We present an inequality that bounds the short-term memory capability of dynamical systems from below. It can be interpreted as an uncertainty relation between a measure of short-term memory and that of the size of state fluctuations induced by input signals. The lower bound can be achieved by a readout weight and thus represents a suboptimal memory called harmonic memory. We examine analytically and numerically the inequality in a number of reservoir systems subject to input noise. We illustrate cases in which equality is achieved exactly, equality holds asymptotically, and the inequality is strict. We also study the effect of a state-space regularization to elucidate the inequality in terms of the fluctuation structure of the state-space. We find that a certain strength of input noise induces extra memory under the regularization, and we refer to this phenomenon as noise-induced memory. We observe that the memory uncertainty relation does not hold in general for the regularized memory and harmonic memory. This fact is explained in terms of the mechanism of noise-induced memory.

By extending the Sanchez-Lacombe lattice-fluid model for mixtures to the case of polymer blends containing solid fillers, we calculate the excess thermodynamic quantities arising from the presence of fillers. These results are then used to derive the spinodal stability condition of a filled polymer blend. In the low-compressibility limit, this condition reduces to a remarkably simple analytical expression that is derived self-consistently within the present framework. Comparison between the exact and approximate spinodal curves shows excellent agreement, with deviations in the spinodal temperature of less than $4\mathrm{K}$, thereby validating the proposed approximation. The obtained analytical approximation enables a straightforward evaluation of the spinodal temperature without the extensive numerical calculations required to determine the exact spinodal condition. Both the exact and approximate spinodal conditions yield good quantitative agreement with experimental data for filled and unfilled blends.

This Letter uncovers five distinct charge transport modes and their transitions in dual-energy electron beam diodes. We via first-principle particle-in-cell (PIC) simulations establish that the specific mode (e.g., space-charge oscillations) and the current transmitted characteristics are essentially governed by the interplay between the electron beam energy and the injected current density. The effective space-charge-limited (SCL) current (lower than the conventional SCL threshold) is unveiled due to the coupled interactions between two electron beams. A generalized analysis is conducted for $n$-component electron beams, and a theoretical piecewise function for the transmitted current density is proposed, which agrees well with the PIC results under designed conditions. The discovery provides a mechanistic picture of multiple electron beam transport in diodes, paving the way for novel designs of high-performance modern vacuum electronic devices.

In complex media, transport and geometric properties deeply influence the kinetics of random encounters between reactants. Here, we consider the situation in which a random walker, moving in a regularly diffusing medium, has to reach and activate a target located inside a compartment characterized by fractal (obstructed) subdiffusion. We focus on dual-site reactions, which end when two activation events occur within a given time window. Each activation event happens with a finite probability whenever the random walker visits the target. For weakly reactive targets, we demonstrate that the reaction time can be minimized for an optimal compartment size and can even be accelerated when compared to the same system without a compartment. Our analytical predictions are validated through simulations of a random walker on a cubic lattice, where some sites inside the compartment are obstructed at the critical percolation threshold. Our theory illustrates the fact that adding a crowded compartment around a target, even if it slows down the motion in its vicinity, can accelerate the kinetics of complex reactions, especially for weakly reactive targets.

Two remote agents with synchronized clocks may use them to act in concert and communicate. This necessitates some means of creating and maintaining synchrony. One method, not requiring any direct interaction between the agents, is to expose them to a common, environmental, stochastic forcing. This “noise-induced synchronization” occurs only under sufficiently mild forcing; stronger forcing disrupts synchronization. We investigate the regime of strong noise, where the clocks' relative phases evolve chaotically. Using a simple realization of disruptive noise, we demonstrate effective synchronization. First, although the relative phases of the two clocks varied erratically, we confirm that they became statistically independent of initial conditions and hence equivalent after a well-defined timescale. Second, we show that an agent can estimate an effective phase that closely agrees with the other's phase. Thus, synchronization is practically attainable beyond the regime of conventional noise-induced synchronization.

