Finding the mean time it takes for a particle to escape from a metastable state due to thermal fluctuations is a fundamental problem in physics, chemistry, and biology. Here, we consider the escape rate of interacting diffusive particles, from a deep potential trap within the framework of the macroscopic fluctuation theory—a nonequilibrium hydrodynamic theory. For systems without excluded volume, our investigation reveals adherence to the well-established Arrhenius law. However, in the presence of excluded volume, a universality class emerges, fundamentally altering the escape rate. Remarkably, the modified escape rate within this universality class is independent of the interactions at play. The universality class, demonstrating the importance of excluded volume effects, may bring insights to the interpretation of escape processes in the realm of chemical physics.

Progressive quenching (PQ) is a process in which we sequentially fix a system's degrees of freedom, which would otherwise evolve according to their stochastic dynamics. Previous studies have discovered what we refer to as the hidden martingale property in PQ. Here we first attribute this martingale property to the canonicity of the two-layer ensemble comprising quenched and thermal ensembles and demonstrate that the Markovian property, coupled with the detailed balance (DB) of the evolution dynamics, underpins this canonicity. We then expand the PQ to the Markovian dynamics on the transition network where the DB is not required. Additionally, we examine the PQ of the systems that evolve through non-Markovian dynamics between consecutive quenching. When non-Markovian dynamics ensure a trajectory-wise DB, such as in an equilibrium spin system with a hidden part, the PQ can occasionally maintain the canonical structure of the overall statistical ensemble but not always. Last, we analytically and numerically investigate the PQ of a non-Markovian spin system with delayed interaction and illustrate how the reduction of spin correlations due to the delay can be compensated by the PQ.

Numerical simulations and finite-size scaling analysis have been carried out to study standard and inverse percolation of triangular tiles of side $k$ ($k$-tiles) on triangular lattices. In the case of standard percolation, the lattice is initially empty. Then, $k$-tiles are randomly and sequentially deposited on the lattice. In the case of inverse percolation, the process starts with an initial configuration where all lattice sites are occupied by single monomers (each monomer occupies one lattice site) and, consequently, the opposite sides of the lattice are connected by nearest-neighbor occupied sites. Then, the system is diluted by randomly removing $k$-tiles [composed by $k(k+1)/2$ monomers] from the lattice. Two schemes are used for the depositing and removing process: the isotropic scheme, where the deposition (removal) of the objects occurs with the same probability in any lattice direction; and the anisotropic (perfectly oriented or nematic) scheme, where one lattice direction is privileged for depositing (removing) the tiles. The study is conducted by following the behavior of four critical concentrations with the size $k$: $\left(i\right) \left[\right(ii\left)\right]$ standard isotropic (oriented) percolation threshold ${\theta }_{c,k}$ (${\vartheta }_{c,k}$), which represents the minimum concentration of occupied sites at which an infinite cluster of occupied nearest-neighbor sites extends from one side of the system to the other. ${\theta }_{c,k}$ (${\vartheta }_{c,k}$) is reached by isotropic (oriented) deposition of $k$-tiles on an initially empty lattice; and $\left(iii\right) \left[\right(iv\left)\right]$ inverse isotropic (oriented) percolation threshold ${\theta }_{c,k}^i$ (${\vartheta }_{c,k}^i$), which corresponds to the maximum concentration of occupied sites for which connectivity disappears. ${\theta }_{c,k}^i$ (${\vartheta }_{c,k}^i$) is reached after removing isotropic (completely aligned) $k$-tiles from an initially fully occupied lattice. The obtained results indicate that $\left(1\right){\theta }_{c,k}$ (${\theta }_{c,k}^i$) is an increasing (decreasing) function of $k$ in the range $1\le k\le 6$. For $k\ge 7$, all jammed configurations are nonpercolating (percolating) states and, consequently, the percolation phase transition disappears. $\left(2\right){\vartheta }_{c,k}$ (${\vartheta }_{c,k}^i$) show a behavior qualitatively similar to that observed for isotropic deposition. In this case, the minimum value of $k$ at which the phase transition disappears is $k=5$. (3) For both isotropic and perfectly oriented models, the curves of standard and inverse percolation thresholds are symmetric to each other with respect to the line $\theta \left(\vartheta \right)=0.5$. Thus, a complementary property is found ${\theta }_{c,k}+{\theta }_{c,k}^i=1$ (and ${\vartheta }_{c,k}+{\vartheta }_{c,k}^i=1$), which has not been observed in other regular lattices. (4) Finally, in all cases, the jamming exponent ${\nu }_j$ was measured, being ${\nu }_j=1$ regardless of the orientation (isotropic or nematic) or the size $k$ considered. In addition, the accurate determination of the critical exponents $\nu , \beta$, and $\gamma$ reveals that the percolation phase transition involved in the system, which occurs for $k$ varying between one and five (three) for isotropic (nematic) deposition scheme, has the same universality class as the standard percolation problem.

