Pinning down a precise understanding of information flow within physical interactions remains a central concern to fields such as stochastic thermodynamics and quantum information science. In both spheres a careful accounting of bits (or qubits) enables a deeper understanding of the physical nature of information. In this work we propose a measure of information flow as a saddle-point solution of the mutual information. This approach places a lower bound on the channel capacity between a particle and an interacting environment. The measure is given by ${\mathcal{P}}_0/2{\mathcal{E}}_0$ in nats/sec, with ${\mathcal{P}}_0$ the average power flux between the particle and its environment, and ${\mathcal{E}}_0$ the initial average energy of the particle, all computed in a frame where the particle has zero average momentum. We use a communication theory lens to suggest an associated channel analogy, in which this bound is interpreted as a signal-to-noise ratio. We find that this measure can also quantify early-time information flow for a particle interacting with a thermal bath.

Understanding the emergent macroscopic behavior of dynamical systems on networks is a crucial but challenging task. One of the simplest and most effective methods to construct a reduced macroscopic model is given by mean-field theory. The resulting approximations perform well on dense and homogeneous networks but poorly on scale-free networks, which, however, are more realistic in many applications. In this paper, we introduce a modified version of the mean-field approximation for voter model dynamics on scale-free networks. The two main deviations from classical theory are that we use degree-weighted shares as coarse variables and that we introduce a correlation factor that can be interpreted as slowing down dynamics induced by interactions. We observe that, for moderate noise and comparable interaction rates, the correlation factor is only a property of the network and not of the state or of parameters of the process. This approach achieves a significantly smaller approximation error than standard methods without increasing dimensionality.

The evolution of natural languages poses a riddle to any theoretical perspective based on efficiency considerations. If languages are already optimally effective means of organization and communication of thought, then why do they change? And if they are driven to become optimally effective in the future, then why do they change so slowly, and why do they diversify, rather than converge toward an optimum? We look here at the hypothesis that disorder, rather than efficiency, may play a dominant role. Most traditional approaches to study diachronic language dynamics emphasize lexical data, but it would seem that a crucial contribution to the effectiveness of a thought-coding device is given by its core generative structure, i.e., its syntax. Based on the reduction of syntax to a set of binary syntactic parameters, we introduce here a model of natural language change in which diachronic dynamics can stem from disordered interactions between/among parameters, even in the idealized limit of identical external inputs. We show in which region of “phase space” such dynamics show the glassy features that are observed in natural language across time. In particular, binary syntactic vectors remain trapped in glassy metastable (i.e., tendentially stable) states when the degree of asymmetry in the disordered interactions is below a critical value, consistent with studies of spin glasses with asymmetric interactions. We further show that an added Hopfield-type memory term would indeed, if strong enough, stabilize syntactic configurations even above the critical value, but losing the multiplicity of stable states. Finally, using a notion of linguistic distance in syntactic state space we show that a phylogenetic signal may remain among related languages, despite their gradually divergent syntax, exactly as recently pointed out for real-world languages. These statistical results appear to generalize beyond the dataset of 94 syntactic parameters across 58 languages used in this study.

Groups of cells, including clusters of cancerous cells, multicellular organisms, and developing organs, may both grow and break apart. What physical factors control these fractures? In these processes, what sets the eventual size of clusters? We first develop a one-dimensional framework for understanding cell clusters that can fragment due to cell motility using an active particle model. We compute analytically how the break rate of cell-cell junctions depends on cell speed, cell persistence, and cell-cell junction properties. Next, we find the cluster size distributions, which differ depending on whether all cells can divide or only the cells on the edge of the cluster divide. Cluster size distributions depend solely on the ratio of the break rate to the growth rate—allowing us to predict how cluster size and variability depend on cell motility and cell-cell mechanics. Our results suggest that organisms can achieve better size control when cell division is restricted to the cluster boundaries or when fracture can be localized to the cluster center. Additionally, we derive a universal survival probability for an intact cluster $S\left(t\right)=e^{-k_{d}t}$ at steady state if all cells can divide, which is independent of the rupture kinetics and depends solely on the cell division rate $k_d$. Finally, we further corroborate the one-dimensional analytics with two-dimensional simulations, finding quantitative agreement with some—but not all—elements of the theory across a wide range of cell motility. Our results link the general physics problem of a collective active escape over a barrier to size control, providing a quantitative measure of how motility can regulate organ or organism size.

