Shear transformations (STs), as the fundamental events of plastic deformation of amorphous solids, remain a great deal of uncertainty regarding their basic characteristics. Here we propose an effective method for extracting these basic characteristics by means of fitting the spatial correlation of strain fields to the solutions of Eshelby's inclusion theory. Our method identifies individual STs from plastic events and eliminates the influence of local fluctuations, which greatly improves the effectiveness of the fitting results. Using this method, the Eshelby characteristics of STs and the relationship between STs and atomic structure are investigated in the atomistic simulations of a $\mathrm{C}{\mathrm{u}}_{50}\mathrm{Z}{\mathrm{r}}_{50}$ model glass. The broad distributions of Eshelby characteristics confirm the heterogeneous and anisotropic nature of STs. The shape of STs closely approximates a sphere, with the inclusion radius approaching 1.5 times the atomic size. Except for the component along the macroscopic loading direction, the other eigenstrain components generally follow a Gaussian distribution. The shear deformation of STs is much smaller than previously believed. The volumetric deformation of STs can be either dilatational or compressive, with a slight preference for dilatation. The further softening induced by STs is due to the fact that the promoting effect of local dilatation overweighs the suppressive effect of structural ordering. Our method can extract key information of STs for establishing a constitutive model that bridges the gap between microscopic atomic rearrangements and macroscopic plastic response.

Multicomponent phase separation is a routine occurrence in both living and synthetic systems. Thermodynamics provides a straightforward path to determine the phase boundaries that characterize these transitions for systems at equilibrium. The prevalence of phase separation in complex systems outside the confines of equilibrium motivates the need for a nonequilibrium theory of multicomponent phase coexistence. Here, we develop a mechanical theory for coexistence that casts coexistence criteria into the familiar form of equality of state functions. Our theory generalizes traditional equilibrium notions such as the species chemical potential and thermodynamic pressure to systems out of equilibrium. Crucially, while these notions may not be identifiable for all nonequilibrium systems, we numerically verify their existence for a variety of systems by introducing the phenomenological multicomponent active model $\mathrm{B}+$. Our work establishes an initial framework for understanding multicomponent coexistence that we hope can serve as the basis for a comprehensive theory for high-dimensional nonequilibrium phase transitions.

We study the fractal properties of depth-first search (DFS) paths in critical configurations of statistical physics models, including the two-dimensional $O\left(n\right)$ loop model for various $n$, and bond percolation in dimensions $d=2$ to 6. In the $O\left(n\right)$ loop model, across both critical and tricritical Potts regimes, the fractal dimension of the DFS path consistently follows $d_{\mathrm{DFS}}=1+g/8$, where $g$ is the coupling constant in Coulomb gas theory, related to $n$ via $n^2=2+2cos(\pi g/2)$ with $g\in [8/3,16/3]$. For bond percolation, the DFS path exhibits nontrivial fractal scaling across all studied dimensions. Interestingly, when DFS is applied to the full lattice without any dilution or criticality, the path is still fractal in two dimensions, with a dimension close to $7/4$, but becomes space-filling in higher dimensions. Our results demonstrate that DFS offers a robust and broadly applicable geometric probe for exploring critical phenomena beyond traditional observables.

Discontinuous phase transitions are closely linked to tipping points, critical mass effects, and hysteresis, phenomena that have been confirmed empirically and recognized as highly important in social systems. The multistate $q$-voter model, an agent-based approach to simulate discrete decision-making and opinion dynamics, is particularly relevant in this context. Previous studies of the $q$-voter model with anticonformity on complete graphs uncovered a counterintuitive result. Changing the model formulation from the annealed (homogeneous agents with varying behavior) to quenched (heterogeneous agents with fixed behavior) produces discontinuous phase transitions. This is contrary to the common expectation that quenched heterogeneity smooths transitions. To test whether this effect is merely a mean-field artifact, we extend the analysis to random graphs. Using pair approximation and Monte Carlo simulations, we show that the phenomenon persists beyond the complete graph, specifically on random graphs and Barabási-Albert scale-free networks. The novelty of our work is twofold: (i) we demonstrate for the first time that replacing the annealed with the quenched approach can change the type of phase transitions from continuous to discontinuous not only on complete graphs but also on sparser networks, and (ii) we provide pair-approximation results for the multistate $q$-voter model with competing conformity and anticonformity mechanisms, covering both quenched and annealed cases, which had previously been studied only in binary models.