We study the multifractal behavior of coherent states projected in the energy eigenbasis of the spin-boson Dicke Hamiltonian, a paradigmatic model describing the collective interaction between a single bosonic mode and a set of two-level systems. By examining the linear approximation and parabolic correction to the mass exponents, we find ergodic and multifractal coherent states and show that they reflect details of the structure of the classical phase space, including chaos, regularity, and features of localization. The analysis of multifractality stands as a sensitive tool to detect changes and structures in phase space, complementary to classical tools to investigate it. We also address the difficulties involved in the multifractal analyses of systems with unbounded Hilbert spaces.

We consider the localization of elastic waves in thin elastic structures with spatially varying curvature profiles, using a curved rod and a singly curved shell as concrete examples. Previous studies on related problems have broadly focused on the localization of flexural waves on such structures. Here, using the semiclassical WKB approximation for multicomponent waves, we show that in addition to flexural waves, extensional and shear waves also form localized, bound states around points where the absolute curvature of the structure has a minimum. We also see excellent agreement between our numerical experiments and the semiclassical results, which hinges on the vanishing of two extra phases that arise in the semiclassical quantization rule. Our findings open up novel ways to fine-tune the acoustic and vibrational properties of thin elastic structures and raise the possibility of introducing new phenomena not easily captured by effective models of flexural waves alone.

We present a mode-coupled weakly nonlinear model for the evolution of perturbations on cylindrical multilayered shells in a decelerating implosion. We show that nonlinear mode-mode interactions among large wave-number fundamental modes are able to induce the growth of small wave number harmonic modes, i.e., forming inverse cascade channels in the wave-number space. When uniform compression and interfacial coupling are taken into consideration, the amplitude of some perturbation modes exhibits an oscillatory growth pattern, which is beyond the intuition that perturbation amplitudes usually have a fast growth tendency in an implosion dominated by the Bell-Plesset effect. Our model accounts well for the previous experiments of Hsing et al. [Hsing et al., Phys. Rev. Lett. 78, 3876 (1997) and Phys. Plasmas 4, 1832 (1997)], which is among the few experiments of multimode multiinterface perturbation development in a cylindrical implosion. In particular, we find that the inverse cascade of modes is the origin of the excitation and growth of the wave number $k=2$ harmonic mode on the inner interface. The observed decrease of the fundamental modes on the inner interface is mainly attributed to the decreasing period of the oscillatory growth process. These results may afford further insight into the distortion of hot spots in inertial confined fusion implosion near the final stage, and also help to design multimode perturbation experiments in converging geometry in the coming future.

We analyze a one-dimensional intermittent random walk on an unbounded domain in the presence of stochastic resetting. In this process, the walker alternates between local intensive search, diffusion, and rapid ballistic relocations in which it does not react to the target. We demonstrate that Poissonian resetting leads to the existence of a non-equilibrium steady state. We calculate the distribution of the first arrival time to a target along with its mean and show the existence of an optimal reset rate. In particular, we prove that the initial condition of the walker, i.e., either starting diffusely or relocating, can significantly affect the long-time properties of the search process. Moreover, we demonstrate the presence of distinct parameter regimes for the global optimization of the mean first arrival time when ballistic and diffusive movements are in direct competition.

We further develop the strong-coupling theory of thermodynamics and stochastic thermodynamics for continuous systems, constructed in the previous work [Phys. Rev. Res. 4, 013015 (2022)]. A small system strongly interacting with $a$ its environment, the dynamics of the system is assumed to be much slower than that of the bath. The system Hamiltonian is defined to be the Hamiltonian of mean force, whereas the system entropy is defined as the Gibbs-Shannon entropy. Equilibrium ensemble theories and thermodynamic theories are established for the system. Variations of three types of parameters are considered: (i) the system parameter $\lambda$ which couples to the system and to the interaction, (ii) the bath parameter ${\lambda }^{\prime }$ which couples to the bath only, and (iii) the temperature $T=1/\beta$. The work done to the system consists of three parts, proportional to $d\lambda , d{\lambda }^{\prime }$, and $d\beta$ respectively. The part proportional to $d\beta$ can be understood as the work done by the bath. As long as ${\lambda }^{\prime }$ and $\beta$ are not fixed, the work is not the change of total energy of the joint system. The differences between our strong-coupling equilibrium thermodynamics and the classical thermodynamics are discussed. The thermodynamic theory is promoted to the nonequilibrium level. Both the first and second laws of thermodynamics, as well as fluctuation theorems, are established for nonequilibrium processes. For processes with varying temperatures, fluctuation theorems cannot be expressed in terms of integrated work alone. Regardless of various subtleties, however, the stochastic thermodynamic theory is formulated in terms of system variables only, and $dS-\beta d\overline{}Q$ is the change of total entropy. Thermodynamic quantities of the system are related to those of the joint system, and the equivalence of theories at two levels of coarse-graining is explicitly demonstrated. Finally we show that there are infinite numbers of equivalent strong-coupling theories, each determined by its definition of system Hamiltonian. Our theory is distinguished by its maximal similarity with the weak-coupling theory.

