Using the framework of generalized exclusion processes, we study mixtures of passive and active particles interacting by steric repulsion. The particles move in a pore with a periodically modulated aperture, which is modeled by a quasi-one-dimensional channel with a periodic tooth-shaped profile. Internal driving of the active particles induces a ratchet current of these particles. In the current-density diagram, we observe three main regimes: of free flow, of thermally activated processes, and of spinodal decomposition. When the density of particles is increased, we observe a transition to a jammed state, where the ratchet current is substantially reduced. In time evolution, the transition to a jammed state is seen as a sudden drop of current at a certain time. The probability distribution of these jamming times follows an exponential law. The average jamming time depends exponentially on the density of active particles. The coefficient in this exponential is nearly independent of the switching rate of the active particles as well as the presence or absence of passive particles. Due to the interaction, the current of active particles imposes a drag on the passive particles. In the limit of both large systems and long times, the current of passive particles always has the same direction as the ratchet current of active particles. However, during the evolution of the system, we observe a very slow (logarithmic in time) approach to the asymptotic value, sometimes accompanied by current reversal, i.e., the current of active and passive particles may go in opposite directions.

We formulate models of segmental relaxation in glasses and supercooled liquids in terms of Poisson processes and stochastic resetting and analyze their properties. This mathematical language allows us to set forth clear, consistent definitions for the various terms used throughout the literature on glassy dynamics. We provide useful algorithms for stochastic simulations of such models and show how they may be properly parameterized from time autocorrelation functions (ACFs), obtained by either simulation or experiment. Interestingly, we find that the time derivative of an ACF provides considerable insight into the distribution of relaxation times or rates and is, therefore, the primary object of analysis. These results allow for physically and mathematically robust modeling of segmental dynamics in molecular and polymeric glasses.

We introduce a stochastic method for simulating the effect of an external magnetic field on coarse-grained models of magnetic colloids for use in discontinuous molecular dynamics (DMD) simulations. Our method for simulating an external field is illustrated with a coarse-grained model for magnetic squares in two dimensions. Square-shaped particles are represented as four disks bonded together in a 2×2 lattice configuration to create a hard colloidal geometry. Two opposite charges are embedded within the square to mimic the magnetic interactions between particles. The method for simulating an external field stochastically during DMD simulations operates by applying impulses randomly to the charges embedded within each square particle. When one square experiences an interaction with the field, each embedded charge within the square is assigned a new momentum with a specific magnitude and orientation. The magnitude of this momentum is equal to the average of a Maxwell-Boltzmann distribution at the simulation temperature. The orientation of the momentum depends on the charge, either positive or negative, and points either in the same or opposite direction as the field, respectively. The strength of the external field is determined by the average frequency at which the particles experience interactions with the field. The relationship between the stochastic frequency of the field and the field strength is derived from Newton's equation of motion. DMD simulations are performed for large systems of magnetic square particles at various temperatures and external field strengths. The simulation temperature is maintained constant with an Andersen thermostat, while the external field is simulated stochastically, as described above. We find that our simulation techniques reproduce a net system magnetization in close agreement with the two-dimensional equivalent of the Langevin function, while maintaining the simulation temperature constant.

The coarsening process is driven by the reduction in interfacial energy density, resulting in an enlargement of the size scale within two-phase systems. It plays a crucial role in the stability and the aging of densely packed arrangements of particles, which are commonly found in alloys, foams, emulsions, supersaturated solutions, etc. It has been shown previously that, when properly confined, such particles undergo the so-called anticoarsening phenomenon, ultimately leading to the one particle-per-pore configuration associated with the arrest of coarsening. In this study, we quantitatively explore the coarsening dynamics of liquid foam confined within the pores of spherical bead packings, where the size of the beads has been adjusted to modify the degree of confinement. We observe that, apart from the final configuration associated with the arrest of coarsening, the more we confine this system within small spaces, the more rapidly it coarsens. Moreover, the broadening of the particle size distribution has an opposite effect with respect to that observed for unconfined systems. This unexpected behavior is shown to arise from the coupling between the liquid trapped at the surface of the grains and the effective liquid volume fraction within the core of the pores.

