In this paper, we consider a dynamic version of the Chung-Lu random graph in which the edges alternate between being present and absent. The main contribution concerns a technique by which one can estimate the underlying dynamics from partial information, in particular from snapshots of the total number of edges present. The efficacy of our inference method is demonstrated through a series of numerical experiments.

The spin-chemical radical pair mechanism (RPM) has emerged as a leading theory for explaining the biological effects of low-intensity magnetic fields. These intriguing effects occur when the quantum system of radicals is well isolated from the disturbing influence of the environment. In other words, these effects are closely related to the spin coherence relaxation time $\tau$, but an explicit relationship has not yet been established. In our study, we found an analytical solution to the Liouville-Neumann equation for an open system made up of two electrons and one nucleus, considering minimal interactions while concentrating on spin relaxation and chemical kinetics. This solution, supported by numerical integration, highlights the crucial role of quantum coherence. A straightforward expression is proposed that describes the RPM effect as a function of $\tau$, within the ranges of magnetic field strength $H$ and rate $\kappa$ of chemical kinetics relevant to magnetobiology. Our findings reveal that RPM effects become significant only when fundamental relation $\gamma H\tau >1+\kappa \tau$ holds: it controls the magnitude of the effects, and it is consistent with the principles of spin chemistry. Additionally, by comparing our results with existing experimental data, we estimate that the plausible spin decoherence times in magnetosensitive radical pairs within cryptochromelike proteins range from units to tens of nanoseconds. The effects of radio-frequency magnetic fields at the nT level were also examined, taking into account decoherence. These effects turned out to be negligible and incapable of disrupting the RPM patterns. The role of the quantum Zeno effect in magnetobiology is inspected from the perspective of the $\tau$ dependence of the RPM effect.

Systems influenced by Gaussian white noise, Poisson white noise, and periodic excitation are common in many engineering and scientific applications, making accurate response prediction essential. Poisson noise introduces impulsive jumps, while high-frequency from the periodic excitation adds complexity, highlighting the need for a new approach to address these combined challenges. In this paper, we propose a novel deep learning framework, the radial-basis-function neural network (RBF-NN), specifically designed to resolve high-frequency oscillatory solutions in the transient probability density function (PDF) of systems under combined Gaussian white noise, Poisson white noise, and periodic excitation. This method utilizes a single-layer network with uniformly distributed neurons, where the distribution matches that of the variables, and employs RBFs as activation functions. The physical information of the equation is used as a constraint to solve the corresponding forward Kolmogorov equation that governs the transient PDF. The presence of Poisson white noise results in the forward Kolmogorov equation being an integro-differential equation, making it challenging to solve. In this method, the Gauss-Legendre quadrature is used to efficiently compute the integrals. Additionally, the Monte Carlo (MC) method is employed to solve the normalization constraint, providing approximate solutions through random sampling. Several numerical examples demonstrate the efficacy of the RBF-NN, which significantly outperforms standard Physics-Informed Neural Networks (PINNs) and PINNs with periodic layer (P-PINNs) in both computational efficiency and accuracy, especially in high-frequency scenarios. RBF-NN expands the applicability of PINNs under Gaussian white noise, Poisson white noise, and high-frequency periodic excitation. Furthermore, the influence of neuron spacing and the shape parameter on the performance and accuracy of the RBF-NN method is investigated. The effects of Poisson noise intensity and frequency of periodic excitation on the three models are explored, with clear advantages of the RBF-NN method demonstrated in handling composite stochastic noise with high frequency.

Fluctuation-dissipation relations elucidate the response of near-equilibrium systems to environmental changes, with recent advances extending response theory to nonequilibrium steady states. However, a general response theory for systems evolving far from steady states has remained elusive. This letter presents a complete trajectory information geometric framework that generalizes response theory for nonstationary Markov processes. By constructing the full trajectory probability manifold and identifying a globally orthogonal coordinate system defined by transition rates, we derive a diagonal Fisher information metric that enables explicit calculations in this high-dimensional space. From the local metric structure, we obtain a Cramér-Rao-type inequality that bounds the linear response of arbitrary nonstationary observables. Furthermore, by analyzing the global geometry of this manifold, we derive a universal nonperturbative (nonlinear) response inequality in terms of geodesic length. This geometric framework reveals deep connections between dynamical activity, observable variance, and system sensitivity, and it encompasses or anticipates several recent results as special cases. Our approach offers new design principles for responsive behaviors in far-from-equilibrium systems.