People's opinions evolve through social interactions, and their social networks evolve as their opinions change. In this paper, we generalize bounded-confidence models of opinion dynamics by incorporating neighborhood effects. In our neighborhood bounded-confidence models (NBCMs), interacting agents are influenced both by each other's opinions and by the opinions of the agents in each other's neighborhoods (through so-called “transitive influence”). We extend our NBCMs to adaptive network models that incorporate “transitive homophily”, with agents rewiring to connect preferentially to agents whose mean neighbor opinions are close to their own opinions. We numerically simulate an asynchronously updating adaptive NBCM on a variety of networks, and we explore how its opinion dynamics and structural properties change as we adjust the relative importances of dyadic and transitive influence. We observe that the transitive influence of neighborhoods can play an important role in shaping the qualitative features of opinion dynamics.

In this study, we employ Langevin dynamics simulations to investigate the self-assembly of anionic surfactants, multichain cationic polyelectrolytes, and counterions. By applying an aggregate indexing scheme (counting the number of surfactants and polyelectrolytes in each assembly), we construct a histogram that reveals a diverse spectrum of supramolecular structures: free surfactant micelles, isolated polyelectrolyte chains, and mixed clusters containing both species. As surfactant hydrophobicity increases, the histogram shifts from a dense distribution—where small aggregates dominate and multipolyelectrolyte mixed clusters are infrequent—to a sparse one, characterized by distinct aggregation zones separated by depletion regions. The emergence of populated zones at high aggregation indices indicates a sharp increase in large, mixed clusters containing multiple polyelectrolytes. Structurally, weakly hydrophobic surfactants result in solutions dominated by free polyelectrolytes, low-aggregation-number micelles, and small mixed clusters. Under strong hydrophobic conditions, surfactants engage in cooperative binding to form elongated micelles that associate with multiple polyelectrolyte chains. Meanwhile, most counterions remain uncondensed and freely diffuse, increasing their translational entropy. Together, our results support a model in which strong Coulomb interactions and counterion release jointly drive the mutual condensation of polyelectrolyte chains and surfactant micelles into large, anisotropic mixed clusters.

We present a general framework for determining the power-efficiency trade-off relations across arbitrary thermal machines, addressing the lack of unified optimization results stemming from their diverse functionalities (e.g., heat engines, refrigerators, and heat pumps). For time-dependent cycle irreversibility $A\left(\tau \right)$ following a ${\tau }^{-\alpha }$ power law, where $\alpha$ is an interaction-dependent parameter, we show that engineering the interactions between thermal machines and reservoirs enables control over the trade-off relations, with the efficiency at maximum power approaching Carnot efficiency as $\alpha$ increases. Setting $\alpha =1$ naturally recovers typical low-dissipation regime results. Additionally, we derive the first power-efficiency trade-off for finite-time quantum adiabatic Otto machines with ${\tau }^{-2}$-scaling. This work establishes a unified constraint for thermodynamic cycles across nonequilibrium regimes, facilitating consistent optimization of diverse thermal devices in practice.

The recently proposed macroscopic quantum phenomenon, Temperature-Induced Quantum Migration (TIQM), causes local heating and cooling and significantly affects the local heat capacity of a noninteracting confined Maxwell-Boltzmann gas. TIQM guarantees the non-negativity of local heat capacity at low temperatures, results in a substantial local heat-capacity overshoot, and provides a physical basis for global heat-capacity maxima and thermal confinement energy. We extend this framework here to Bose gases in three different rectangular domains, effectively providing three-dimensional (3D)/two-dimensional (2D)/one-dimensional (1D) confinement at high temperatures while transitioning to 2D/1D/zero-dimensional (0D) at low temperatures, thus inducing dimensional crossovers during temperature changes. We demonstrate that quantum degeneracy enhances the TIQM process, resulting in dimension-dependent effects on local and global heat capacities. For the 3D-2D crossover, TIQM leads to a giant excess local heat capacity and explains the mechanism for the enhancement of the global heat-capacity maximum, which surpasses the unconfined ideal Bose gas limit (1.93), reaching 1.97 at a finite density. Conversely, for the 2D-1D and 1D-0D crossovers, the excess local heat capacity diminishes with increasing quantum degeneracy (density), while it is TIQM alone that becomes responsible for excess global heat capacity. For the 1D-0D crossover, we find that only single-particle ergodic systems can have a global excess heat capacity; otherwise, the maximum behavior disappears completely. TIQM also provides a mechanism for the thermal confinement energy in Bose gases.