Human mobility, enabled by diverse transportation modes, is fundamental to urban functionality. Studying these movements across scales—from microscopic to macroscopic—yields valuable insights into urban dynamics. Local adaptation and (self-)organization in such systems are expected to result in dynamical behaviors that are represented by stationary trajectories of an appropriate effective action. In this study we develop a Lagrangian dynamical model for movement processes, using local population functions as the coordinate variables. An efficient gradient descent algorithm is introduced to estimate the optimal Lagrangian parameters minimizing a local error function of the dynamical process. We show that even a quadratic Lagrangian, incorporating dissipation, effectively captures the dynamics of synthetic and empirical movement data. The inferred models reveal that inertia and dissipation are of comparable importance, while interactions and randomness in the movements induce significant qualitative changes in model parameters. Our results provide an interpretable and generative model for human mobility, with potential applications in movement prediction.

We investigate the self-diffusiophoretic motion of a catalytically active spherical particle confined within a wedge-shaped domain. Using the Fourier-Kontorovich-Lebedev transform, we solve the Laplace equation for the concentration field in the diffusion-dominated regime. The method of images is employed to obtain the first and second reflections of the concentration field, accounting for both monopole and dipole contributions of the particle's surface activity. Based on these results, we derive leading-order expressions for the self-induced phoretic velocity in the far-field limit and examine how it varies with the wedge opening angle and the particle's position within the domain. We focus on the contributions to the phoretic velocities arising from phoretic interactions, without accounting for hydrodynamic effects. Our findings reveal that the wedge geometry significantly affects both the magnitude and direction of particle motion. Our study provides a systematic framework for calculating the contributions to the phoretic velocity arising from concentration disturbances near corners, with implications for microfluidic design and control of autophoretic particles in confined geometries.

We study the self-propulsive motion of Janus rectangular rods with high aspect ratios ($\ge 5$), emphasizing the influence of morphological anisotropy on their dynamics. These metallodielectric rods self-propel via induced-charge electrophoresis (ICEP), moving perpendicular to their long axis. The pronounced anisotropic shape gives rise to distinct behaviors, including a discontinuous transition in translational mode, self-entrapment at small obstacles, and self-excited oscillations when trapped. Our findings highlight the pivotal role of shape in determining the motion and interactions of microscale active agents, with implications for the design and control of active matter systems and microengineered devices.

The coherent Ising machine (CIM) is a nonconventional hardware architecture for finding approximate solutions to large-scale combinatorial optimization problems. It operates by annealing a laser gain parameter to adiabatically deform a high-dimensional energy landscape over a set of soft spins, going from a simple convex landscape to the more complex optimization landscape of interest. We address how the evolving energy landscapes guides the optimization dynamics against problems with hidden planted solutions. We study the Sherrington-Kirkpatrick spin-glass with ferromagnetic couplings that favor a hidden configuration by combining the replica method, random matrix theory, the Kac-Rice method and dynamical mean-field theory. We characterize energy, number, location, and Hessian eigenspectra of global minima, local minima, and critical points as the landscape evolves increasing the laser gain. We find that low-energy global minima develop soft modes which the optimization dynamics can exploit to descend the energy landscape. Even when these global minima are aligned to the hidden configuration, there can be exponentially many higher-energy local minima that are all unaligned with the hidden solution. Nevertheless, the annealed optimization dynamics can evade this cloud of unaligned high-energy local minima and descend near to aligned lower-energy global minima. Eventually, as the landscape is further annealed, these global minima become rigid, terminating any further optimization gains from annealing. We further consider a second optimization problem, the Wishart planted ensemble, which contains a hidden planted solution in a landscape with tunable ruggedness. We describe CIM phase transitions between recoverability and nonrecoverability of the hidden solution. Overall, we find intriguing relations between high-dimensional geometry and dynamics in analog machines for combinatorial optimization.