The Fisher information (FI) metric is a Riemannian metric that allows a geometric treatment of stochastic thermodynamics, introducing the possibility of computing thermodynamic lengths and deviations from equilibrium. At the trajectory level, a related quantity can be introduced, the stochastic Fisher information (SFI), which, on average, is equivalent to the FI. In this work, we discuss two fundamental questions regarding the SFI; namely, (i) what is the thermodynamic interpretation of the SFI, and (ii) are there any trajectory-level thermodynamic bounds. We find that, contrary to previous results in the literature for the FI, the thermodynamic interpretation of the SFI depends only on the entropy produced by the system and on the thermodynamic force. Moreover, we find that the SFI allows one to derive single-trajectory speed limits, which we demonstrate to hold for a Brownian particle under a saturating drive force and a Brownian particle under a decreasing drive force. From the ensemble of single-trajectory bounds, one can derive a hierarchy of average speed limits that are always less tight than the one derived from the FI. We test our results for speed limits on the adopted models and find that the hierarchy of average speed limits is respected and that the single-trajectory speed limits behave qualitatively similar to the average and stochastic speed limits, with some trajectories achieving velocities higher than the tightest average bound whenever it does not saturate. Our results open avenues for the exploration of uncertainty relations at the trajectory level.

We study random dichotomous stationary ergodic processes with nonlocal in-time memory. These processes are characterized by a conditional transition probabilities distribution containing an integral term involving the memory function, which takes into account the past of the process. For the first time, we present a method for solving the integro-differential equation, which connects the arbitrary memory and pair correlation functions in an analytical closed form. Conditions of stationarity for the telegraph process with exponential memory are found. It is shown that the pair correlation function of this process can be of two types: either exponentially decreasing with two different decrements or oscillating with exponentially decreasing amplitude.

We study how spatiotemporal chaos in dynamical systems can be controlled by stochastically returning them to their initial conditions. Focusing on discrete nonlinear maps, we analyze how key measures of chaos—the Lyapunov exponent and butterfly velocity, which quantify sensitivity to initial perturbations and the ballistic spread of information, respectively—are reduced by stochastic resetting. We identify a critical resetting rate that induces a dynamical phase transition, characterized by the simultaneous vanishing of the Lyapunov exponent and butterfly velocity, effectively arresting the spread of information. These theoretical predictions are validated and illustrated with numerical simulations of the celebrated logistic map and its lattice extension. Beyond discrete maps, our findings are applicable to virtually any chaotic extended classical many-body system.

We present a two-loop field-theoretic analysis of incompressible helical magnetohydrodynamics (MHD) in fully developed stationary turbulence. A key feature of helical MHD is the appearance of an infrared-unstable “masslike” term in the loop diagrams of the magnetic response function. Physically, this term corresponds to the relevant perturbation of the Joule damping, proportional to $\mathbf{\nabla }\times \mathit{b}$ ($\mathit{b}=$ magnetic field). Its presence destabilizes the trivial ground state $\langle \mathit{b}\rangle =0$ and forces us to look for a mechanism for stabilizing the system. We show that such stabilization can be achieved in two ways: (i) by introducing into induction equation an external masslike parameter that precisely cancels these dangerous loop corrections (kinematic regime), or (ii) via spontaneous breaking of the rotational symmetry, leading to a new ground state with nonzero large-scale magnetic field (turbulent dynamo regime). For the latter case, we study the two-loop correction to the spontaneously generated magnetic field and demonstrate that Goldstone-like corrections to Alfvén modes along with some other anisotropic structures arise. Our results also confirm that the emergent mean magnetic field leads to a steeper slope of the magnetic energy spectrum, $-11/3+2{\gamma }_{b★}$ (with ${\gamma }_{b★}=-0.1039-0.4202{\rho }^2$, for $\left|\rho \right|⩽1$ as the degree of helicity), compared to the Kolmogorov velocity spectrum of $-11/3$, thereby breaking equipartition.