The one-dimensional spin-1/2 XXZ model with the limited case of the staggered Gamma interaction which includes the staggered DM and KSEA interactions is investigated by utilizing the infinite-time evolving block decimation method in the infinite matrix product state representation. It is shown that the staggered DM interaction does not lead to any new phase but expands the XY phase. Contrasted to the DM interaction, the region of the ferromagnetic phase expands into the nematic-ferromagnetic and dimer-Haldane phases with the deconfined quantum phase transition happening in the case of KSEA interaction. We observe a pronounced effect in the entanglement entropy and Schmidt gap, the odd-bond and even-bond von Neumann entropies exhibit different values, and the value of the Schmidt gap on the even bond becomes zero in the dimer-Haldane phase. This implies that quantum entanglement and the Schmidt gap can distinguish the two degenerate ground states caused by the existence of dimerized interaction. The zero value of the Schmidt gap works as a sign of the topological phase, which is also evidenced by the string correlation. From the perspective of magnetism, the existence of chiral order and nematic order suggests the helical magnetic structure induced by Gamma interaction. By comparing the DM and KSEA interactions, it is found that DM interaction does not change ferromagnetism, whereas the KSEA interaction inhibits ferromagnetism and destroys the product state in the ferromagnetic phase. Furthermore, the behaviors of the spin structure factor for the transversal spin correlation can distinguish different phases. From an appropriate fitting exponent of the spin correlation oscillating decay, commensurate or incommensurate phases can be identified.

Generative diffusion models apply the concept of Langevin dynamics in physics to machine learning, attracting a lot of interest from engineering, statistics, and physics, but a complete picture of inherent mechanisms is still lacking. In this paper, we provide a transparent physics analysis of diffusion models, formulating the fluctuation theorem, entropy production, equilibrium measure, and Franz-Parisi potential to understand the dynamic process and intrinsic phase transitions. Our analysis is rooted in a path integral representation of both forward and backward dynamics, and in treating the reverse diffusion generative process as a statistical inference, where the time-dependent state variables serve as a quenched disorder akin to that in spin glass theory. Our study thus links stochastic thermodynamics, statistical inference and geometry-based analysis together to yield a coherent picture of how the generative diffusion models work.

Periodically driven thermodynamic systems support stable nonequilibrium oscillating states with properties drastically different from equilibrium. They exhibit even more exotic features for low viscous drives, which is a regime that is hard to probe due to singular behavior of the underlying Langevin dynamics near vanishing viscosity. We propose a method, based on singular perturbation and Floquet theories, that allows us to obtain oscillating states in this limit. We then find two distinct classes of distributions, each exhibiting interesting features that can be exploited for a range of practical applicability, including cooling a system and triggering chemical reactions through weakly interacting driven environments.

We address the counting of level crossings for the generalized Brownian motion in which the motion of a Brownian particle (unbound as well as linearly bound) is governed by an integrodifferential stochastic equation with a memory dissipation kernel: the generalized Langevin equation. We suppose that the driving noise is internal and the fluctuation-dissipation relation holds. The most common assumption is that the driving noise is Gaussian, which allows us to make a complete analytical treatment of the whole problem, including crossing statistics. We obtain the general asymptotic behavior for regular driving noises having finite intensity and fast decaying correlations, as well as for fractional noises with long-time tail correlations and slow decay, which are related to anomalous diffusion. For the generalized Brownian oscillator we study the stationary (equilibrium) state and the approach to equilibrium.

The connection between measure theoretic optimal transport and dissipative nonequilibrium dynamics provides a language for quantifying nonequilibrium control costs, leading to a collection of thermodynamic speed limits, which rely on the assumption that the target probability distribution is perfectly realized. This is almost never the case in experiments or numerical simulations, so here we address the situation in which the external controller is imperfect. We obtain a lower bound for the dissipated work in generic nonequilibrium control problems that (1) is asymptotically tight and (2) matches the thermodynamic speed limit in the case of optimal driving. Along with analytically solvable examples, we refine this imperfect driving notion to systems in which the controlled degrees of freedom are slow relative to the nonequilibrium relaxation rate, and identify independent energy contributions from fast and slow degrees of freedom. Furthermore, we develop a strategy for optimizing minimally dissipative protocols based on optimal transport flow matching, a generative machine learning technique. This latter approach ensures the scalability of both the theoretical and computational framework we put forth. Crucially, we demonstrate that we can compute the terms in our bound numerically using efficient algorithms from the computational optimal transport literature and that the protocols we learn saturate the bound.

