The stochastic dynamics of a rigid inclusion constrained to move on a curved surface has many applications in biological and soft matter physics, ranging from the diffusion of passive or active membrane proteins to the motion of phoretic particles on liquid-liquid interfaces. Here we construct intrinsic Langevin equations for an oriented rigid inclusion on a fixed curved surface using Cartan's method of moving frames. We first derive the Hamiltonian equations of motion for the translational and rotational momenta in the body frame. Surprisingly, surface curvature couples the linear and angular momenta of the inclusion. We then add to the Hamiltonian equations linear friction, white noise, and arbitrary configuration-dependent forces and torques to obtain intrinsic Langevin equations of motion in phase space. We provide the integrability conditions, made nontrivial by surface curvature, for the forces and torques to admit a potential, thus distinguishing between passive and active stochastic motion. We derive the corresponding Fokker-Planck equation in geometric form and obtain fluctuation-dissipation relations that ensure Gibbsian equilibrium. We extract the overdamped equations of motion by adiabatically eliminating the momenta from the Fokker-Planck equation, showing how a peculiar cancellation leads to the naively expected Smoluchowski limit. The overdamped equations can be used for accurate and efficient intrinsic Brownian dynamics simulations of passive, driven, and active diffusion processes on curved surfaces. Our work generalizes to the collective dynamics of many inclusions on curved surfaces.

Colloidal gels formed from patchy rods provide a promising platform to design novel functional materials and formulations. Yet, the case for localized interactions at the rod tips remains relatively unexplored. Here we probe the structure and dynamics of such systems by means of coarse-grained computer simulations, and show that the emerging tipped gel networks are fundamentally different to uniform ones. Structurally, tipped networks are better connected, and, unlike in the uniform gels, the connectivity increases with the length of the constituent rods. The dynamics are also fundamentally different, with the gelation time in the tipped networks (contrary to the uniform gels) exhibiting an inverse relationship with rod length.

We investigate the validity of the Landauer principle in the context of a non-Markovian environment, employing a quantum autonomous thermal machine (QATM) comprised of two qubits, attached to different Markovian thermal reservoirs coupled to a single qubit acting as a quantum coherence reservoir, interpreted as a working qubit. We numerically demonstrate that the non-Markovianity, arising from the exchange of correlations between the QATM qubits and the work qubit, influences the Landauer bound. We analyze two distinct reservoir types: fermionic and bosonic, and show that the QATM, operating as a single entity, interacts with the work qubit at an effective virtual temperature, leading to a violation of the conventional Landauer bound. Consequently, we derive a lower bound for the minimal dissipation energy required to erase information during the energy exchange between the QATM and the work qubit. The QATM's information engine character and impact on the work qubit is further characterized by monitoring its information content, including coherence and population dynamics. Our analysis reveals that the work qubit's populations oscillate in time, while the coherence dissipates nonmonotonically.

Time series of thermal emissions from water vapor and air molecules at $\approx 2.8\mathrm{GHz}$, collected by the National Center for Atmospheric Research's (NCAR) S-band polarimetric radar S-Pol are examined for polarization probability distributions. A nearly uniform distribution of states on the Poincaré sphere surface is found. This uniformity is consistent with the four-dimensional circular Gaussian distribution of electric fields (pairs of in-phase and quadrature components for two orthogonal directions) for unpolarized radiation. Analysis of experimental data and the derived sampling distribution of the degree of polarization of the finite time series both yield a mean of about $0.02$, within bounds of sampling variability of unpolarized Gaussian-distributed radiation. Weak inhomogeneity of polarization states on the Poincaré sphere detected in the experimental data is within the error bounds of the radar receiver.

Whole brain neural oscillation activities exhibit multiple wave phase patterns and seem to be supported by the common circuit network structure. We proposed a Hopfield Kuramoto model based entirely on heterogeneous connectivity strength rather than phase delay. Multiple wave phase patterns can be encoded in heterogeneous connectivity networks via Hebbian rule and retrieved as attractors. We systematically investigated how the model dynamic landscape influenced by attractors and their corresponding eigenvalues, as well as how to control the stability of equilibrium points and the occurrence of high dimensional bifurcations. This framework enables us to reproduce the dominant wave activity components in human brain functional MRI signal, and provides a canonical model for the multi-body physical system spatio-temporal pattern attractor dynamics.

