Excessive wealth concentration can undermine economic and social development. Random asset exchange models provide valuable tools to investigate this phenomenon. Assuming that economic systems may operate optimally near the critical point of a continuous phase transition, the extended yard sale (EYS) model introduced by Boghosian et al. [Physica A 476, 15 (2017)] offers a compelling framework. This model captures the interplay between wealth redistribution and accumulation, exhibiting a continuous phase transition marked by a broad wealth distribution at criticality, separating a condensed phase—where a microscopic fraction of agents holds a macroscopic share of total wealth—from a distributed phase with a light-tailed wealth distribution. While the original EYS model assumes fully connected interactions, this work introduces and studies a networked variant where agents interact over Erdős-Rényi random networks. The analysis combines Monte Carlo simulations with Quenched Mean Field and Mean Field approximations, exploring a variety of interaction and taxation schemes. A scaling analysis shows that, although the networked model also undergoes a continuous phase transition, it leads to local wealth condensation rather than the global condensation found in the fully connected case. These results deepen our understanding of wealth dynamics in structured populations and may help inform the development of more effective economic and social policies.

A primary technical challenge for harnessing fusion energy is to control and extract energy from a nonthermal distribution of charged particles. The fact that phase space evolves by symplectomorphisms fundamentally limits how a distribution may be manipulated. While the constraint of phase-space volume preservation is well understood, other constraints remain to be fully appreciated. To better understand these constraints, we study the problem of extracting energy from a distribution of particles using area-preserving and symplectic linear maps. When a quadratic potential is imposed, we find that the maximal extractable energy can be computed as trace minimization problems. We solve these problems and show that the extractable energy under linear symplectomorphisms may be much smaller than the extractable energy under special linear maps. The method introduced in the present study enables an energy-based proof of the linear Gromov nonsqueezing theorem.

Determining the onset of rigidity in gels is a fundamental challenge with significant practical implications across different applications. Limited-valence, or patchy-particle, systems have proven to be a valuable model to study the relationship between microscopic interactions and macroscopic mechanical properties. It has been suggested that the emergence of rigidity coincides with the formation of an infinitely spanning cluster of particles with at least three bonds. This work explores this hypothesis, its implications, and its broader applicability across a range of system parameters, by associating the emergence of rigidity with $m$-percolation transition for $m=3$. The properties of $m$-percolation are developed using a mean-field theoretical approach validated with numerical simulations, and used to build phase and rigidity diagrams for different particle valences of both single-component systems and binary mixtures of patchy particles. The difference between connectivity and rigidity percolation thresholds is found to reduce with increasing valence, providing an explanation for the challenges encountered in experimental attempts to distinguish isotropic connectivity percolation from the onset of rigidity. For binary mixtures, we found a robust minimum average valence, below which the gel is never rigid.

We examine the impact of the maintenance cost of social links on cooperative behavior in the prisoner's dilemma game on the Barabási-Albert scale-free network with a pairwise stochastic imitation. We show by means of Monte Carlo simulations and pair approximation that the cooperation frequency changes abruptly from an almost full cooperation to a much smaller value when we increase the cost of maintaining links. In the critical region, the stationary distribution is bimodal and the system oscillates between two states: the state with almost full cooperation and one with coexisting strategies. We show that the critical region shrinks with the increasing size of the population. However, the expected time the system spends in a metastable state before switching to the other one does not change as a function of the system's size, which precludes the existence of two stationary states in the thermodynamic limit of the infinite population.

Identifying the conditions for rigidity onset in gels is challenging. We propose a model that distinguishes attractive bonds from repulsive steric constraints, allowing the systematic variation of the number of bonded and nonbonded neighbors. Using simulations, rheology, and percolation analysis, we find that rigidity coincides with the percolation of particles with three or more bonds, occurring after connectivity percolation. This interplay of bonding and steric interactions, which is not a local but a large-scale effect, provides the mechanism for the rigidity of low-valence colloidal gels.

We design several examples of constrained, symmetric quantum circuit dynamics that generate nonequilibrium steady states. The qubit networks maintain local memory of the initial conditions and display inhomogeneous subsystem dynamics over long times, clearly distinguishable from approximately thermalizing networks of the same size. Each network can be described as an ensemble of open systems, a collection of qubits evolving with phase-covariant dynamics. Constraints from the conservation law and global unitary dynamics of the entire network bound the distribution of single-qubit dynamics in the ensemble, but different steady states are distinguishable by several measures. We quantify the distance of the steady states from the homogeneous steady state and further characterize them using the complexity of their mutual information networks, the volume of state space explored, a thermodynamic utility measure using extractable work, and correlated structure in the occurrence of noncompletely positive qubit propagator maps.

