A position-space renormalization-group study is done for the Ashkin-Tellerized XY model, as an exact solution on the $d=2$ hierarchical lattice and an approximate solution on the square lattice. A multiplicity of algebraic order is found in the phase diagram, in the form of renormalization-group fixed lines composed of a continuous sequence of interaction potential surfaces. In the Ashkin-Tellerized XY model, each site has two continuously varying spins, each spin being an XY spin, that is, having orientation continuously varying in $2\pi$ radians. Nearest-neighbor sites are coupled by two-spin and four-spin interactions. The phase diagram has algebraically ordered phases that are ferromagnetic and antiferromagnetic in each of the spins, and algebraically ordered phases that are ferromagnetic and antiferromagnetic in the combined spin variable. These phases are subtended by fixed lines of potential surfaces that are multiplicatively different Berezinskii-Kosterlitz-Thouless fixed potentials. The evolution of continuously varying criticality is traced within each of the four phases. The renormalization-group flows, the fixed lines, and the interaction surfaces are in terms of the doubly composite Fourier coefficients of the exponentiated energy of the four nearest-neighbor spins. The disordered phase is maintained along two semi-infinite a priori quasi-disorder lines.

The advection of entities induced by gradients in attractant concentration fields is observed through diffusiophoresis in colloids and chemotaxis in microorganisms. Mathematically, both diffusiophoresis and chemotaxis follow similar descriptions and display a variety of interesting behaviors that are not observed through other transport mechanisms. However, the application of such a mathematical framework has largely been restricted to entities influenced by forcings of a single scale. In this article, we argue that this framework is more general and can be expanded to study entities migrating along terrains that induce forcings of many scales. We extend the Fisher-KPP reaction-diffusion model, foundational to population dynamics for both small (cellular) and large (ecological) scales, to incorporate chemotactic advection. Furthermore, we introduce a fractal terrain to better mimic the population dispersal phenomena. Simulations demonstrate that, by including chemotaxis of a population toward attractants that are dispersed heterogeneously over fractal terrains, population hotspots can appear from initially uniformly dispersed states, whereas Fisher-KPP without chemotaxis predicts a persistent tendency toward population uniformity. Varying the chemotactic migration yields fine control over inter- or intrapopulation segregation, and thus the population growth rates may be substantially altered by considering the population-attractant coupling. This framework may be useful for characterizing population hotspots over heterogeneous landscapes.

Avalanche precursors are small, quasiperiodic surface displacements observed experimentally during the slow inclination of a granular bed. In spite of being studied experimentally since the mid-2000s, they have eluded numerical models. One recent contribution is a one-dimensional model where a line of sliders linked by springs is placed on a slowly inclined frictional plane. In this paper, we present a two-dimensional model that stands between this one-dimensional model and the three-dimensional experimental setup. In our model, disks are placed on a frictional plane, and interact with their neighbors and boundaries with typical granular molecular dynamics interactions. The model robustly produces quasiperiodic compaction events. The angular period (change in inclination between two events) is proportional to the difference between the static and dynamic friction coefficients. The first event occurs systematically earlier than predicted by the coefficient of static friction: The inclination can be predicted by subtracting the angular period from the static friction angle. The inclination at the initial event and the angular period decrease for large systems. When the inclination is varied cyclically, longer sequences of events can be observed, as in recent experiments. Finally, the relation between the observed compaction events and avalanches and avalanche precursors are discussed.

We theoretically investigate the thermodynamic performance characteristics of an active magneto gyrator taking into account the two-dimensional motion of an inertial charged active particle confined in an asymmetric parabolic potential and in contact with two heat baths kept at two different temperatures. A magnetic field of constant magnitude is applied in a direction perpendicular to the plane of motion. In such a system, the particle exhibits a gyrating motion across the potential minimum and exerts a torque on the confining potential as long as there is a potential asymmetry and temperature gradient. Hence, this system can operate as an active magneto heat engine or pump in the presence of a load force. Interestingly, we observe that the activity or self-propulsion impacts the thermodynamic performance characteristics of the gyrator only in the presence of the magnetic field. We examine two scenarios: first, by applying a load in a direction opposing the torque and, second, by applying a load in the same direction as that of torque. In the first case, for a fixed parameter regime, the gyrator is found to act as a heat engine or a heat pump depending on the strength of the applied load, whereas in the latter case, it can only operate as a heat pump. Moreover, unlike the Brownian gyrator or Brownian magneto gyrator, captivatingly, the efficiency is found to have no universal upper bound and can be made $100\%$ by tuning the system parameters. Additionally, when the system is suspended in a viscoelastic medium characterized by the presence of a finite memory, for a short persistence of memory and a fixed duration of activity, the efficiency can be $100\%$ even for more than one value of viscoelastic memory timescale. In the first case, the duration of the activity has a nonmonotonic impact on the system performing either as an engine or a pump, whereas the magnetic field has a similar impact on the performance of an engine, but it degrades the performance of the system as a heat pump. In the latter case, the coefficient of performance has a nonmonotonic dependence on the duration of the activity, whereas the magnetic field favors the system performing as a heat pump. Our analytical results are supported by numerical simulation.