Quantum states exhibiting single-particle entanglement (SPE) can encode and process quantum information more robustly than their multiparticle analogs. Understanding the vulnerability and resilience of SPE to disorder is therefore crucial. This letter investigates phase, coin, and position disorder via discrete-time quantum walks on odd and even cyclic graphs to study their effect on SPE. The reduction in SPE is insignificant for low levels of phase or coin disorder, showing the resilience of SPE to minor perturbations. However, SPE is seen to be more vulnerable to position disorder. We analytically prove that maximally entangled single-particle states (MESPS) at time step $t=1$ are impervious to phase disorder regardless of the choice of the initial state. Further, MESPS at timestep $t=1$ is also wholly immune to coin disorder for phase-symmetric initial states. Position disorder breaks odd-even parity and distorts the physical time cone of the quantum walker, unlike phase or coin disorder. SPE saturates toward a fixed value for position disorder, irrespective of the disorder strength at large timestep $t.$ Furthermore, SPE can be enhanced with moderate to significant phase or coin disorder strengths at specific time steps. Interestingly, disorder can revive single-particle entanglement from absolute zero in some instances, too. These results are crucial in understanding single-particle entanglement evolution and dynamics in a laboratory setting.

In contrast to equilibrium systems, inertia can profoundly impact the phase behavior of active systems. This has been made particularly evident in recent years, with motility-induced phase separation (MIPS) exhibiting several intriguing dependencies on translational inertia. Here, we report extensive simulations characterizing the phase behavior of inertial active Brownian particles and develop a mechanical theory for the complete phase diagram without appealing to equilibrium notions. Our theory qualitatively captures all aspects of liquid-gas coexistence, including the critical value of inertia above which MIPS ceases. Notably, our findings highlight that particle softness, and not inertia, is responsible for the MIPS reentrance effect at the center of a proposed active refrigeration cycle.

We investigated the directed transport and collective patterns of pulsing particles with periodic size variation in topological lattices. Self-pulsing provides energy input at the individual level and serves as nonequilibrium driving. The distribution of the topological lattice determines the direction of particle motion, with pulsing particles preferentially moving toward high-density lattice regions, in contrast to the behavior of conventional active particles. The competition dynamics of repulsion contraction and synchronization give rise to deformation waves in dense particle environments, including both planar and circular waves, corresponding to a disordered state. These deformation waves exhibit local order but global disorder. Notably, directed transport is most pronounced in the disordered state, whereas particles exhibit no directed transport in the arrested ordered state. Additionally, optimal values of the self-pulsing parameters (the driving frequency, the self-pulsation amplitude, and the strengths of synchronization) lead to a peak in the average velocity. The particle number density also significantly influences directed transport, as an increase in number density promotes directed transport.

Many combinatorial optimization problems (COPs) can be mapped to Ising Hamiltonians. Oscillator Ising machines (OIMs) are built to minimize the Ising Hamiltonians, thereby indirectly solving the COPs. Specifically, the dynamics of an OIM evolve in the direction of decreasing value of the Ising Hamiltonian, and its state converges to a steady state, known as an asymptotically stable equilibrium point. Such an equilibrium point represents a candidate solution of the underlying COP. Although OIMs show great potential in solving COPs, they, like many heuristic algorithms, are prone to getting stuck in local minima. Even for trivial problems, e.g., unfrustrated Ising Hamiltonians, an OIM may get trapped in local minima if its parameters and its initial condition are not properly selected. In this work, we examine the impacts of the graph structure underlying an OIM on the computational properties of the OIM. In particular, we identify graph structures of OIMs for which the parameters of the OIMs can be properly designed such that only the equilibrium points representing global minima are asymptotically stable and all other equilibrium points are unstable. Thus, an OIM with such a graph structure, possibly with a small perturbation, can converge to the globally optimal solutions from any initial condition.

