Recurrent neural networks (RNNs) have recently been extensively applied to model the time evolution in fluid dynamics, weather predictions, and even chaotic systems due to their ability to capture temporal dependencies and sequential patterns in data. Here we present an RNN model based on convolutional neural networks for modeling the nonlinear nonadiabatic dynamics of hybrid quantum-classical systems. The dynamical evolution of the hybrid systems is governed by equations of motion for classical degrees of freedom and von Neumann equation for electrons. The Physics-Aware Recurrent Convolution (PARC) neural network structure incorporates a differentiator-integrator architecture that inductively models the spatiotemporal dynamics of generic physical systems. We apply our RNN approach to learn the space-time evolution of a one-dimensional semiclassical Holstein model after an interaction quench. For shallow quenches (small changes in electron-lattice coupling), the deterministic dynamics can be accurately captured using a single-CNN-based recurrent network. In contrast, deep quenches induce chaotic evolution, making long-term trajectory prediction significantly more challenging. Nonetheless, we demonstrate that the PARC-CNN architecture can effectively learn the statistical climate of the Holstein model under deep-quench conditions.

Foam coarsening refers to the process by which gas diffuses between bubbles, leading to an increase in their average size and a corresponding evolution of the foam's physical properties. When foam is confined within a porous medium, this process can continue, albeit in a modified manner. Anticipating the rate of coarsening under such conditions is therefore crucial. In this study, we examine the coarsening dynamics of liquid foam confined within a packing of spherical grains, systematically varying both the grain size and the foam's liquid fraction, in the range of 7% to 25%. Our key finding is that, under confinement, the coarsening rate is much less sensitive to the liquid fraction than in bulk foams. Instead, the dynamics are more strongly governed by the ratio of bubble size to grain size. This behavior is well captured by a model based on the effective liquid fraction—a measure that accounts for the substantial amount of liquid retained at grain surfaces and contacts in the form of liquid bridges. Additionally, we observe numerous small, persistent bubbles located at the periphery of the liquid bridges. These structures act as hosts, facilitating the accumulation of such bubbles, particularly at higher liquid fractions. Depending on the context, this phenomenon may be either advantageous or detrimental to the intended application.

Power and efficiency are fundamental criteria for evaluating the performance of thermodynamic cycles. However, it is generally impossible to maximize both simultaneously. In particular, achieving maximum efficiency inevitably leads to vanishing power as the cycle duration approaches infinity. A quantitative characterization of this trade-off yields significant theoretical and practical implications. In this Letter, we analytically derive an exact bound constraining power and efficiency in low-dissipation finite-time heat engines. This bound specifies the maximum power attainable at any prescribed efficiency, thereby providing a benchmarking for evaluating the performance of heat engines.

While quantum measurements have been shown to constitute a resource for operating quantum thermal machines, the nature of the energy exchanges involved in the interaction between system and measuring apparatus is still under debate. In this work, we show that a microscopic model of the apparatus is necessary to unambiguously determine whether quantum measurements provide energy in the form of heat or work. We illustrate this result by considering a measurement-based refrigerator, made of a double quantum dot embedded in a two-terminal device, with the charge of one of the dots being continuously monitored. Tuning the parameters of the measurement device interpolates between heat- and work-fueled regimes with very different thermodynamic efficiency. Notably, we demonstrate a trade-off between a maximal thermodynamic efficiency when the measurement-based refrigerator is fueled by heat and a maximal measurement efficiency quantified by the signal-to-noise ratio in the work-fueled regime. Our analysis sheds light on the nature of the energy exchanges occurring during a quantum measurement, paving the way for energy optimization in quantum protocols and quantum machines.

