe their collective dynamics. In this work, we introduce an oscillator model that accommodates at least three mutually coupled state variables, each of which evolves on a circle. Consequently, the dynamics of the system are constrained to a 3-torus manifold ($T^3=S^1\times S^1\times S^1$) that allows analytical treatment of the distinct collective states. This framework reveals a variety of collective behaviors and offers broad applicability to systems in sociology, collective animal motion, neuroscience, and beyond.

In dynamical systems with a time-dependent parameter, i.e., parameter drift, after crossing a saddle-node bifurcation, the so-called ghost state formed by the disappeared equilibria or periodic orbit can influence transient dynamics, causing a delayed transition. This phenomenon has been investigated previously. However, the effect of chaotic ghosts on the critical transition in drifting systems has been less studied. In this paper, we explore how chaotic ghosts and drifting rates influence critical transitions from the perspective of the ensemble. The results reveal the mechanism of the delayed transition related to chaos and how trajectories on the initial ensemble composed of a chaotic attractor transition to a qualitatively different object during the drift. In addition, we quantify the delayed transition and further find that the delay follows a power-law scaling with respect to the drifting rate. Finally, we show that the critical transition is fully avoided as long as the reversal rate of the parameter exceeds a certain critical rate, even though the bifurcation point has been crossed.

The time-dependence of multipoint observable correlation functions are essential quantities in analysis and simulation of quantum dynamics. Open quantum systems approaches utilize two-point correlations to describe the influence of an environment on a system of interest, and in studies of chaotic quantum system, the out-of-time-ordered correlator (OTOC) is used to probe chaoticity of dynamics. In this work we analytically derive the time dependence of multipoint observable correlation functions in quantum systems from a random matrix theoretic approach, with the highest-order function of interest being the OTOC. We find in each case that dynamical contributions are related to a simple function, related to the Fourier transform of coarse-grained wave functions. We compare the predicted dynamics to exact numerical experiments in a spin chain for various physical observables. We comment on implications toward the emergence of Markovianity and quantum regression in closed quantum systems, as well as relate our results to known bounds on chaotic dynamics.

Permutation symmetry plays a central role in the understanding of collective quantum dynamics. By introducing power-law couplings that algebraically decay with the distance between the spins $r$ as $1/r^{\alpha }$, we break this symmetry with a nonzero $\alpha$. This allows us to probe the emergence of new dynamical behaviors, including thermalization in an otherwise permutation symmetric Hamiltonian with all-to-all spin interactions along the $x$ direction subjected to periodic kicks in the transverse direction. As we increase $\alpha$, the system interpolates from an infinite-range spin system at $\alpha =0$ exhibiting permutation symmetry to a short-range integrable model as $\alpha \to \infty$ where this permutation symmetry is absent. We focus on this change in the behavior of the system as $\alpha$ is tuned, using dynamical quantities such as total angular momentum and von Neumann entropy. Starting from the chaotic limit of the permutation symmetric Hamiltonian at $\alpha =0$, for the finite system sizes that are considered, we find that for small $\alpha$, the steady-state values of these quantities remain close to the permutation symmetric subspace values corresponding to $\alpha =0$. At intermediate $\alpha$ values, these show signatures of thermalization exhibiting values corresponding to that of random states in full Hilbert space. On the other hand, the large $\alpha$ limit approaches the values corresponding to the integrable kicked Ising model. In addition, we also study the dependence of thermalization on the driving period $\tau$, with results indicating the onset of thermalization for smaller values of $\alpha$ when $\tau$ is large, thereby extending the thermalizing window in the intermediate range of $\alpha$. We further confirm these results using effective dimension and spectral statistics.