We consider a one-dimensional array of particles interacting via an infinite well potential. We explore the properties of energy spreading from an initial state where only a group of particles has nonzero velocities, while others are at rest. We characterize anomalous diffusion of the active domain via moments and entropies of the energy distribution. Only in the special cases of a single-well potential (hard-particle gas) and when the distance between particles is half the potential width, does diffusion exhibit a single scale; otherwise, multiscale anomalous diffusion is observed.

Time nonlocality, or memory, is a nonequilibrium property shared by all physical systems. Here, we show that memory is sufficient to induce a phase of spatial long-range order (LRO) even if the system's primary dynamical variables are coupled locally. This occurs when the memory degrees of freedom have slower dynamics than the primary degrees of freedom. In addition, such an LRO phase is nonperturbative, and can be understood through the lens of a correlated percolation transition of the fast degrees of freedom mediated by memory. When the two degrees of freedom have comparable time scales, the length of the effective long-range interaction shortens. We exemplify this behavior with a model of locally coupled spins and a single dynamic memory variable, but our analysis is sufficiently general to suggest that memory could induce a phase of LRO in a much wider variety of physical systems.

To bypass the reliance on local observables in verifying the eigenstate thermalization hypothesis (ETH), we introduce an observable-independent measure of distinguishability based on the variance of a rescaled local operator. We establish a universal trade-off relation between the diagonal and off-diagonal elements of this measure, rigorously connecting it to eigenstate typicality and spatially averaged observables. This trade-off reveals that exponential growth in the number of off-diagonal terms enforces their suppression, indirectly constraining diagonal deviations. Numerical simulations on a one-dimensional Ising spin chain with tunable transverse and longitudinal fields demonstrate stark contrasts between integrable and non-integrable regimes: While off-diagonal elements are universally suppressed with system size, diagonal suppression fails in integrable systems due to the absence of chaotic dynamics. Our results unify subsystem ETH, weak ETH, and macroscopic observables under a single framework, offering new insights into thermalization mechanisms.

A quasi-irrotational approximation is used to calculate the growth rate of the Rayleigh-Taylor instability in uniformly accelerated elastic or viscous layers, which, in addition to the unstable interface, also have a free surface. The approximation yields simple and analytical expressions for the growth rate which are still very accurate. In the limiting case of semi-infinite media, for which the well-known results of the purely irrotational approximation are retrieved, the maximum error is about $11–15\%$, and the accuracy progressively improves for finite thickness layers becoming exact in the very thin limit. This excellent agreement with the exact growth rate obtained by normal modes would indicate that vorticity, while introducing a considerable complexity in the mathematical problem, does not play a very significant role in the development of the instability.

Deformation of material lines drives transport and dissipation in many industrial and natural flows. Here, we report an exact Eulerian formula for the stretching rate of a material line, also known as the topological entropy, in a prototype two-dimensional fluid. The only requirement is a distribution of eigenvalues of the strain rate tensor and their decorrelation time. This eliminates the need for Lagrangian tracking in experimental turbulence where particle trajectories are entangled, and thus poorly resolved. Numerical simulations reveal an excellent agreement between our Eulerian estimate and the stretching rate of a Lagrangian material line, over a wide range of Reynolds number.

The transport of energetic particles in the heliosphere is profoundly influenced by interactions with coherent structures in the turbulent magnetic field of the solar wind, particularly current sheets. While prior studies have largely relied on idealized turbulence models, this work quantifies the role of solar wind current sheets (quasi-1D plasma structures characterized by strong magnetic field gradients) in driving pitch-angle scattering. We present an analytical Hamiltonian framework coupled with test particle simulations, informed by observational data from the ARTEMIS and Wind missions, to model particle dynamics through current sheets with realistic parameters. Our results demonstrate that the scattering efficiency depends critically on the current sheet's shear angle, the relative magnitude of the magnetic field component directed along the normal to the current sheet surface, and the ratio of the particle gyroradius to the current sheet thickness. Large pitch-angle jumps, arising from nonadiabatic separatrix crossings in phase space, lead to rapid chaotization, whereas diffusive scattering broadens the pitch-angle distributions. Statistical analysis of solar wind current sheets at 1 AU reveals significant scattering rates for 100 keV to 1 MeV protons, with implications for particle transport mechanisms. The derived diffusion rates enable the inclusion of coherent structures into global transport models for a more accurate modeling of energetic particle dynamics in the heliosphere. These findings underscore the importance of current sheets in shaping energetic particle spatial distributions and provide practical methods for incorporating them in space and astrophysical plasmas.