We investigate the critical relaxational dynamics of the three-dimensional (3D) lattice ${\mathbb{Z}}_N$ gauge models with $N=6$ and $N=8$, whose equilibrium critical behavior at their topological transitions belongs to the inverted $\mathit{XY}$ (IXY) universality class [this is also the universality class of the continuous transitions of the 3D lattice $U$(1) gauge Higgs models with a one-component complex scalar field], which is connected to the standard $\mathit{XY}$ universality class by a nonlocal duality relation of the partition functions. Specifically, we consider the purely relaxational dynamics realized by a locally reversible Metropolis dynamics, as commonly used in Monte Carlo simulations. To determine the corresponding dynamic exponent $z$, we focus on the out-of-equilibrium critical relaxational flows arising from instantaneous quenches to the critical point, which are analyzed within an out-of-equilibrium finite-size scaling framework. We obtain the estimate $z=2.59\left(3\right)$. A numerical analysis of the equilibrium critical dynamics give consistent, but less accurate, results. This dynamic exponent is expected to characterize the critical slowing down of the purely relaxational dynamics of all topological transitions that belong to the 3D IXY universality class. We note that this result implies that the critical relaxational dynamics of the 3D IXY universality class is slower than that of the standard 3D $\mathit{XY}$ universality class, whose relaxational dynamic exponent $z\approx 2.02$ is significantly smaller, although they share the same length-scale critical exponent $\nu \approx 0.6717$.

In traditional models of opinion dynamics, each agent in a network has an opinion and changes in opinions arise from pairwise (i.e., dyadic) interactions between agents. However, in many situations, groups of individuals possess a collective opinion that can differ from the opinions of their constituent individuals. In this paper, we study the effects of group opinions on opinion dynamics. We formulate a hypergraph model in which both individual agents and groups of three agents have opinions, and we examine how opinions evolve through both dyadic interactions and group memberships. We find for some parameter values that the presence of group opinions can lead to oscillatory and excitable opinion dynamics. In the oscillatory regime, the mean opinion of the agents in a network has self-sustained oscillations. In the excitable regime, finite-size effects create large but short-lived opinion swings (as in social fads). We develop a mean-field approximation of our model and obtain good agreement with direct numerical simulations. We also show—both numerically and via our mean-field description—that oscillatory dynamics occur only when the numbers of dyadic and polyadic interactions of the agents are not completely correlated. Our results illustrate how polyadic structures, such as groups of agents, can have important effects on collective opinion dynamics.

We revisit the elementary problem of moving a particle in a harmonic trap in finite time with minimal work cost and extend it to the case of an active particle. By comparing the Gaussian case of an Active Ornstein-Uhlenbeck particle and the non-Gaussian run-and-tumble particle, we establish general principles for thermodynamically optimal control of active matter beyond specific models. We show that the open-loop optimal protocols, which do not incorporate system-state information, are identical to those of passive particles but result in larger work fluctuations due to activity. In contrast, closed-loop (or feedback) control with a single (initial) measurement changes the optimal protocol and reduces the average work relative to the open-loop control for small enough measurement errors. Minimum work is achieved by particles with finite persistence time. As an application, we propose an active information engine which extracts work from self-propulsion. This periodic engine achieves higher information efficiency with run-and-tumble particles than with active Ornstein-Uhlenbeck particles. Complementing a companion paper that gives only the main results [Garcia-Millan et al., companion paper, Phys. Rev. Lett. 135, 088301 (2025)], here we provide a full account of our theoretical calculations and simulation results. We include derivations of optimal protocols, work variance, impact of measurement uncertainty, and information-acquisition costs.

We study a generalized Langevin equation framework that incorporates stochastic resetting of a truncation power-law memory kernel. The inclusion of stochastic resetting enables the emergence of resonance phenomena even in parameter regimes where conventional settings (without resetting) do not exhibit such behavior. Specifically, we explore the response of the system to an external field under three scenarios: (i) a free particle, (ii) a particle in a harmonic potential, and (iii) the effect of truncation in the memory kernel. In each case, the primary focus is on understanding how the resetting mechanism interacts with standard parameters to induce stochastic resonance. In addition, we explore the effect of resetting on the dielectric loss.