We present an analytical model of integrable turbulence in the focusing nonlinear Schrödinger (fNLS) equation, generated by a one-parameter family of finite-band elliptic potentials in the semiclassical limit. We show that the spectrum of these potentials exhibits a thermodynamic band/gap scaling compatible with that of soliton and breather gases depending on the value of the elliptic parameter $m$ of the potential. We then demonstrate that, upon augmenting the potential by a small random noise (which is inevitably present in real physical systems), the solution of the fNLS equation evolves into a fully randomized, spatially homogeneous breather gas, a phenomenon we call breather gas fission. We show that the statistical properties of the breather gas at large times are determined by the spectral density of states generated by the unperturbed initial potential. We analytically compute the kurtosis of the breather gas as a function of the elliptic parameter $m$, and we show that it is greater than 2 for all nonzero $m$, implying non-Gaussian statistics. Finally, we verify the theoretical predictions by comparison with direct numerical simulations of the fNLS equation. These results establish a link between semiclassical limits of integrable systems and the statistical characterization of their soliton and breather gases.

Synchronization analysis of real-world systems is essential across numerous fields, including physics, chemistry, and life sciences. Generally, the governing equations of these systems are unknown, and thus, the phase is calculated from measurements. Although existing phase calculation techniques are designed for oscillators that possess no spatial structure, methods for handling spatiotemporal dynamics remain undeveloped. The presence of spatial structure complicates the determination of which measurements should be used for accurate phase calculation. To address this, we explore a method for calculating the phase from measurements taken at a single spatial grid point. The phase is calculated to increase linearly between event times when the measurement time series intersects the Poincaré section. The difference between the calculated phase and the isochron-based phase, resulting from the discrepancy between the isochron and the Poincaré section, is evaluated using a linear approximation near the limit-cycle solution. We found that the difference is small when measurements are taken from regions that dominate the rhythms of the entire spatiotemporal dynamics. Furthermore, we investigate an alternative method where the Poincaré section is applied to time series obtained through orthogonal decomposition of the entire spatiotemporal dynamics. We present two decomposition schemes that utilize principal component analysis. For illustration, the phase is calculated from the measurements of spatiotemporal dynamics exhibiting target waves or oscillating spots, simulated by weakly coupled FitzHugh-Nagumo reaction-diffusion models.

Patterns, spatiotemporal ordered structures, are prevalent in diverse systems, arising from the emergence of complexity. Turing proposed a mechanism that involves a short-range activator and a long-range inhibitor to explain the formation of patterns, and patterns that satisfy this mechanism are called Turing patterns. Patterns with similar structures but not caused by the Turing mechanism are referred to as Turing-like patterns. In the absence of external influences, the structure of Turing patterns is generally determined by control parameters. In this study, we revealed that the structure of Turing-like patterns in discrete-time systems is only determined by the ratio of states in the initial conditions. As the ratio changes, the structure of patterns transitions from spots to labyrinth and eventually to inverse spots. We proposed the structure parameter for the quantitative description of the structure of the patterns. And the structure parameter is directly proportional to the ratio in the initial conditions. The mechanism underlying this structure control is attributed to the traversability of multiperiodic states in discrete-time systems, where each local point will go through all states in the periodic orbit. Our findings shed light on the pattern formation for Turing-like patterns in discrete-time systems.

We introduce a model of an optical cavity based on the one-dimensional Lugiato-Lefever (LL) equation, which includes the pump represented by a symmetric pair of tightly localized “hot spots” (HSs) with phase shift $\chi$ between them, and self-focusing or defocusing cubic nonlinearity. Families of bound states, pinned to the double HS, are found in the system's parameter space. They feature the effect of the symmetry breaking (SB) between peaks pinned to individual HSs, provided that the phase shift takes values $0<\chi <\pi$, and the LL equation includes the loss term. The SB, which is explained analytically, takes place in the full LL model and its linearized version alike. The same phenomenology is also explored in the framework of the LL equation with the double HS and quintic self-focusing. In that case, there are stable symmetric and asymmetric bound states, in spite of the presence of the background instability driven by the critical collapse.

A stable limit cycle as a stabilized mechanical oscillation is the primary result of the dynamical evolution of an optomechanical system under a sufficiently powerful pump. Because this dynamical process is highly nonlinear, it was not clear whether there exists a quantitative law to relate an evolved mechanical oscillation (the limit cycle of the dynamical process) to the given parameters of the fabricated system. Here, by means of the numerical simulations based on nonlinear dynamics, we demonstrate the existence of such quantitative relations that are generally valid to the nonlinear optomechanical processes. These quantitative relations can be summarized to a scaling law that is seemingly similar to those in phase transitions of many-body systems but has very different properties. Such a quantitative law enables one to find the more feasible system parameters for realizing the same or a similar dynamical evolution result, so it will be useful to the relevant experimental research.