Turing patterns, arising from a reaction-diffusion system, play a crucial role in comprehending diverse patterns in nature. These patterns often manifest new features on curved surfaces that are absent on flat surfaces. With this motivation, the present work systematically analyzes the phenomena of preferential positioning and positional transitions of localized Turing patterns or a single spot on curved surfaces, emphasizing the interplay between the surface shape and the parameters in the reaction-diffusion system. In particular, we examine analytically and numerically single-spot formation in the Turing system evolving with Schnakenberg kinetics on nonaxisymmetric ellipsoids to illustrate the remarkable effect of surface shapes and reaction-diffusion parameters in tuning the positions and their transitions on curved surfaces. The work attempts to provide a generic understanding of the interplay between reaction-diffusion models and the system geometry crucial in deciding specific positions and positional transitions of localized Turing patterns on curved surfaces. The present analysis may provide useful insights into the role of cellular surface shape on various symmetry-breaking mechanisms in cellular processes.

Models for complex, heterogeneous systems such as ecological communities vary in the level of organization they describe. When the dynamics at the species level is unknown, one typically resorts to heuristic "macroscopic" models that capture relationships among a few degrees of freedom, e.g., groups of similar species, and commonly display out-of-equilibrium dynamics. These models, however, exactly reflect the species-level "microscopic" dynamics only when microscopic heterogeneity can be neglected. Here, we address the robustness of such macroscopic descriptions to the addition of disordered microscopic interactions. While disorder is known to destabilize equilibria at the microscopic level, leading to asynchronous (typically chaotic) fluctuations, we show that it can also stabilize synchronous species fluctuations driven by macroscopic structure. We analytically find the conditions for the existence of heterogeneity-stabilized equilibria and relate their stability to a mismatch in the time scales of individual species. This may shed light on the empirical observation that many-species ecosystems often appear stable despite highly diverse and potentially destabilizing interactions between species and functional groups.

In our work, we study the coevolution of cooperative behavior and individual perception through the lens of evolutionary game theory, considering the adoption of a disease containment measure as a cooperative act. We introduce this general game-theoretical framework as the “norm compliance dilemma,” where the evolution of agents' behaviors depends on their distinct, time-evolving perceptions. Starting from a simplified model of a well-mixed infinite population having homogeneous perceptions, we study and analytically solve a system of ordinary differential equations to predict the game equilibria. Subsequently, we compare the theoretical results with those obtained in finite populations having heterogeneous individual perceptions and organized in a network structure. We show that disease prevalence promotes cooperation, finding that this result is confirmed regardless of the spatial arrangement of individuals or the heterogeneity of their perception. However, networked structures can hinder and slow the evolution of cooperation with respect to well-mixed populations. Our findings highlight the crucial role of individual perception in shaping cooperative behavior and suggest that while disease prevalence increases norm compliance, the underlying population structure significantly influences the dynamics of cooperation.

Molecular motors are in charge of almost every process in the life cycle of cells, such as protein synthesis, DNA replication, and cell locomotion, hence being of crucial importance for understanding the cellular dynamics. However, given their size scales on the order of nanometers, direct measurements are rather challenging, and the information that can be extracted from them is limited. In this work, we propose strategies based on martingale theory in stochastic thermodynamics to infer thermodynamic properties of molecular motors using a limited amount of available information. In particular, we use two recent theoretical results valid for systems arbitrary far of equilibrium: the integral fluctuation theorem at stopping times and a family of bounds to the maximal excursions of entropy production. The potential of these strategies is illustrated with a simple model for the F1-ATPase rotary molecular motor, where our approach is able to estimate several quantities determining the thermodynamics of the motor, such as the rotational work of the motor performed against an externally applied force or the effective environmental temperature.

Delimiting the optimal performance bounds of heat engines (HEs), refrigerators (REs), and heat pumps (HPs) is a core thermodynamic challenge. While low-dissipation (LD) models are valuable for this, the impact of heat leak–unavoidable in real systems–are underexplored. In this paper, we present a unified framework for LD Carnot-like (CL) HEs, REs, and HPs with heat leak, deriving new results for efficiency at maximum power and power at maximum efficiency. Using these, we construct the Pareto fronts, which delineate the optimal power-efficiency trade-offs under realistic conditions. We prove that the bounds of power at fixed efficiency and efficiency at fixed power coincide, forming these fronts, and show that they are achieved by optimizing the average entropy production rate, a principle applicable to all CL devices and beyond the LD assumption.

Cardiac models are examples of excitable systems and can support stable spiral waves. For certain parameter values, however, these spiral waves can become unstable, resulting in spiral defect chaos (SDC), characterized by the continuous creation and annihilation of spiral waves and thought to underlie atrial fibrillation. During SDC, the number of spiral waves fluctuates and drops to zero at termination. In this work, we demonstrate that varying a single parameter allows the system to transition from SDC to a single spiral wave, passing through an intermediate regime of intermittency. In such intermittent dynamics, intervals of SDC are sandwiched between non-SDC intervals during which the number of spiral waves remains small and constant. We quantify this intermittency and show that the mean termination time increases significantly as the control parameter approaches values for which a single spiral wave is stable. In addition, we observe that quasistable spiral waves may intermittently persist in part of the computational domain, while the rest of the domain exhibits SDC. Our results may have implications for clinical atrial fibrillation, which often shows intermittency, switching back-and-forth between fibrillation and normal sinus rhythm.