Relativistic electrons colliding with intense counterpropagating laser pulses are expected to lose energy through radiation reaction. However, we reveal a counterintuitive regime where reflected leptons (including incident electrons, generated electrons, and positrons) gain significant energies when an ultraintense laser pulse interacts with counterpropagating electrons. Because of strong radiation reaction, these particles can be halted and reflected near the laser peak. The subsequent asymmetric laser field then accelerates the reflected leptons to energies far exceeding their initial values. Using three-dimensional particle-in-cell simulations, we demonstrate the generation and acceleration of quasimonoenergetic positrons to multi-GeV energies with a high number conversion efficiency employing forthcoming multipetawatt lasers, which provide conceptually a simple single-stage solution for positron creation and acceleration. The proposed mechanism of lepton acceleration is scalable to the astrophysical scenario and can be related to the origin of ultrahigh-energy cosmic rays in environments with intense fast radio bursts.

Understanding the self-propulsion behavior of active particles and predicting their trajectories is crucial for achieving desired paths by using external stimuli, such as chemical and thermal gradients, electric and magnetic fields, etc. This phenomenon plays a vital role in various fields, such as drug delivery, cargo transportation, and environmental remediation. In this regard, anisotropic magnetic microswimmers (platinum-coated core-shell cube particles) with different intrinsic magnetic strengths have been employed to study the self-propulsion trajectories under a geomagnetic field, using hydrogen peroxide as a fuel medium. Interestingly, these particles exhibit three different types of self-propulsion trajectories based on their intrinsic magnetic strength: random, meandering, and straight tracks, each with a distinct mean-squared displacement. The experimental and simulation studies revealed that the self-propulsion trajectories are determined by the interplay between rotational diffusivity ($D_R$) and characteristic magnetic frequency (${\omega }_c$) of the particle under the geomagnetic field. Where $D_R$ attempts to randomize the direction of the self-propelled particle, while the ${\omega }_c$ aligns the particles in the geomagnetic field direction by constraining the particle angle. This is further confirmed by using another shape of magnetic microswimmer (platinum-coated core-shell spherocylindrical particles), which show similar trajectory behavior for different ${\omega }_c$ values, confirming that the intrinsic magnetic strength of the particle defines the type of trajectories in the Earth's magnetic field. These distinct trajectories of magnetic active particles were characterized by the ratio of rotational diffusion time (${\tau }_R=D_R^{-1}$) and magnetic constraint time (${\tau }_M={\omega }_c^{-1}$), irrespective of particle shape. Where a particle with ${\tau }_R/{\tau }_M \ll 1$ shows a random trajectory, while a particle having ${\tau }_R/{\tau }_M \gg 1$ shows a straight trajectory, and for ${\tau }_R/{\tau }_M \approx 1$, the particle shows meandering-like trajectories. Finally, we have demonstrated the practical applicability of the core-shell magnetic particles by creating complex patterns with controlled fluctuations by using an external magnetic field.

Characterizing correlations in a quantum system on the basis of the results of the projective measurements can be performed with different means including the calculation of the classical mutual information. Generally, estimating such information-entropy-based quantities requires having complete statistics of the system's states. Here we explore the possibility to reconstruct the classical mutual information and specific entropy of a quantum system with a neural network approach on the basis of a limited number of projective measurements. As a prominent example we consider the antiferromagnetic quantum Ising model in transverse and longitudinal magnetic fields which is in demand in both condensed matter physics and quantum computing. We show that the neural network approach gives reliable estimates of the classical mutual information even in the case of paramagnetic wave functions delocalized in the state space. In addition, the phase diagram of the considered quantum system is reconstructed with a special focus on discriminating various types of disordered states.

We propose two methods for computing the large deviations of the first-passage-time statistics in general open quantum systems. The first method determines the region of convergence of the joint Laplace transform and the $z$ transform of the first-passage time distribution by solving an equation of poles with respect to the $z$-transform parameter. The scaled cumulant generating function, which is the logarithm of the boundary values within this region, is subsequently obtained. The theoretical basis is that the dynamics of open quantum systems can be unraveled into a piecewise deterministic process and that a tilted Liouville master equation exists in Hilbert space. The second method uses a simulation-based approach that is built on the wave-function cloning algorithm. To validate both methods, we derive analytical expressions for the scaled cumulant generating functions in field-driven two-level and three-level systems. In addition, we present numerical results and cloning simulations for a field-driven system comprising two interacting two-level atoms.