We investigate the nature of the transition to synchronization and death states in nonidentical Stuart-Landau oscillators adaptively coupled with pairwise and higher-order interactions. Our findings reveal that nonidentical Stuart-Landau oscillators globally coupled with higher-order interactions exhibit asynchronous oscillations. In contrast, systems coupled with pairwise interactions exhibit a continuous transition to synchronization. Introducing adaptation in pairwise interactions results in an explosive transition to synchronization. Furthermore, when the system is coupled with both pairwise and higher-order interactions, adaptation leads to an explosive transition to synchronization. For higher values of coupling strength, the coupled system also exhibits an explosive transition to the death state. Extending our analysis to random networks, we observe similar results. These findings align with the behavior observed in coupled Kuramoto oscillators, offering new insights into synchronization dynamics in complex systems with adaptive coupling and higher-order interactions.

We develop the off-lattice Eden model to simulate the growth of bacterial colonies in the three-dimensional geometry of a Petri dish. In contrast to its two-dimensional counterpart, our model takes a three-dimensional set of possible growth directions and employs additional constraints on growth, which are limited by access to the nutrient layer. We rigorously test the basic off-lattice Eden implementation against literature data for a planar cluster. We then extend it to three-dimensional growth. Our model successfully demonstrates the nontrivial dependency of the cluster morphology, nonmonotonous dependency of the cluster density, and power law of the thickness of the boundary layer of clusters as a function of the nutrient layer's height. Moreover, we reveal the fractal nature of all the clusters by investigating their fractal dimensions. Our density results allow us to estimate the basic transport properties, namely, the permeability and tortuosity of the bacterial colonies.

We study the calorimetric properties and structural relaxation of glassy films using a distinguishable particle lattice model (DPLM). We determine the glass transition temperature versus film thickness from the heat capacity during heating as well as from the local relaxation time. The results based on both approaches are in good agreement with the experimentally observed Keddie-Cory-Jones relation. The thus demonstrated interplay between calorimetric properties and structural relaxation is further corroborated by successfully reconstructing the simulated heat capacity during heat and cooling from the local relaxation times. Our results suggest DPLM as a useful lattice model for studying glassy films.

Employing extensive 2D contact dynamics simulations, we analyze the effects of grain shape angularity on the quasistatic shear strength properties of cohesive granular packings. We consider sticky irregular polygons ranging from disklike shapes to triangle. We find that the Mohr-Coulomb cohesion (i.e., the cohesive strength) is an increasing function of grain angularity. Meanwhile, the macroscopic friction angle increases with angularity and saturates for the most angular shapes, similar to dry cases. Using an effective stresslike approach, we show that the Mohr-Coulomb cohesion emerges from the cohesive force network for all shapes. From this, a micromechanical model reminiscent of the so-called “Rumpf” formula, is derived and reveals the increasing competition between the macroscopic friction, the anisotropy of the cohesive contacts network, and the grain shape parameter (i.e., the number of sides of the polygons) in the variation of Mohr-Coulomb cohesion with increasing angularity.

Using the electrostatic analogy, we derive an exact formula for the limiting Yang-Lee zero distribution in the random allocation model of general weights. This exhibits a real-space condensation phase transition, which is induced by a pressure change. The exact solution allows one to read off the scaling of the density of zeros at the critical point and the angle at which the locus of zeros hits the critical point. Since the order of the phase transition and critical exponents can be tuned with a single parameter for several families of weights, the model provides a useful testing ground for verifying various relations between the distribution of zeros and the critical behavior, as well as for exploring the behavior of physical quantities in the mesoscopic regime, i.e., systems of large but finite size. The main result is that asymptotically the Yang-Lee zeros are images of a conformal mapping, given by the generating function for the weights, of uniformly distributed complex phases.

Odd systems do not conserve energy, violate time-reversal symmetry, and remain far from equilibrium. How odd interactions between particles affect their diffusion remains unknown. To investigate this issue, we studied the diffusion and glass transition of a two-dimensional Kob-Andersen mixture, where Brownian particles interact via the Lennard-Jones potential and nonconservative odd forces. Our findings indicate a significant influence of odd interactions on the system's diffusion dynamics. Odd interactions always promote diffusion. These interactions lead to a nonmonotonic relationship between the effective diffusion coefficient and particle number density. Specifically, in systems with low oddness, the diffusion coefficient decreases steadily with increasing particle number density. Conversely, in systems with moderate oddness, an optimal particle number density exists that maximizes the diffusion coefficient. For systems with high oddness, we observe two distinct peaks in the diffusion coefficient-particle number density relationship. Furthermore, our investigation into the glass transition under dense conditions reveals that adjusting the oddness at low temperatures can induce a transition from a glassy state to a liquid state. Our findings offer a deeper insight into the diffusion processes in systems with odd interactions from a critical perspective.