We explore the framework based on the Kirkwood-Dirac quasiprobability distribution to quantify the contribution of coherence to work extraction during generic, cyclic quantum evolutions. In particular, we focus on “anomalous processes,” counterintuitive scenarios in which, due to the negativity of the quasiprobability distribution, work can be extracted even when individual processes are associated with energy gain. Applying this framework to qubits undergoing sequences of single- and two-qubit gate operations, we identify specific conditions under which such anomalous work exchanges occur. Furthermore, we analyze the quasiprobabilistic structure of deep quantum circuits and establish a compositional relation linking the work statistics of full circuits to those of their constituent gates. Our work highlights the role of coherence in the thermodynamics of basic elements of quantum computation and provides a foundation for systematically studying potential thermodynamic relevance of specific quantum circuits.

For continuous-time Markov jump processes on irreducible networks with time-independent rate constants, we employ a transition-based formalism to express the long-time precision of a single integrated current over an observable channel in terms of precisions of the recurrence times of the forward and backward jumps, and of an effective affinity that captures the thermodynamic driving on that channel. This leads to a general inequality that, similarly to the well-known thermodynamic uncertainty relation (TUR), links the stationary entropy production rate with the fluctuations of an integrated current, but also incorporates the statistics of the forward and backward recurrence times. Such inequality can be saturated in less-restrictive conditions than the TUR, and potentially offers new opportunities for the optimization and design of biological and chemical out-of-equilibrium systems at the nanoscale.

The master stability function (MSF) formalism provides a powerful framework for analyzing the stability of the synchronization manifold (SM) in networks of coupled oscillators, yielding a necessary condition for synchronization. In this work, we show that the MSF approach naturally extends to dynamical systems possessing rotation symmetry. As a representative case, we consider the Lorenz system, which is invariant under the transformation $(x,y,z)\mapsto (-x,-y,z)$. This corresponds to a rotation symmetry in which $z$ is the invariant variable. We demonstrate that coupling oscillators through an invariant variable preserves the validity of the MSF formalism and leads to the coexistence of multiple SMs, all of which are governed by the same MSF for stability determination. These results highlight how some symmetries can lead to the emergence of multiple SMs and extend the range of collective behaviors that can be analyzed within the MSF framework.

Higher-order interactions have recently emerged as key determinants of collective dynamics in complex networks, driving phenomena such as synchronization and multistability. However, how different higher-order groups interact and jointly shape global behavior remains poorly understood. Here, we introduce the model of hyperorder interactions (HpOI), a framework that captures competitive and cooperative couplings between higher-order groups. Using numerical simulations of real-world networks (neural, social, and natural systems) and theoretical analysis based on the Ott-Antonsen method, we reveal a nonmonotonic effect of HpOI on synchronization stability. Cooperative HpOI consistently enlarges the synchronization region. By contrast, the effect of competitive HpOI depends on the overlap among higher-order groups: under low overlap, strong competition can also enhance synchronization stability, whereas under high overlap, it suppresses global synchronization. This work incorporates coupling between higher-order groups into higher-order networks and provides insights into structure-function coupling within real-world systems.

The brain criticality hypothesis has largely only characterized brain dynamics in terms of their self-similarity, although experimental evidence suggests that the brain exhibits significant multifractality. To understand how multifractality may emerge in critical-like systems modeling neuronal activity, we used a neural field model exhibiting neural oscillations and a critical phase transition. We find that multifractality emerges near a synchronization phase transition, and that the pattern of variation in multifractality changes when placing the model at a different phase transition. These findings show that multifractality in temporal dynamics emerges near criticality in neural fields, providing a formal basis for interpreting multifractality in brain recordings.