In this study, we generalize the theory of stochastic resetting for the non-Markovian dynamics of a free Brownian particle (BP) with arbitrary damping strength and correlation time of the thermal noise. To apply this theory, we calculate the properties of the BP under thermal Ornstein-Uhlenbeck noise and compare the results with those from the Markovian dynamics case. We find that, at long times, the evolution of the distribution function toward the steady state in non-Markovian dynamics can resemble that observed in Markovian systems. In the asymptotic limit, the stationary distribution function reveals that the probability density at a given position can increase exponentially with memory time. Notably, the difference in probability density between the two cases tends to be maximal at an intermediate stage of the dynamics for a fixed memory time. Using the exact distribution function, we also calculate the variance of the position to explore a central question: How the nature of diffusion for a free particle is influenced by resetting, which can lead to a steady state. This analysis suggests that, although ballistic diffusion and memory effects may not significantly impact the long-time behavior of free Brownian motion or equilibrium in the presence of an external conservative force field, they play a crucial role in the formation of a resetting-induced localized stationary state. Additionally, we observe that the survival probability decreases exponentially at all times. Finally, we compute the mean first-passage time and uncover interesting results that provide further insights into the system's behavior.

We analyze the subsystem size scaling of the entanglement entropy of a nonergodic pure state that can be described by a multiparametric Gaussian ensemble of complex matrices in a bipartite basis. Our analysis indicates, for a given set of global constraints, the existence of an infinite number of universality classes of local complexity, characterized by the complexity parameter, for which the entanglement entropy reveals a universal scaling with subsystem size. A rescaling of the complexity parameter helps us to identify the critical regime for the entanglement entropy of a broad range of pure nonergodic states.

The increasing relevance of Haar ensembles of pure ergodic quantum states for quantum information processes has been eclipsed by the challenges in their experimental realization. As a result, alternative ensembles are needed that can approach them approximately. This motivates us to begin from a multiparametric ensemble of pure bipartite states, nonuniformly distributed in Hilbert space, and to seek a route to Haar ensembles by changing the ensemble parameters and thereby the entanglement entropy distribution. We show that the latter's variation is not sensitive to individual details of the ensemble parameters, rather it is governed collectively, i.e., it is a function of all of them and can thus be described by a common mathematical formulation for a wide range of nonergodic states. This has important implications for quantum state engineering: access from an arbitrary initial state ensemble to Haar ensembles can be controlled just by a single function representing collective information about the ensemble parameters.

Perturbing a system far away from equilibrium via a time-dependent protocol can formally be described by a nonlinear Volterra series expansion. Here we derive identities for the nonlinear memory kernels arising in such nonlinear expansion, including the possibility of a nonlinear coupling between perturbation and system. These identities rely on local detailed balance, and they include the fluctuation dissipation theorem as the lowest-order identity. We test them in simulations for driven over- and underdamped Brownian particles. These identities for memory kernels can be recast in a series relation for the nonequilibrium cumulants of the observable conjugate to the driving and the observable described by the Volterra series. We discuss the relation to previously found identities.

Close to a saddle-node bifurcation, when two invariant solutions collide and disappear, the behavior of a dynamical system can closely resemble that of a solution which is no longer present at the chosen parameter value. For bifurcating equilibria in low-dimensional ordinary differential equations (ODEs), the influence of such “ghosts” on the temporal behavior of the system, namely delayed transitions, has been studied previously. We consider spatiotemporal partial differential equations (PDEs) and characterize the phenomenon of ghosts by defining representative state-space structures, which we term “ghost states,” as minima of appropriately chosen cost functions. Using recently developed variational methods, we can compute and parametrically continue ghost states of equilibria, periodic orbits, and other invariant solutions. We demonstrate the relevance of ghost states to the observed dynamics in various nonlinear systems, including chaotic maps, the Lorenz ODE system, the spatiotemporally chaotic Kuramoto–Sivashinsky PDE, the buckling of an elastic arc, and 3D Rayleigh–Bénard convection.

Laboratory plasma production almost always preferentially heats either the ions or electrons, leading to a two-temperature state. In this state, density functional theory molecular dynamic simulation is the state of the art for modeling bulk material properties. We construct a statistical mechanics model for the two-temperature limit that is theoretically consistent with the molecular dynamics method. We proceed to derive the electron-ion multitemperature quantum Ornstein-Zernike equations for the first time. This allows the construction of a two-temperature, two-component plasma model using the average atom from which we can compute bulk material properties at a fraction of the computation time of the two-temperature density functional theory simulation. The accuracy of the model is benchmarked against ion pair correlation and self-diffusion results from ab initio simulation. We proceed to compute the viscosity and ion thermal conductivity as a function of both ion and electron temperature.