The theory of diffusion seeks to describe the motion of particles in a chaotic environment. Classical theory models individual particles as independent random walkers, effectively forgetting that particles evolve together in the same environment. Random walks in a random environment models treat the environment as a random space-time field that biases the motion of particles based on where they are in the environment. We provide a universality result for the moderate deviations of the transition probability of this model over a wide class of choices of random environments. In particular, we show the convergence of moments to those of the multiplicative noise stochastic heat equation, whose logarithm is the Kardar-Parisi-Zhang equation. The environment only filters into the scaling limit through one parameter, which depends explicitly on the statistical description of the environment. This forms the basis for our introduction, in Hass et al. [Phys. Rev. Lett. 133, 267102 (2024)], of the extreme diffusion coefficient.

Lattice-based random walk models are widely used to study populations of migrating cells with motility bias and proliferation. Crowding is typically represented by volume exclusion, where each lattice site can be occupied by at most one agent and conflicting moves are aborted. This framework enables simulations that yield both population-level spatiotemporal agent density profiles and individual agent trajectories, comparable to experimental cell-tracking data. Previous continuum models for tagged-agent trajectories captured trajectory information only, and overlooked any measure of variability. This is an important limitation since trajectory data is inherently variable. To address this limitation, here we derive partial differential equations for the probability density function of tagged-agent trajectories. This continuum description has a clear physical interpretation, agrees well with distributional data from stochastic simulations, reveals the role of stochasticity in different contexts, and generalizes to multiple subpopulations of distinct agents.

The Spectral Form Factor (SFF) is defined for Hermitian matrices as the modulus squared of the partition function in complex temperature, with a suitable generalization existing in the non-Hermitian case. In this work, we study the properties of what we refer to as the quenched SFF, namely the logarithm of the SFF and in particular its average, and compare them with those of its ordinary (annealed) counterpart, namely the average of the SFF (and eventually its logarithm). While the SFF is famously not self-averaging, the opposite is true for the quenched SFF, in both the Hermitian and non-Hermitian cases. Nonetheless, the quenched and the annealed averages coincide up to subleading constants, at least for high enough temperatures. The fluctuations of $ln\mathrm{SFF}$ are deep and one encounters thin spikes when moving close to a zero of the partition function. In order to study the fluctuations of the quenched SFF at late times we consider a suitable change of variable of $ln\mathrm{SFF}$ which turns out to be compatible with a Gumbel distribution. We note that the exponential tail of this distribution can indeed be obtained by sampling the deep spikes of $ln\mathrm{SFF}$, namely the Fisher zeros of the partition function. We compare with the results obtained in isolated many-body systems and we show that same results hold at late times also for non-Hermitian Hamiltonians and non-Hermitian random matrices.

We discuss the statistics of additive thermal (internal) noise in systems governed by the generalized Langevin equation with linear dissipation. To assess the equation's validity, it is common to assume that the system is ergodic and to verify that solutions approach correct equilibrium values at asymptotically long times. In this paper, we instead consider the consistency of the generalized Langevin equation with the Jarzynski equality at finite times and do not assume the system's ergodicity. Specifically, we consider a classical Brownian oscillator whose initial stiffness, or frequency, is perturbed by a rectangular pulse of duration $\tau$. We find that the Jarzynski equality is satisfied unconditionally only up to the seventh order in $\tau$; in higher orders, the Jarzynski equality holds if and only if the noise is Gaussian. These results imply that, unless it is exact, the Langevin equation can only be used to evaluate properties that are linear or quadratic in noise and its derivatives. Such properties are insensitive to the noise statistics, so the Langevin equation with linear dissipation and non-Gaussian noise (though not inconsistent by itself) is superfluous.

Dark solitons and interactions are investigated in nonlocal media under the condition of fourth-order diffraction (FOD). In the case of weak nonlocality or rectangular nonlocal response function, analytical solutions of dark solitons are obtained via Lagrangian (variational) method. Numerical results show that solitons are unstable (stable) when FOD is anomalous (normal). Interactions of dark soliton with FOD are described analytically with an interacting potential and confirmed by numerical simulations. With the help of attractive force originated from strong degree of nonlocality and anomalous FOD, bound states of dark solitons are generated, otherwise they are always repulsive.