Understanding how structural organization shapes dynamical performance is essential for designing efficient multilayer infrastructures. As modern transportation systems become increasingly multimodal, integrating layers with distinct connectivity patterns raises a fundamental yet underexplored question: How should structurally heterogeneous layers be arranged to maximize global traffic capacity? To address this, we develop a multilayer framework with heterogeneous intralayer connectivity and examine how different choices of which layer occupies the structural core affect overall transport efficiency. A notable phenomenon emerges: placing the structurally strongest layer at the core does not always deliver the best performance. Although this arrangement enhances path efficiency when within-layer traffic dominates, increasing cross-layer flow causes the strongly connected core to become the first bottleneck, sharply reducing capacity. Beyond a critical regime, positioning the weakest layer instead at the core becomes the superior strategy, as it naturally disperses load across layers and mitigates congestion. This performance reversal arises from a fundamental trade-off between path efficiency and load balancing, governed by bottleneck migration across layers. A theoretical framework based on effective betweenness accurately predicts these transitions and matches extensive simulations. Importantly, the positioning effect remains robust across varying degrees of heterogeneity, network scales, and representative network topologies. These results establish layer positioning as a universal and tunable structural mechanism, offering guidance for the design of multilayer communication and transportation systems.

Vegetation in arid and semi-arid ecosystems often exhibits self-organized spatial patterns as a collective adaptation to water limitation. While reaction-diffusion models have successfully captured such pattern formation, the influence of individual-level traits, particularly root phenotypic plasticity, whereby plants adjust root architecture in response to environmental conditions, remains underexplored. Here, we develop a minimal reaction-diffusion framework that integrates vertical soil stratification with adaptive root conversion to explain the coexistence of multiple spatial scales commonly observed in dry-land vegetation. Building on the single-layer model of Hardenberg et al. [Phys. Rev. Lett. 87, 198101 (2001)], we introduce a second soil layer and a unidirectional biomass conversion from shallow- to deep-rooted phenotype. Analytical and numerical analyses reveal that strong contrasts in diffusion scales, coupled with adaptive conversion, generate two coexisting Turing modes that give rise to robust multiscale vegetation structures. Shallow-rooted biomass with higher diffusivity forms broad vegetation bands, whereas deep-rooted biomass with lower diffusivity clusters at finer scales. The proposed framework provides a mechanistically transparent and ecologically grounded model for multiscale pattern formation, linking adaptive plant traits with the physics of coupled soil-water interactions.

Diffuse interface methods for multiphase flow simulations often exhibit nonphysical droplet or bubble shrinkage, particularly when based on the Cahn-Hilliard equation. This well-known artifact introduces a critical radius below which droplets vanish, thereby limiting the fidelity of simulations involving small-scale structures. In this study we examine a conservative Allen-Cahn model and demonstrate, through both analytical and numerical investigations, that it inherently avoids this shrinkage behavior. We show that the conservative Allen-Cahn model enforces an exact local balance of interfacial terms, enabling the stable preservation of droplets with radii larger than the interface thickness, regardless of the initial droplet size or domain geometry. Our analysis also provides a different theoretical treatment of the shrinkage phenomenon in the Cahn-Hilliard equation, distinguishing itself from earlier works by providing a rigorous explanation of why conservative Allen-Cahn models avoid this problem. The analysis reveals that conservative Allen-Cahn formulations achieve exact cancellation of curvature-driven terms through a local geometric force balance, while Cahn-Hilliard models exhibit systematic shrinkage due to unbalanced curvature effects that create driving forces for mass transport. Theoretical and numerical findings show that there is a shrinkage relation between interface radius $r_I$ and time $t$ in the form of $r_I^3\left(t\right)\sim -t$, which leads to a power law $t_f\propto r_0^3$ for the disappearance time $t_f$ versus initial radius $r_0$. Numerical experiments across a wide range of droplet sizes corroborate the theoretical predictions. These results position the conservative Allen-Cahn model as a robust and accurate phase-field approach, particularly well suited for applications demanding the resolution of fine features or long-time integration, such as multiphase transport in porous media.