In this paper, the theoretical model of weak decaying collective excitations characteristic of many-particle systems with long-range interaction potentials is developed using the example of one-component strongly coupled Yukawa plasmas. The proposed model is based on the self-consistent relaxation theory of collective dynamics and covers spatial scales from extended hydrodynamics to scales related to the mean interparticle distance. The theoretical model reproduces the dynamic structure factor spectra and the corresponding dispersion characteristics in agreement with molecular dynamics simulation data without using any fitting parameters. In the limit of small wave numbers, the correspondence of the proposed theoretical model with the damped harmonic oscillator model is established. The simple analytical expression for the sound attenuation coefficient of strongly coupled Yukawa plasmas is obtained.

Building upon the Integer Lattice Gas Automata framework of Blommel and Wagner [Phys. Rev. E 97, 023310 (2018)], we introduce a simplified, fluctuation-free variant. This approach relies on floating-point numbers and closely mirrors the Lattice Boltzmann Method (LBM), with the key distinction being a different collision operator. This operator, derived from the ensemble average of transition probabilities, generates nonlinear terms. We propose this float lattice gas automata collision as a computationally efficient alternative to traditional and quantum LBM implementations.

We study the self-assembly of magnetic colloids using the Stockmayer (SM) model characterized by short-range Lennard-Jones interactions and long-range dipole-dipole interactions. Using molecular dynamics simulations, we design cooling protocols that yield perfectly assembled single-domain magnetic crystals. We identify cooling rates at which the system transforms from an amorphous glass to a crystal, where magnetic ordering promotes crystalline order. Remarkably, we observe that the latter develops via a spontaneous transition rather than through the traditional nucleation and growth mechanism. For a weakly dipolar fluid ($\mu =1$), this self-assembly results in a face-centered cubic (FCC) colloidal crystal with dipole moments chained along the (111) direction. For fluids with higher dipole moment ($\mu =2.5$), the crystal structure shifts toward a body-centered orthorhombic (BCO) arrangement due to the compression of chains from strong dipolar attractions. These results provide valuable insights into the mechanisms driving crystallization in magnetic fluids, opening new avenues for understanding the formation of magnetically responsive colloidal magnetic crystals with promising applications.

The framework of partial information decomposition (PID) unveils complex nonlinear interactions in network systems by dissecting the mutual information (MI) between a target variable and several source variables. PID measures have been formulated mostly for discrete variables, with only recent extensions to continuous systems. In the case of mixed variables where the target is discrete and the sources are continuous, the application of existing PID schemes requires the manipulation of the data generated by the analyzed system, thus altering their information content. To overcome this issue, we introduce a PID scheme whereby the MI between a specific state of the discrete target and (subsets of) the continuous sources is expressed as a Kullback-Leibler divergence and is estimated through a nearest-neighbor strategy. The effectiveness of this PID is demonstrated in simulated systems of mixed variables and on benchmark data. Our approach is relevant to many scientific problems, including sensory coding in neuroscience and feature selection in machine learning.

Large language models show a surprising in-context learning ability—being able to use a prompt to form a prediction for a query, yet without additional training, in stark contrast to old-fashioned supervised learning. Providing a mechanistic interpretation and linking the empirical phenomenon to physics are thus challenging and remain unsolved. We study a simple yet expressive transformer with linear attention and map this structure to a spin glass model with real-valued spins, where the couplings and fields explain the intrinsic disorder in data. The spin glass model explains how the weight parameters interact with each other during pretraining, and further clarifies why an unseen function can be predicted by providing only a prompt yet without further training. Our theory reveals that for single-instance learning, increasing the task diversity leads to the emergence of in-context learning, by allowing the Boltzmann distribution to converge to a unique correct solution of weight parameters. Therefore, the pretrained transformer displays a prediction power in a prompt setting. The proposed analytically tractable model thus offers a promising avenue for thinking about how to interpret many intriguing but puzzling properties of large language models.