Chimera states, marked by the coexistence of order and disorder in systems of coupled oscillators, have captivated researchers with their existence and intricate patterns. Despite ongoing advances, a full understanding of the genesis of chimera states remains challenging. This work formalizes a systematic method by evoking pattern formation theory to explain the emergence of chimera states in complex networks, in a similar way to how Turing patterns are produced. Employing linear stability analysis and the spectral properties of complex networks, we show that the randomness of network topology, as reflected in the localization of the graph Laplacian eigenvectors, determines the emergence of chimera patterns, underscoring the critical role of network structure. In particular, this approach explains how amplitude and phase chimeras arise separately and explores whether phase chimeras can be chaotic or not. Our findings suggest that chimeras result from the interplay between local and global dynamics at different timescales. Validated through simulations and empirical network analyses, our method enriches the understanding of coupled oscillator dynamics.

Synchronization is a ubiquitous phenomenon in nature. Although it is necessary for the functioning of many systems, too much synchronization can also be detrimental; e.g., (partially) synchronized brain patterns support high-level cognitive processes and bodily control, but hypersynchronization can lead to epileptic seizures and tremors, as in neurodegenerative conditions such as Parkinson's disease. Consequently, a critical research question is how to develop effective pinning control methods capable to reduce or modulate synchronization as needed. Although such methods exist to control pairwise-coupled oscillators, and pinning control for synchronization has been developed in higher-order systems in recent years, there are no desynchronizing control methods for higher-order interactions, despite the increasing evidence of their relevant role in brain dynamics. In this work, we fill this gap by proposing a generalized control method designed to desynchronize Kuramoto oscillators connected through higher-order interactions. Our method embeds a higher-order Kuramoto model into a suitable Hamiltonian flow, and builds upon previous work in Hamiltonian control theory to analytically construct a feedback control mechanism. We numerically show that the proposed method effectively prevents synchronization in synthetic and empirical higher-order networks. Although our findings indicate that pairwise contributions in the feedback loop are often sufficient, the higher-order generalization becomes crucial when pairwise coupling is weak. Finally, we explore the minimum number of controlled nodes required to fully desynchronize oscillators coupled via an all-to-all hypergraph.

We consider the recently proposed growing directed network models that aim at minimizing the weighted connection expenses while at the same time favoring weighted local inward and outward node degrees. Theoretical expressions for the in-degree and out-degree distributions of the optimized networks are derived for general edge weight as well as inward and outward node weight distributions. In particular, it is shown that for exponentially distributed node weights and narrow edge weight distributions, the emerged optimized degree distributions resulted in scale-free power-law decay in broad regimes. Furthermore, it is shown that the exponents of the scale-free distribution are related to the mean values of the node weight distributions in a universal way. Simulations explicitly verify all the theoretical results. Implications of the results are also discussed and compared with data in realistic networks, suggesting that the ratio of the out-degree power-law exponent to that of the in-degree can possibly reveal some intrinsic characteristic features of the node population.

This study explores the evolution of cooperation in populations with mixed pairwise and three-body interactions, investigating the impact of higher-order interaction density $\rho$ and individual interaction preference $\alpha$. Our results reveal that sparse higher-order interactions markedly boost cooperation, exhibiting two critical phase transitions as $\rho$ changes. These transitions underscore the delicate equilibrium needed for optimal cooperation, as excessive higher-order interactions can diminish returns. The preference parameter $\alpha$ significantly influences cooperation sustainability, with intermediate values maximizing cooperative outcomes, particularly when the temptation to defect $r$ is not strong. Crucially, our findings demonstrate that hybrid social dilemmas structurally encode emergent cooperation pathways that are unattainable within homogeneous interaction frameworks, emphasizing the importance of modeling mixed interactions to capture real-world complexity. These insights offer valuable guidance for designing systems aimed at promoting cooperative behavior across social, ecological, and artificial domains.

We extract electron transport properties from atomistic simulations of a two-component plasma by mapping the long-wavelength behavior to a two-fluid model. The mapping procedure is performed via Markov Chain Monte Carlo sampling over multiple spectra simultaneously. The free-electron dynamic structure factor and its properties have been investigated in the hydrodynamic formulation to justify its application to the long-wavelength behavior of warm dense matter. We have applied this method to warm dense hydrogen modeled with wave packet molecular dynamics and showed that the inferred electron transport properties are in agreement with a variety of reference calculations, except for the electron viscosity, where a substantive decrease is observed when compared to classical models.