The generalized pseudospectral method has been established as a powerful numerical method to solve the three-dimensional atomic systems. In this work, we extend this method to the one-dimensional quantum systems in both free and confined situations, and focus especially on atoms with soft-core Coulomb interaction, a model that has been widely employed in the simulation of laser-atom interaction. The efficiency and robustness of the numerical method are thoroughly tested to ensure that the obtained eigenenergies are close to the working precision. Based on the highly accurate results, spectral properties of the one-dimensional atoms with soft-core Coulomb interaction are explored, including the asymptotic laws of eigenenergies, the quantum defects of bound states of different parities, and the variation and transition of eigenenergies and wave functions in different spatial confinements. These results complement the structural and spectral properties of one-dimensional atoms and promote further application of the low-dimensional models.

To accurately represent disease spread, epidemiological models must account for the complex network topology and contact heterogeneity. Traditionally, most studies have used random heterogeneous networks, which ignore correlations between the nodes' degrees. Yet, many real-world networks exhibit degree assortativity—the tendency for nodes with similar degrees to connect. Here we explore the effect degree assortativity (or disassortativity) has on long-term dynamics and disease extinction in the realm of the susceptible-infected-susceptible model on heterogeneous networks. We derive analytical results for the mean time to extinction (MTE) in assortative networks with weak heterogeneity, and show that increased assortativity reduces the MTE and that assortativity and degree heterogeneity are interchangeable with regard to their impact on the MTE. Our analytical results are verified using the weighted ensemble numerical method, on both synthetic and real-world networks. Notably, this method allows us to go beyond the capabilities of traditional numerical tools, enabling us to study rare events in large assortative networks, which were previously inaccessible.

In a transition between nonequilibrium steady states, the entropic cost associated with the maintenance of steady-state currents can be distinguished from that arising from the transition itself through the concepts of excess (housekeeping) entropy flux and adiabatic (nonadiabatic) entropy production. The thermodynamics of this transition is embodied by the Hatano-Sasa relation. In this letter, we show that for a slow transition between quantum nonequilibrium steady states the nonadiabatic entropy production is, to leading order, given by the path action with respect to a Riemannian metric in the parameter space, which can be connected to the Kubo-Mori-Bogoliubov quantum Fisher information. We then demonstrate how to obtain minimally dissipative paths by solving the associated geodesic equation and illustrate the procedure with a simple example of a three-level maser. Furthermore, by identifying the quantum Fisher information with respect to time as a metric in state space, we derive an upper bound on the excess entropy flux that holds for arbitrarily fast processes.

Nonreciprocity and permutation symmetry, despite their mutual exclusivity in two-component systems, coexist in multicomponent biological and synthetic systems, ranging from neural circuits to active metamaterials. While these phenomena have been extensively studied independently in the contexts of nonreciprocal phase transitions (e.g., flocking, synchronization, and pattern formation) and cluster synchronization (e.g., oscillator networks), their synergistic effects remain largely unexplored. This study introduces a framework, integrating mean-field theory and group representation theory, to investigate collective behaviors in synchronization and pattern formation systems exhibiting both nonreciprocity and permutation symmetry. Analyzing two three-species scenarios with $S_2$ (transposition) and $C_3$ (cyclic) permutation groups, we identify distinct symmetry-constrained traveling wave phases in synchronization system. Both phases exhibit parity-time symmetry breaking, but their dynamics and phase transitions diverge due to differing symmetry constraints. Spontaneous permutation symmetry breaking transforms the phase transition points of the traveling wave phase from exceptional points to Hopf bifurcations. Furthermore, we discover a time-dependent phase in scenario with $S_2$, absent in two-species systems. This phase features a dynamic interplay between unidirectional, time-crystal-like oscillations in one species and symmetrical pendulumlike motions in the other two. Our results demonstrate that permutation symmetry significantly expands the repertoire of symmetry-constrained collective behaviors and phase transitions in nonreciprocal systems, exceeding the constraints of two-species systems. The identified mechanism, symmetry-constrained organization of nonreciprocal fluxes, provides a design principle for engineering collective behaviors in neuronal circuits and active metamaterials.

We study the evolution of two-point correlation functions of the one-dimensional Bose-Hubbard model in the semiclassical regime in the framework of truncated Wigner approximation with quantum jumps as first-order corrections. At early times, the correlation functions show strong superdiffusion with universal integer exponents determined solely by the initial conditions and completely insensitive to system parameters and chaos. Only after a long time does this regime crosse over to the normal diffusion regime which is most robust when nonintegrability is strong. For strong nonintegrability, the system ends up in a homogeneous state, while for weak nonintegrability, the oscillations and inhomogeneities persist, despite the fact that chaos is nearly always strong and only weakly depends on the nonintegrability parameter. We conclude that the superdiffusive regime is neither prethermalized nor a precursor to thermalization but an early-time phenomenon related to a special scaling symmetry of the Bose-Hubbard Hamiltonian.