Coarse-graining methods are crucial for characterizing complex systems across different levels of description. Inspired by renormalization group ideas, such approaches have been applied to structural compression studies in complex networks, where a Laplacian renormalization group based on spectral coarse graining has been shown to preserve the static properties of diffusion systems. However, their capacity to preserve dynamics in network reaction-diffusion (RD) systems remains underexplored. This paper addresses this gap by investigating network RD systems, particularly epidemic models. We propose a Laplacian renormalization group-inspired spectral coarse-graining scheme based on multiorder Laplacian matrix and validate its advantages in both random and empirical networks. Based on simplicial complexes, we construct a network susceptible-infected-recovered-dead system and employ Turing patterns as a testing platform to evaluate the preservation of dynamic behavior under coarse graining. The results demonstrate that the proposed method effectively preserves key dynamic behaviors, including the infected density distributions and the time required for stable pattern formation, while maintaining the necessary conditions for Turing instability. This preservation is achieved alongside a significant reduction in system complexity.

Genes are connected in complex networks of interactions where often the product of one gene is a transcription factor that alters the expression of another. Many of these networks are based on a few fundamental motifs leading to switches and oscillators of various kinds. And, yet, there is more to the story than knowing which transcription factors control these various circuits. These transcription factors are often themselves under the control of effector molecules that bind them and alter their level of activity. Traditionally, much beautiful work has shown how to think about the stability of the different states achieved by these fundamental regulatory architectures by examining how parameters such as transcription rates, degradation rates, and dissociation constants tune the circuit, giving rise to behavior such as bistability. Such studies, however, explore dynamics without asking how these quantities are altered in real time within living cells as opposed to at the fingertips of the synthetic biologist's pipette or on the computational biologist's computer screen. In this paper, we make a departure from the conventional dynamical systems view of these regulatory motifs by using statistical mechanical models to focus on endogenous signaling knobs such as effector concentrations rather than on the convenient but more experimentally remote knobs such as transcription rates, degradation rates, and dissociation constants. We also contrast the traditional use of Hill functions to describe transcription factor binding with more detailed thermodynamic models. This approach provides insights into how biological parameters are tuned to control the stability of regulatory motifs in living cells, sometimes revealing quite a different picture than is found using Hill functions and tuning circuit parameters by hand.

The locomotion of microorganisms near solid-liquid interfaces is of significant scientific interest due to its relevance in various natural and industrial contexts, including biofilm formation and marine biofouling. In this study, we investigate the swimming behavior of $C.\mathit{reinhardtii}$ near a sinusoidal wave-like microstructure. Using fluorescence microscopy and a three-dimensional tracking technique, we observe that the swimming direction of $C.\mathit{reinhardtii}$ is strongly influenced by the geometric constraints imposed by the microstructure. Our results reveal that cells preferentially accumulate at the valley of the microstructure rather than the peak and exhibit a directional swimming tendency in the vicinity of the microstructure. We attribute this behavior to a combination of the “memory effect” and hydrodynamic attraction. By modifying the geometry of the microstructure, we successfully achieve directed guidance of cell swimming, which demonstrates potential applications in micro and nanorobotics and antifouling technologies. This work provides alternative insights into the locomotion mechanisms of microorganisms near solid-liquid interfaces and underscores the potential for manipulating their behavior through microstructure design.

Neurons are notably rich in structure and functioning, so rather diverse in their response to stimuli. Consequently, the proper characterization of their dynamical response to external signals is a crucial step in understanding stimulation mechanisms. In particular, kilohertz (kHz) neuronal electrical stimulation tends to induce comportment and drives unseen in (more conventional) lower frequency ranges. Here, we investigate neuronal response of conductance-based models to kHz frequencies stimulation in a broad and often unexplored parameter space region. First, we show that the time evolution exhibited by the paradigmatic Hodgkin-Huxley model under kilohertz stimulation is highly diverse, ranging from regular spiking to chaotic dynamics, as well as displaying regions of complete activity suppression. However, to unveil all these features, a certain level of technical caution is required. For example, we demonstrate that common simplifications of sodium dynamics become inaccurate under these frequency regimes. Also, based on suitable markers, we propose a method for mapping the mentioned behaviors on a stimulation parameter space. Second, by extending the study to models of mammalian central nervous system regions, a comprehensive dynamical atlas is obtained. It provides a rather systematic way to typify the response of rapidly forced conductance-based neurons. Thus, the present findings seems to point to an useful scheme for stimulation-based computational neuroscience research at kilohertz frequencies.