We investigate the role of frequency-weighted interactions in a solvable model of one-dimensional swarmalators confined to a ring, where both spatial and phase couplings are scaled by the heterogeneous natural frequencies of individual agents. Our analysis identifies three distinct collective states: the asynchronous state, the phase-wave state, and the bistrip mixed state characterized by antipodal clusters that are internally split into frequency-dependent substrips. We further establish that the onset of abrupt transitions are driven by heterogeneous coupling. Using a self-consistency analysis, we precisely determine the conditions for dynamical transitions among the identified states, thereby extending the theoretical understanding of swarmalator dynamics under heterogeneous interaction rules, which are in good agreement with the numerical simulation results.

An agent-based model of the economy is generalized to incorporate investment and guaranteed income mechanisms in addition to the exchange and distribution mechanisms considered in an earlier model. We use the tools of statistical physics to show that the system is effectively ergodic, is not in equilibrium, but reaches a steady state with occasional large fluctuations because of the effects of multiplicative noise from the investment mechanism. We find realistic wealth distributions and realistic values of the Gini coefficients and the Pareto index.

Most networks encountered in nature, society, and technology have weighted edges, representing the strength of the interaction or association between their vertices. Randomizing the structure of a network is a classic procedure used to estimate the statistical significance of properties of the network such as transitivity, centrality, and community structure. Randomization of weighted networks has traditionally been done via the weighted configuration model (WCM), a simple extension of the configuration model, where weights are interpreted as bundles of edges. It has previously been shown that the ensemble of randomizations provided by the WCM is affected by the specific scale used to compute the weights, but the consequences for statistical significance were unclear. Here we find that statistical significance based on the WCM is scale dependent, whereas in most cases results should be independent of the choice of the scale. A two-step approach, originally introduced for network reconstruction, in which one first randomizes the structure and then the weights, with a suitable distribution, restores scale invariance and allows us to conduct unbiased assessments of significance on weighted networks.

Focusing on the conservative/nonconservative physical information of infinite-dimensional dissipative system, the generalized multi-symplectic physics informed neural network (GMPINN) method is proposed to improve the reproducing ability of dissipative effects for the physics informed neural network (PINN) in this paper. The core idea of GMPINN is to embed the geometric structures of dissipative systems into the loss function, thereby preserving the geometric structures as well as intrinsic conservation laws of the physical system to reproduce the dissipative effects reliably. The above merits of GMPINN are illustrated in the simulations on the dissipative quantum tunneling problem formulated by the dissipative Schrödinger equation. In the simulations by using GMPINN, the influences of the dissipation coefficient and the square potential barrier thickness on the probability distribution are presented. From the numerical results, the inverse proportion laws between the dissipation coefficient/square potential barrier thickness and the probability distribution density on right side of the square potential barrier are found. Comparing with the effect of the square potential barrier thickness, it is found that the effect of the dissipation coefficient on the quantum coherence on the left side of the square potential barrier is more remarkable. The above findings illustrate the excellent ability of GMPINN in reproducing the dissipative effects of the nonconservative systems and give guidance on the parameter design of the devices based on the principle of the quantum tunneling effect.

Directional solidification of water-based solutions has emerged as a versatile technique for templating hierarchical porous materials. However, the underlying mechanisms of pattern formation remain incompletely understood. In this work, we present a detailed derivation and analysis of a quantitative phase-field model for simulating this nonequilibrium process. The phase-field model extends the thin-interface formulation of dilute binary alloy solidification with antitrapping to incorporate the highly anisotropic energetic and kinetic properties of the partially faceted ice-water interface. This interface is faceted in the basal plane normal to the $\langle 0001\rangle$ directions and atomically rough in other directions within the basal plane. On the basal plane, the model reproduces a linear or nonlinear relationship between the interface growth rate and the kinetic undercooling that can be linked to experimental measurements. In both cases, spontaneous parity breaking of the solidification front is observed when the preferred growth direction is aligned with the temperature gradient. This phenomenon leads to the formation of partially faceted ice lamellae that drift laterally in one of the $\langle 0001\rangle$ directions. We demonstrate that the drifting velocity of the ice lamellae is controlled by the kinetics on the basal plane and converges as the thickness of the diffuse solid-liquid interface decreases. Furthermore, we examine the effect of the form of the kinetic anisotropy, which is chosen here such that the inverse of the kinetic coefficient varies linearly from a finite value in the $\langle 0001\rangle$ directions to zero in all other directions within the basal plane, consistent with the assumption that the interface grows in local thermodynamic equilibrium in this plane. Our results indicate that the drifting velocity of ice lamellae is not affected by the slope of this linear relation, and the radius and undercooling at the tip of an ice lamella converge at relatively small slope values. Consequently, the phase-field simulations remain quantitative with computationally tractable choices of both the interface thickness and the slope assumed in the form of the kinetic anisotropy.