This work addresses the problem of improving synchronization quality in oscillator networks. To this end, the approach replaces some couplings involving one variable with couplings involving another, without increasing the total number of connections. When a network uses multiple coupling variables, it is referred to as a hypernetwork. The results include simulations of six different network topologies and three chaotic oscillators. Validation is performed through Monte Carlo simulations on the considered oscillator networks. A key finding is that using two coupling variables—while keeping the same number of connections as in a single-variable network and ensuring a fair scale for comparing coupling strengths—can significantly enhance synchronization quality.

Biological molecular motors are high-performance nanomachines that convert chemical energy into mechanical motion via chemomechanical coupling. Their reaction cycles typically comprise a series of intermediate chemical states between the initial and final primary states. However, the influence of these intermediate states on motor performance has not yet been fully explored. In this study, we investigate the impact of intermediate states on the motor kinetics using a reaction-diffusion model. In most cases, the intermediate states accelerate the motor by lowering the effective barrier height. This acceleration is particularly pronounced when an external load is applied to the motor, implying the practical importance of the intermediate states. The intermediate states can also slow down the reaction in some cases, such as the slow reaction limit with asymmetric kinetics. Our findings provide practical insights into the design principles behind the high performance of biological molecular motors, as well as the development of efficient artificial molecular motors.

We present a machine learning approach based on symbolic regression to derive, from either numerically generated or experimentally measured spectral data, closed-form expressions that model the optical properties of biological materials. To evaluate the performance of our approach, we consider three case studies with the aim of retrieving the refractive index of the materials that constitute the biological structures considered. The results obtained show that, in addition to retrieving readable and dimensionally homogeneous dispersion models, the expressions found have a physical meaning and their algebraic form is similar to that of the models often used to characterize the dispersive behavior of transparent dielectrics in the visible region.

We propose a method for training dynamical systems governed by Lagrangian mechanics using equilibrium propagation. Our approach extends equilibrium propagation—initially developed for energy-based models—to dynamical trajectories by leveraging the principle of action extremization. Training is achieved by gently nudging trajectories toward desired targets and measuring the response of the variables conjuguate to the trainable parameters. This method is particularly suited to systems with periodic boundary conditions or fixed initial and final states, enabling efficient parameter updates without requiring explicit backpropagation through time. In the case of periodic boundary conditions, this approach yields the semiclassical limit of quantum equilibrium propagation. Applications to systems with dissipation are also discussed.

The solution of the nonlinear gray radiative transfer system composed of the radiative transfer equation (RTE) and the material energy balance equation encounters significant challenges in multiscale problems where both optical thick and optical thin regions coexist. In this paper, an asymptotic-preserving (AP) scheme based on the discrete unified gas-kinetic scheme (DUGKS) framework is proposed. The microscopic RTE is solved by a simplified DUGKS, where the cell interface intensity is simply constructed from the averaging along the characteristic line, and the macroscopic material energy balance equation is solved by a finite volume method consistent with the DUGKS. The time marching of the present method exhibits the implicit characteristic, and the mesh size is not strictly constrained by the photon mean free path. As a result, the present method has the AP property. Theoretical analysis is conducted to prove the AP property, and several single- and multiscale tests are carried out to confirm the accuracy and robustness of the present method.

The structure and dynamics of fluids confined in nanoporous media differ from those in bulk, which can be probed using NMR relaxation measurements. We here show, using atomistic molecular dynamics simulations of water in a slit nanopore, that the behavior of the NMR relaxation rate, $R_1$, with varying surface interaction and confinement strength can be estimated from the exchange statistics of fluid molecules between the adsorbed surface layer and the bulk region. In detail, we test the applicability of intermittent molecular water dynamics, a theoretical framework that relates NMR relaxation to the statistics of molecular exchange between these two states. We confront this framework with the direct evaluation of dipolar NMR relaxation rates from atomistic molecular dynamics simulations of water confined in a slit nanopore, allowing to assess its accuracy across varying surface interactions. We employ first return passage time calculations to quantify the molecular exchange statistics, thereby linking microscopic parameters of the confined fluid—such as adsorption time, pore size, and diffusion coefficient—to the NMR relaxation rate. Our results show that the theoretical framework proposed by Levitz et al. captures the qualitative trends of NMR relaxation rates observed in our molecular simulations. This approach allows to predict, interpret, and analyze the molecular relaxation of fluids at interfaces using merely concepts of statistical mechanics that can be generalized to closed and open geometries and thus yields direct insights into the experimental study of NMR relaxation with varying surface chemistry or confinement strength.