The Madelung equations offer a hydrodynamic description of quantum systems, from single particles to quantum fluids. In this formulation, the probability density is mapped onto the fluid density and the phase is treated as a scalar potential generating the velocity field. As examples of potential flows, quantum fluids described in this way are inherently irrotational, but quantum vortices may arise at discrete points where the phase is undefined. In this paper, starting from this irrotational description of a quantum fluid, a coarse-graining procedure is applied to arrive at a macroscopic description of the quantum fluid in terms of a hierarchy of moments in which the role of velocity is played by a Favre average of the microscopic velocity field. This hierarchy is truncated using an explicit closure derived from an expansion in a finite length scale. The resulting coarse-grained fields are shown to allow for finite vorticity at any point in the fluid. Furthermore, it is shown that this vorticity obeys a similar equation to the vorticity equation in classical hydrodynamics and includes a vortex-stretching term. The particular closure employed here also gives rise to a novel stress term in the fluid equations, which in the appropriate limit appears analogous to an artificial viscous stress from computational fluid dynamics.

In this paper, based on the idea of directly discrete modeling using equilibrium distribution functions (EDFs), we develop a general framework of the mesoscopic numerical method for macroscopic partial differential equations (PDEs), including but not limited to the nonlinear convection-diffusion equation (NCDE) and the Navier-Stokes equations (NSEs). Unlike the mesoscopic lattice Boltzmann method, this kind of mesoscopic numerical method is an EDF-based mesoscopic finite-difference (MesoFD) scheme. The macroscopic version of the MesoFD (MMFD) method can be derived directly through taking the moments of the MesoFD scheme. Both MesoFD and MMFD schemes are multilevel FD methods and have the form of the central FD scheme. The macroscopic moment equations can be derived from either the MesoFD or MMFD scheme through the Taylor expansion method, and the common PDEs can be recovered from these moment equations by using the direct Taylor expansion method. Furthermore, the stability of the MMFD scheme is analyzed for the linear CDE and linear wave equation with anisotropic diffusion. The stability conditions of a two-level explicit MMFD scheme, a two-level $\theta$-MMFD scheme (hybrid explicit and implicit MMFD scheme) and a three-level MMFD scheme are obtained, respectively. Finally, we note that some existing lattice-Boltzmann-based macroscopic FD schemes for the NSEs and NCDE are the special cases of the present MMFD method, which can be considered as a unified framework of FD schemes for PDEs from this point of view.

This paper presents simulations of the physical aging of a binary Kob-Andersen-type Lennard-Jones liquid following large temperature up jumps from equilibrated states of high relaxation time. The purpose is to investigate how well the Tool-Narayanaswamy (TN) material-time concept works for this rather extreme case of aging. First, the triangular relation of the potential energy is investigated. This is found to be well obeyed, making it possible to define a potential-energy-based material time $\xi$. We proceed to study aging toward equilibrium at the final temperature 0.48 for jumps from the two temperatures 0.43 and 0.37 (primarily), monitoring the following five quantities: the potential energy, the self-intermediate scattering function, the mean-square displacement, the dynamic susceptibility ${\chi }_4$, and the non-Gaussian parameter ${\alpha }_2$. The TN material-time prediction is that all time-autocorrelation functions should collapse to only depend on the material-time difference ${\xi }_2-{\xi }_1$. This is found to work better for the $0.43\to 0.48$ temperature jump than for the $0.37\to 0.48$ jump. Our findings thus confirm the general understanding that the TN aging formalism works best for systems that are never very far from equilibrium. This raises two questions for future work: Is the collapse significantly improved if each aging quantity is allowed its own material time? Can better collapse be obtained if the material time is generalized to be locally defined (in order to reflect dynamic heterogeneity)?