Phylogenetic trees capture evolutionary relationships among species and reflect the forces that shaped them. While many studies rely on branch length information, the topology of phylogenetic trees—–particularly their degree of imbalance—–offers a robust framework for inferring evolutionary dynamics when timing data are uncertain. Classical metrics, such as the Colless and Sackin indices, quantify tree imbalance and have been extensively used to characterize phylogenies. Empirical phylogenies typically show intermediate imbalance, falling between perfectly balanced and highly skewed trees. This regime is marked by a power-law relationship between subtree sizes and their cumulative sizes, governed by a characteristic exponent. Although a recent niche-size model replicates this scaling, its mathematical origin and the exponent's value remain unclear. We present a generative model inspired by Kingman's coalescent that incorporates nichelike dynamics through preferential node coalescence. This process maps to Smoluchowski's coagulation kinetics and is described by a generalized Smoluchowski equation. Our model produces imbalanced trees with power-law exponents matching empirical and numerical observations, revealing the mathematical basis of observed scaling laws and offering new tools to interpret tree imbalance in evolutionary contexts.

Assembling reacting molecules (“targets”) into clusters slows down the kinetics of their reactions with mobile particles from a solution due to competition between the targets. Recently, we used a simple probabilistic approach to predict the dependence of this slowing down on the structures of clusters and on the energy barriers for reactions. Within this approach, the key parameters that define the kinetic effect of clustering are “double-visiting” probabilities: the probabilities that a random-walking “searching” particle that visited one target would visit some other target before diffusion to the bulk solution. The kinetic effect of clustering is defined by the entire set of pairwise double-visiting probabilities for all targets within the cluster that depends on the cluster geometry. The greater the double-visiting probabilities, the stronger the kinetic effect of clustering. Now we generalized our approach to systems that oscillate between active and nonactive states, such as reactants switching between steric conformations, or nanopores (channels) switching between the open and closed states. We also considered the impact of a drift of searching particles on the kinetic effect of clustering. We show that in the presence of a drift, starting from some critical distance equivalent to the ratio of the effective diffusion coefficient and the characteristic velocity of the drift, the double-visiting probabilities decay as the inverse square of the distance between the targets (or, in some cases, as the inverse of the distance to the power of 3/2), in contrast to a slower decay as the inverse of the distance in the absence of a drift. The faster decay of the double-visiting probabilities with the distance in the presence of a drift makes the kinetic effect of clustering smaller, i.e., the drift can partially suppress the kinetic effect of clustering. Our results could be applicable to natural biological systems (e.g., receptors and channels on the cellular membranes), and to technological procedures (e.g., reactions with the targets tethered together or attached to solid supports).

We study experimentally how the double-twist (DT) configuration of cylindrically confined lyotropic chromonic liquid crystals (LCLCs) responds to axial magnetic fields. Our director field model unveils the energetics behind the magnetic-field-induced transition in the twist profile of the DT configuration. Additionally, we catalog three different types of topological defects—residing between the DT domains of opposite handedness—before and after the field application, and propose a new director field model for the defect with a ring disclination. Lastly, we report a symmetry-breaking instability occurring when the field strength exceeds a critical value, suggesting an eccentric DT director field model that reproduces a helixlike optical texture. Our systematic investigation not only enhances our understanding of LCLC energetics but also provides potential for precise control over DT configurations.

Brownian motion with stochastic resetting—a process combining standard diffusion with random returns to a fixed position—has emerged as a powerful framework with applications spanning statistical physics, chemical kinetics, biology, and finance. In this study, we investigate the mutual correlations among three global characteristic times for one-dimensional resetting Brownian motion $x\left(\tau \right)$ over the interval $\tau \in [0,t]$: the occupation time $t_o$ spent on the positive semiaxis, the time $t_m$ at which $x\left(\tau \right)$ attains its global maximum, and the last-passage time $t_{\ell }$ when the process crosses the origin. For the process starting from the origin and undergoing Poissonian resetting back to the origin, we analytically compute the pairwise joint distributions of these three times (in the Laplace domain) and derive their pairwise correlation coefficients. Our results reveal that these global times display rich correlations, with a nontrivial dependence on the resetting rate $r$. Specifically, we find that (i) while $t_o$ and $t_{\ell }^m$ are uncorrelated for any positive integer $m$, $t_o^2$ and $t_{\ell }^m$ display anticorrelation, (ii) a positive correlation exists between $t_o$ and $t_m$, which decays toward zero following a logarithmically corrected power law with an exponent of $-2$ as $r\to \infty$, and (iii) the correlation between $t_m$ and $t_{\ell }$ shifts from positive to negative as $r$ increases. All analytical predictions are validated by extensive numerical simulations.