We study how disorder and finite temperature modify the indirect exchange interaction between magnetic impurities in one, two, and three dimensions by replacing the standard quadratic dispersion with a fractional dispersion ${\epsilon }_{\mathbf{k}}\sim k^{\alpha }$ (Lévy index $\alpha <2$ plays a role of the phenomenological disorder descriptor) in the thermal Green's function. In this fractional framework, increasing disorder suppresses and spatially localizes Friedel oscillations, while finite temperature further damps their amplitude and reduces the spatial and temporal coherence of the spin response, leading to an aperiodic, strongly attenuated behavior at large distances and long times. The resulting dynamic spin density exhibits a shortened interaction range, enhanced retardation, and features reminiscent of subdiffusive spin transport. We derive explicit relations between the generalized diffusion coefficient $D_{\alpha }$, the Lévy index $\alpha$, and microscopic parameters such as Fermi energy and carrier density, opening a route to experimentally determine these phenomenological quantities. Our results provide a compact description of disordered, thermally driven RKKY interactions and suggest practical strategies for tuning spin coupling in low-dimensional spintronic devices via temperature and controlled disorder.

Directional solidification of water-based solutions has emerged as a versatile technique to template hierarchical porous materials, but this nonequilibrium process remains incompletely understood. Here, we use phase-field simulations to shed light on the mechanism that selects the growth direction of the lamellar ice structure that templates those materials. Our results show that this selection can be understood within the general framework of spontaneous parity breaking, yielding quantitative predictions for the tilt angle of lamellae with respect to the thermal axis. The results provide a theoretical basis to interpret a wide range of experimental observations.

We study a generalized Ehrenfest urn model that interpolates between the Ehrenfest and voter dynamics through a mixing parameter $\alpha$. This model can be interpreted in two different ways: adding noise to the voter model, where $\alpha$ represents the intensity of the noise; or adding interaction to the Ehrenfest model, where $(1-\alpha )$ represents the level of the interaction. We focus on a thermodynamic limit where the system size $N\to \infty$ and $\alpha \to 0$ with $N\alpha$ held constant, and show that the stationary distribution converges to a $q$-Gaussian law. In this regime, the entropic index $q$ is determined explicitly by the constant $N\alpha$. The definition of $q$-Gaussians with compact support is extended to include boundary-singular but integrable densities, thereby allowing two equivalent representations: a compact-support and a real-line $q$-Gaussian, establishing a duality between them. Moreover, after a suitable change of variable, we prove that the extended version of the $q$-Gaussian is the symmetric beta distribution. The analysis also reveals an order-disorder phase transition structure, being the Cauchy's distribution, (supported on the entire real line); and the arcsine distribution, (their equivalent with compact support), the limit distributions when the susceptibility becomes maximal. These results provide a direct microscopic link between interacting urn models and generalized entropies.

Starting from the multispecies Boltzmann equation for a gas mixture, we propose the formal derivation of the isentropic two-phase flow model introduced in E. Romenski, D. Drikakis, and E. Toro [J. Sci. Comput. 42, 68 (2010)]. We examine the asymptotic limit as the Knudsen numbers approach zero, in a regime characterized by resonant intraspecies collisions, where interactions between particles of the same species dominate. This specific regime leads to a multivelocity and multipressure hydrodynamic model, enabling the explicit computation of the coefficients for the two-phase macroscopic model. Our derivation also accounts for the inclusion of the evolution of the volume fraction, which is a key variable in many macroscopic multiphase models.

We investigate the emergence of self-organized criticality (SOC) in the single-defect Olami-Feder-Christensen (OFC) model by quantifying the ordered phase and deriving theoretical phase boundaries. Using both square and honeycomb lattices, we analytically obtain expressions for the ordered-SOC transition boundary and the characteristic period, validating them against numerical simulations. The results show that while synchronization alone governs the transition to the ordered phase, the onset of SOC requires desynchronization triggered by supercritical toppling energies exceeding a certain threshold. These findings characterize the threshold-dependent nature of desynchronization under minimal inhomogeneity, providing a fundamental perspective that clarifies the mechanisms observed in the original OFC model.

In many biological systems, localized mechanical information is transmitted by mechanically neutral chemical signals. Typical examples include contraction waves in the actomyosin cortex at the cellular scale, and peristaltic waves at tissue level. In such systems, chemical activity is transformed into mechanical deformation by distributed motor-type mechanisms. To elucidate the underlying principles of chemomechanical coupling, we present the simplest example of a directional motion in a distributed mechanical system, guided by a purely chemical cue. It shows that localized mechanical signals can be driven by chemical activity in a highly efficient manner.