We explore the use of the nested sampling technique to sample the configuration space of nonspherical hard particles. We employ the technique on the hard dumbbell system consisting of two hard spheres connected by a rigid bond, and investigate the phase stability across a wide pressure range and for bond lengths from completely overlapping to tangential hard spheres. Nested sampling recovers all previously identified features of the phase diagram and identifies a family of new packing variants. The fluid phase, plastic crystal, close-packed solid phases, and aperiodic crystal are all sampled, and the transition points between these are mapped. Our results show good agreement with predictions made by existing equations of state and former Monte Carlo simulations. Nested sampling also identified a close-packed structure with $Pnma$ symmetry which has not previously been considered.

We introduce and systematically investigate the generation of dispersive shock waves, which arise naturally in physical settings such as optical waveguide arrays and superfluids confined within optical lattices. The underlying physically relevant model is a nonlinear Schrödinger (NLS) equation with a periodic potential. We consider the evolution of piecewise smooth initial data composed of two distinct nonlinear periodic eigenmodes. To begin interpreting the resulting wave dynamics, we employ the tight-binding approximation, reducing the continuous system to a discrete NLS (DNLS) model with piecewise constant initial data (i.e., a Riemann problem), where each constant state represents a discrete Floquet-Bloch mode at the continuum model level. The resulting tight-binding approximation is shown to display higher fidelity for deeper periodic potentials. This reduced DNLS model effectively models the dynamics at the minima of the periodic potential of the original continuum NLS. Within such a single-band DNLS framework, we apply tools from Whitham modulation theory and long-wave quasicontinuum reductions to uncover and analyze a rich spectrum of nonconvex, discrete dispersive hydrodynamic phenomena, comparing the resulting phenomenology with that of the periodic-potential-bearing continuum model.

Regulation of contraction in striated muscle is controlled by a dual mechanism involving both thin filaments containing actin and thick filaments containing myosin. The thin filament is activated by calcium ions binding to troponin, leading to tropomyosin azimuthal displacement, which allows the activation of a regulatory unit (composed of one troponin, one tropomyosin, and seven actin monomers) that exposes the actin sites for interaction with the myosin motors. Motor attachment to actin contributes to spreading activation within and beyond a regulatory unit along the thin filament through a cooperative mechanism. We introduce a one-dimensional Ising model to elucidate the mechanism of cooperativity in thin filament activation in relation to the force generated by the attached myosin motor. The model characterizes thin filament activation and cooperativity using only two parameters: one related to calcium concentration and the other to the force exerted by the attached myosin motor, which is modulated by temperature. At any force, the model is able to determine the extent of actin-myosin interactions on a correlation length ranging from two to seven actin monomers, in addition to the seven actin monomers of the regulatory unit. Our theoretical predictions are successfully tested on experimental data, and our tests also include the condition of hindered filament activation by the use of the specific drug omecamtiv mecarbil (OM). According to our model, the effect of OM results in an anticooperativity mechanism accounting for the experimental data.

An analytical solution based on a diffuse-interface model is presented for an isothermal evaporation problem at subsaturated vapor pressure. The macroscopic equations are derived from the free-energy formulation widely used in the lattice Boltzmann literature, distinguishing our approach from conventional evaporation models that rely on jump conditions or purely kinetic theory. The interface behavior is fully described by differential equations, eliminating the need for assumptions such as local thermodynamic equilibrium at the interface. We derive an exact analytical solution for the inviscid case and propose an approximate solution that accounts for viscous effects. Our model reveals a relationship between evaporation rate and viscosity within the diffuse-interface framework. The analytical results are validated against numerical simulations using the open-source parallel library openlb, demonstrating excellent agreement within the framework of diffuse-interface methods.