Extraction of useful work from the chaotic environments remains a captivating challenge. A gear in the bath of self-propelling eccentric particles is investigated by computer simulation. We find that the asymmetrical gear can rotate in a specific direction, with the angular speed first increasing and then decreasing as the eccentricity increases. Besides, a machine-learning model is trained to predict the angular speeds and the optimal one. Additionally, we observe that the directional rotation of a symmetric gear depends on the particle-area fraction, the persistence length of motion, and the eccentricity. Eccentricity is not conducive to the rotation of a symmetric gear, but a small degree of eccentricity can help increase the angular speed of the gear. There exist two mechanisms working for gear rotation at low eccentricity of particles: edge alignment with corner trapping and biased trapping with positive feedback. These insights suggest the tunable particle-level parameter, eccentricity, offers a promising strategy to regulate and optimize gear rotation.

Introduced by Boltzmann under the name “monode,” the microcanonical ensemble serves as the fundamental representation of equilibrium thermodynamics in statistical mechanics by counting all possible realizations of a system's states. Ensemble theory connects this idea with probability and information theory, leading to the notion of Shannon-Gibbs entropy and, ultimately, to the principle of maximum caliber describing trajectories of systems—in and out of equilibrium. While the latter phenomenological generalization reproduces many results of nonequilibrium thermodynamics, given a proper choice of observables, its physical justification remains an open area of research. What is the microscopic origin and physical interpretation of this variational approach? What guides the choice of relevant observables? We address these questions by extending Boltzmann's method to a microcanonical caliber principle and counting realizations of a system's trajectories—all assumed equally probable. Maximizing the microcanonical caliber under the imposed constraints, we systematically develop generalized local detailed-balance relations, clarify the statistical origins of inhomogeneous transport, and provide an independent derivation of key equations from stochastic thermodynamics. This approach introduces a dynamical ensemble theory for nonequilibrium steady states in spatially extended and active systems. While verifying the equivalence of ensembles, e.g., those of Norton and Thévenin, our framework contests other common assumptions about nonequilibrium regimes, with supporting evidence provided by stochastic simulations. Our theory suggests further connections to the first principles of microscopic dynamics in classical statistical mechanics, which are essential for investigating systems where the necessary conditions for thermodynamic behavior are not satisfied.

The partial synchronization states of collective activity, as well as the spike avalanches realization in systems of interacting neurons, are extremely important distinguishing features of the neocortical circuits that have multiple empirical validations. However, at this stage, there is a limited number of studies highlighting their potential interrelationship at the level of nonlinear mathematical models. In this study, we investigate the development of chimera states and the emergence of spike avalanches in superdiffusive neural networks, as well as analyze the system's approach to quasicriticality. The analysis of the available ideas suggests that partial synchronization states, spike avalanches, and quasicritical neuronal dynamics are all directly implicated in core cognitive functions such as information processing, attention, and memory. Given this fundamental role, the results presented in this work could have significant implications for both theoretical neuroscience and applied machine learning, particularly in the development of reservoir computing systems.