We report on direct microscopic observations of thermally driven fluctuating dynamics in a narrow temperature region between the isotropic and low-temperature phases in achiral, chiral, and strongly chiral (blue phase) liquid crystal materials. We observe the dynamics in samples strongly confined between two glass surfaces which act as disordering surfaces at thicknesses above the critical confinement thickness below which the phase transition is gradual. In achiral and long-pitch chiral materials the fluctuating appears as formation and disappearance of small structureless nematic domains, whereas in strongly chiral materials, which exhibit blue phase I at larger thicknesses, these fluctuations are real-time formation and annihilation of topologically nontrivial nematic half-skyrmions. We study the dynamics of these fluctuations and present a simple model that explains how such dynamics is possible in ultraconfined systems.

Disorder and noise in physical systems often disrupt spatial and temporal regularity, yet chaotic systems reveal how order can emerge from unpredictable behavior. Complex networks, spatial analogs of chaos, exhibit disordered, non-Euclidean architectures with hidden symmetries, hinting at spontaneous order. Finding low-dimensional embeddings that reveal network patterns and link them to dimensionality that governs universal behavior remains a fundamental open challenge, as it needs to bridge the gap between microscopic disorder and macroscopic regularities. Here, the minimal space revealing key network properties is introduced, showing that non-integer dimensions produce chaotic-like attractors.

We study the occupation time statistics for non-Markovian random walkers based on the formalism of the generalized master equation for the continuous-time random walk. We also explore the case when the random walker additionally undergoes a stochastic resetting dynamics. We derive and solve the backward Feynman-Kac equation to find the characteristic function for the occupation time in an interval and for the half occupation time in the semi-infinite domain. We analyze the behavior of the probability density functions, the moments, the limiting distributions, and the ergodic properties for both occupation times when the underlying random walk is normal or anomalous. For the half occupation time, we revisit the well-known arcsine law and examine its validity pertaining to various regimes of the rest period of the walker. Our results have been verified with Monte Carlo–based numerical simulations exhibiting an excellent agreement.

The physics of glass has been a significant topic of interest for decades. Dynamical facilitation is widely believed to be an important characteristic of glassy dynamics, but the precise mechanism is still under debate. We propose a lattice model of glass called the facilitated random walk (FRW). Each particle performs a continuous time random walk in the presence of its own random local kinetic constraints. The particles do not interact energetically. Instead, they interact kinetically with a hopping rate resampling rule under which motions of a particle can randomly perturb the local kinetic constraints of other particles. This dynamic interaction is reversible, following a rate restoration rule. A step-by-step reversal of the particle motions exactly restores the previous constraints, modeling randomness quenched in the configuration space of glass. The model exhibits stretched exponential relaxation and dynamical heterogeneity typical of glasses. Despite the lack of an explicit facilitation rule, the FRW shows facilitation behaviors closely analogous to those of the kinetically constrained models (KCM). The FRW is a coarse-grained version of the distinguishable particle lattice model (DPLM) and this exemplifies that compatible defect and atomistic models can complement each other in the study of glass.

The one-dimensional extended Hubbard model (EHM) in the atomic limit has recently been found to exhibit a curious thermal pseudo-transition behavior, which closely resembles first and second-order thermal phase transitions. This phenomenon, occurring at half-filling, is influenced by the quantum phase transition between the alternating pair (AP) and paramagnetic (PM) phases at zero temperature. In this study, we leverage this anomalous behavior to investigate the performance of quantum many-body machines, using the EHM as the working substance. Our analysis reveals that the quantum Otto engine, when operating in the anomalous region, closely mimics the ideal Carnot engine. In this region, both the work output and thermal efficiency of the Otto engine increase, approaching the performance of a Carnot engine. This highlights the potential of many-body systems, such as the EHM, in enhancing quantum thermodynamic performance. Our findings demonstrate that, although the second law of thermodynamics prevents engines from surpassing Carnot efficiency, the Otto engine can operate remarkably close to this limit in the anomalous region, offering insights into new directions for future research on quantum thermodynamic cycles and working substances.