Random walks on lattices with preferential relocation to previously visited sites provide a simple framework for modeling the displacements of animals and humans. When the lattice contains a few impurities or resource sites where the walker spends more time on average at each visit than on the other sites, the long-range memory can suppress diffusion and induce by reinforcement a steady state localized around a resource. This phenomenon can be identified with a spatial learning process. Here we study theoretically and numerically how the decay of memory impacts learning in a model with one impurity. If memory decays as $1/\tau$ or slower, where $\tau$ is the time backward into the past, the localized solution is the same as with perfect, nondecaying memory and it is linearly stable. If forgetting is faster than $1/\tau$, for instance exponential, an unusual regime of intermittent localization is observed, where well-localized periods of exponentially distributed duration are disrupted by possibly long intervals of diffusive motion. At the transition between the two regimes, for a kernel in $1/\tau$, the approach to the stable localized state is the fastest, opposite to the expected critical slowing down effect. Hence, forgetting can allow the walker to save a lot of memory without compromising learning and to achieve a faster learning process. These findings agree with biological evidence on the benefits of forgetting.

Advancements in noisy intermediate-scale quantum (NISQ) computing are steadily pushing these systems toward outperforming classical supercomputers on specific well-defined computational tasks. In this work we explore and control quantum chaos in NISQ systems using discrete-time quantum walks (DTQWs) on cyclic graphs. To efficiently implement quantum walks on NISQ hardware, we employ the quantum Fourier transform to diagonalize the conditional shift operator, optimizing circuit depth and fidelity. We experimentally realize the transition from quantum chaos to order via DTQW dynamics on both odd and even cyclic graphs, specifically 3- and 4-cycle graphs, using the counterintuitive Parrondo paradox strategy across three different NISQ devices. While the 4-cycle graphs exhibit high-fidelity quantum evolution, the 3-cycle implementation shows significant fidelity improvement when augmented with dynamical decoupling pulses. Our results demonstrate a practical approach to probing and harnessing controlled chaotic dynamics on real quantum hardware, laying the groundwork for future quantum algorithms and cryptographic protocols based on quantum walks.

Our recent study on the Bethe lattice reported that a discontinuous-percolation transition emerges as the number of occupied links increases and each node rewires its links to locally suppress the growth of neighboring clusters. However, since the Bethe lattice is a tree, a macroscopic cluster forms as an infinite spanning tree but does not contain a finite fraction of the nodes. In this paper, we study a bipartite network that can be regarded as a locally treelike structure with long-range neighbors. In this network, each node in one of the two partitions is allowed to rewire its links to nodes in the other partition to suppress the growth of neighboring clusters. We observe a discontinuous-percolation transition characterized by the emergence of a single macroscopic cluster containing a finite fraction of nodes, followed by critical behavior of the cluster-size distribution. We also provide an analytical explanation of the underlying mechanism.

Microswimmer locomotion in heterogeneous media is increasingly relevant in biological physics due to the prevalence of microorganisms in complex environments. A model for such porous media is the Brinkman fluid, which accounts for a sparse matrix of stationary obstacles via a linear resistance term in the momentum equation. We investigate two models for the locomotion and the flow field generated by a swimmer in such a medium. First, we analyze a dumbbell swimmer composed of two spring-connected spheres and driven by a flagellar force and derive its swimming velocity as a function of the Brinkman medium resistance, showing that the swimmer monotonically slows down as the medium drag monotonically increases. In the limit of no resistance the model reduces to the classical Stokes dipole swimmer, while finite resistance introduces hydrodynamic screening that attenuates long-range interactions. Additionally, we derive an analytical expression for the far-field flow generated by a Brinkmanlet force dipole, which can be used for propulsive point-dipole swimmer models. Remarkably, this approximation reproduces the dumbbell swimmer's flow field in the far-field regime with high accuracy. These results provide analytical tools for understanding locomotion in complex fluids and offer foundational insights for future studies on collective behavior in active and passive suspensions within porous or structured environments.

We study effective mixing behavior of solutes in steady flows through three-dimensional random fracture networks and find that mixing in these systems is characterized by phenomena distinct from continuous porous media. Network-scale heterogeneity leads to the complex spatio-temporal organization of the flow-field that determines a mixing interface between transported solutes. The growth of the mixing interface is characterized by splitting events as it crosses between fracture intersections, which does not occur in a continuous porous medium. We derive an analytical model for growth of the mixing interface, which is a function of network properties. Agreement of the model with high-fidelity simulations of flow and transport indicates a link between network topology and mixing dynamics unique to fractured media. The model also provides asymptotic predictions that are intractable with current numerical simulations. Moreover, we do not observe the chaotic exponential growth of the mixing interface that is commonly observed in porous media. The observations and model development indicate a foundational difference in mixing behavior between fractured and porous media.

We analyze a generalization of Zöttl and Stark's model of active spherical particles [Phys. Rev. Lett. 108, 218104 (2012)] and prolate spheroidal particles [Eur. Phys. J. E 36, 4 (2013)] suspended in cylindrical Poiseuille flow, to particle dynamics in an arbitrary unidirectional steady laminar flow through a straight duct geometry. Our primary contribution is to describe a Hamiltonian formulation of these systems and provide explicit forms of the constants of motions in terms of the arbitrary fluid velocity field. The Hamiltonian formulation provides a convenient and robust approach to the computation of particle orbits while also providing new insights into the dynamics, specifically the way in which orbits are trapped within basins defined by a potential well. In addition to considering spherical and prolate spheroidal particles, we also illustrate that the model can be adapted to oblate spheroidal particles.