Disease spreading models such as the ubiquitous SIS compartmental model and its numerous variants are widely used to understand and predict the behavior of a given epidemic or information diffusion process. A common approach to imbue more realism to the spreading process is to constrain simulations to a network structure, where connected nodes update their disease state based on pairwise interactions along the edges of their local neighborhood. Simplicial contagion models (SCM) extend this to hypergraphs such that groups of three nodes are able to interact and propagate the disease along higher-order hyperedges (triangles). Though more flexible, it is not clear the extent to which the inclusion of these higher-order interactions results in dynamics that are characteristically different from those attained from simpler pairwise interactions. Here, we propose an agent-based model that unifies the classical SIS/SIR compartmental model and SCM, and extends it to allow for interactions along hyperedges of arbitrary order. Using this model, we demonstrate how the steady-state dynamics of pairwise interactions can be made to replicate those of simulations that include higher-order topologies by linearly scaling disease parameters based on a proposed measure of network activity. By allowing disease parameters to dynamically vary over time, lower-order pairwise interactions can be made to closely replicate both the transient and steady-state dynamics of higher-order simulations. We demonstrate that this relationship is robust to misspecification in the assumed higher-order interaction model, and applies to non-clique complex hypergraphs with nontrivial heterogeneous topology. For the latter case, it is found that heterogeneities in hypergraph topology result in weakened approximations of higher-order dynamics by pairwise interactions.

We propose a method for the laser-excitation of terahertz surface magnetoplasmons via the linear mode conversion of terahertz radiation on a graphene sheet deposited on an $n$-type semiconductor in the presence of an external magnetic field parallel to the semiconductor surface. An obliquely incident $p$-polarized laser beam interacting with the graphene–$n$-InSb semiconductor surface imparts linear oscillatory velocity to the free electrons. This oscillatory velocity couples with the modulated electron density to generate a linear current density, which resonantly excites terahertz surface magnetoplasmons. It is shown that the amplitude of a terahertz surface magnetoplasmon wave can be tuned by adjusting the external magnetic field $\left({\text{B}}_0\right)$, the graphene's Fermi energy $\left(E_F\right)$, the semiconductor's temperature $\left(T\right)$, and the incident angle $\left(\theta \right)$ of laser. This mechanism has the potential to enable the development of an actively tunable plasmonic device.

Uhlenbeck and Ornstein presented their theory of a passive Brownian particle in a harmonic potential in 1930. Despite intensive research on active Brownian particles since the 1990s, a complete theory of their inertial motion in a confining force field has yet to be developed. Here, we present rigorous calculations of the steady-state position and velocity autocorrelation functions of an active (self-propelled) Brownian particle with translational and rotational inertia in a two-dimensional harmonic trap. Our results show that the well-known active Ornstein-Uhlenbeck particle inertial model can be used as an approximated treatment of the dynamics of a fully inertial active Brownian particle in a trap, but only within a relatively small range of system parameters. Beyond this range, rotational inertia significantly impacts particle dynamics. In particular, for sufficiently strong confinement, the theory predicts a new mode of active particle dynamics that differs radically from all known dynamical modes of trapped active and passive Brownian particles. In this case, rotational inertia suppresses the oscillatory behavior of the mean-square displacement evolution function, resulting in additional quasiballistic motion. We discuss possible experimental implementations of this dynamical mode.

We investigate the impact of random pinned disorder on a collection of self-propelled particles. To achieve this, we construct a continuum model by formulating the coupled hydrodynamic equations for slow variables: local density and momentum density of particles. The disorder in the system acts as pinning sites, effectively immobilizing the particles that come into contact with them. Our numerical results reveal that weak disorder leads to phase separation in the system at density and activity lower than the typical values for motility-induced phase separation. We construct a phase diagram using numerical simulations as well as linearized approximation in the plane of activity and packing fraction of particles at weak disorder densities. On increasing disorder density, the system shows the microphase separation, while at large disorder densities the system becomes heterogeneous and eventually undergoes kinetic arrest. The structure factor tail deviates from Porod's law, indicating increased roughness at domain interfaces under strong disorder. Furthermore, we analyze the fractal dimension of the interface as a function of disorder density, highlighting the increasing irregularity of phase-separated domains. We also find that disorder significantly suppresses number fluctuations in the system.