We consider the phase transition induced by compressing a self-avoiding walk in a slab where the walk is attached to both walls of the slab in two and three dimensions, and the resulting phase once the polymer is compressed. The process of moving between a stretched situation where the walls pull apart to a compressed scenario is a phase transition with some similarities to that induced by pulling and pushing the end of the polymer. However, there are key differences in that the compressed state is expected to behave like a lower dimensional system, which is not the case when the force pushes only on the end point of the polymer. We use scaling arguments to predict the exponents both associated with the phase transition and in the compressed state and find good agreement with Monte Carlo simulations.

We study the correlation function of the one-dimensional Ising model at fixed magnetization. Focusing on the scaling limit close to the zero-temperature fixed point, we show that this correlation function, in momentum space, exhibits surprising oscillations as a function of the magnetization. We show that these oscillations have a period inversely proportional to the momentum and give an interpretation in terms of domain walls. This is in sharp contrast with the behavior of the correlation function in constant magnetic fields and sheds light on recent results obtained by Monte Carlo simulations for the correlation functions of the critical two-dimensional Ising model at fixed magnetization.

Renyi entropy with multiple disjoint intervals are computed from the improved swapping operations by two methods: One is from the direct diagonalization of the Hamiltonian and the other one is from the state-of-the-art machine learning method with neural networks. We use the paradigmatic transverse-field Ising model in one dimension to demonstrate the strategy of the improved swapping operation. In particular, we study the second Renyi entropy with two, three, and four disjoint intervals. We find that the results from the above two methods match each other very well within errors, which indicates that the machine learning method is applicable for calculating the Renyi entropy with multiple disjoint intervals. Moreover, as the magnetic field increases, the Renyi entropy grows as well until the system arrives at the critical point of the phase transition. However, as the magnetic field exceeds the critical value, the Renyi entropy will decrease since the system enters the paramagnetic phase. Overall, these results match the theoretical predictions very well and demonstrate the high accuracy of the machine learning methods with neural networks.

We design a thermal bath that preserves the conservation of a system's angular momentum or allows it to fluctuate around a specified nonzero mean while maintaining a Boltzmann distribution of energy in the steady state. We demonstrate that classical particles immersed in such baths exhibit position-momentum uncertainties with a strictly positive lower bound proportional to the absolute value of the mean angular momentum. The proportionality constant, $c$, is dimensionless and does not depend explicitly on the system's parameters. Remarkably, while $c$ is universally bounded by unity, it attains the exact value $c=\frac{1}{2}$ for particles in central potentials.

A scenario frequently encountered in real-world complex systems is the temporary failure of a few components. For spatially extended chaotic systems whose functionality hinges on the collective dynamics of the interacting components, a viable approach to dealing with the failures is replacing the malfunctioning components with their backups, so that the collective dynamics of the systems can be precisely maintained for a duration long enough to resolve the problem. Here, taking the chaotic dynamics of the paradigmatic Kuramoto model as an example and considering the scenario of oscillator failures, we propose substituting the failed oscillators with digital twins trained by the data measured from the system evolution. Specifically, leveraging the technique of an adaptable reservoir computer (RC) in machine learning, we demonstrate that a single, small-size RC can substitute any oscillator in the Kuramoto model such that the time evolution of the synchronization order parameter of the repaired system is identical to that of the original system for a certain time period. The performance of adaptable RC is evaluated in various contexts, and it is found that the sustaining period is influenced by multiple factors, including the size of the training dataset, the overall coupling strength of the system, and the number of substituted oscillators. Additionally, though the synchronization order parameter diverges from the ground truth in the long-term running, the functional networks of the oscillators are still faithfully sustained by the machine substitutions.

When taking place under fluctuating environments, some classical results of evolutionary dynamics in fitness landscapes need to be reconsidered. Under such nonequilibrium conditions, the properties of adaptive evolution might escape from the expectations grounded in equilibrium systems. Here, an important contribution to this nonequilibrium dynamics results from the presence of a geometry (Berry) phase in the Crow-Kimura model of molecular evolution with asymmetric mutations. By considering changes in fitness alone as well as changes in both fitness and mutation, analytical expressions for the Berry phase are derived, showing strong singularities at bulk transition points. Periodically varying parameters are also analyed for the two-dimensional case. The potential implications for evolutionary and prebiotic scenarios are discussed.