We report on high-precision measurements that were performed with superconducting waveguide networks with the geometry of a tetrahedral and a honeycomb graph. They consist of junctions of valency three that connect straight rectangular waveguides of equal width but incommensurable lengths. The experiments were performed in the frequency range of a single transversal mode, where the associated Helmholtz equation is effectively one-dimensional and waveguide networks may serve as models of quantum graphs with the joints and waveguides corresponding to the vertices and bonds. The tetrahedral network comprises T junctions, while the honeycomb network exclusively consists of Y junctions, that join waveguides with relative angles ${90}^{\circ }$ and ${120}^{\circ }$, respectively. We demonstrate that the vertex scattering matrix, which describes the propagation of the modes through the junctions, strongly depends on frequency and is nonsymmetric at a T junction and thus differs from that of a quantum graph with Neumann boundary conditions at the vertices. On the other hand, at a Y junction, similarity can be achieved in a certain frequency range. We investigate the spectral properties of closed waveguide networks and fluctuation properties of the scattering matrix of open ones and find good agreement with random matrix theory predictions for the honeycomb waveguide graph.

In networked dynamical systems, inferring governing parameters is crucial for predicting nodal dynamics, such as gene expression levels, species abundance, or population density. While many parameter estimation techniques rely on time-series data, particularly systems that converge over extreme time ranges, only noisy steady-state data is available, requiring a new approach to infer dynamical parameters from noisy observations of steady states. However, the traditional optimization process is computationally demanding, requiring repeated simulation of coupled ordinary differential equations. To overcome these limitations, we introduce a surrogate objective function that leverages decoupled equations to compute steady states, significantly reducing computational complexity. Furthermore, by optimizing the surrogate objective function, we obtain steady states that more accurately approximate the ground truth than noisy observations and predict future equilibria when topology changes. We empirically demonstrate the effectiveness of the proposed method across ecological, gene regulatory, and epidemic networks. Our approach provides an efficient and effective way to estimate parameters from steady-state data and has the potential to improve predictions in networked dynamical systems.

Swarming behavior in systems of self-propelled particles, whether biological or artificial, has received increased attention in recent years. Here, we show that even a small number of particles with anomalous behavior can change dramatically collective dynamics of the swarming system and can impose unusual behavior and transitions between dynamic states. Our results pave the way to practical approaches and concepts of multiagent dynamics in groups of flocking animals: birds, insects, and fish, i.e., active and living soft matter.

Self-oscillating systems possess the ability to convert ambient energy directly into mechanical work, and new types of self-oscillating systems are worth designing for practical applications in energy harvesters, engines and actuators. Taking inspiration from the four-stroke engine. A concept for a self-rotating engine is presented on the basis of photothermally responsive materials, consisting of a liquid crystal elastomer (LCE) fiber, a hinge and a turnplate, which can self-rotate under steady illumination. Based on the photo-thermal-mechanical model, a nonlinear theoretical model of the LCE-based engine under steady illumination is proposed to investigate its self-rotating behaviors. Numerical calculations reveal that the LCE-based engine experiences a supercritical Hopf bifurcation between the static regime and the self-rotation regime. The self-rotation of the LCE-based engine originates from the photothermally driven strain of the LCE fiber in illumination, and its continuous periodic motion is sustained by the correlation between photothermal energy and damping dissipation. The Hopf bifurcation conditions are also explored in detail, as well as the vital system parameters affecting self-rotation frequency. Compared to the abundant existing self-oscillating systems, this conceptual self-rotating LCE-based engine stands out due to its simple and lightweight structure, customizable dimensions and high speed, and it is expected to offer a broader range of design concepts applicable to soft robotics, energy harvesters, medical instruments, and so on.

We study bridging transitions between a pair of nonplanar surfaces. We show that the transition can be described using a generalized Kelvin equation by mapping the system to a slit of finite length. The proposed equation is applied to analyze the asymptotic behavior of the growth of the bridging film, which occurs when the confining walls are gradually flattened. This phenomenon is characterized by a power-law divergence with geometry-dependent critical exponents that we determine for a wide class of walls' geometries. In particular, for a linear-wedge model, a covariance law revealing a relation between a geometric and Young's contact angle is presented. These predictions are shown to be fully in line with the numerical results obtained from a microscopic (classical) density functional theory.

Macroscopic dipole moments formed in electrolytic cells influence dielectric properties of the cells, and their magnitudes can be quantified by dielectric spectroscopy. We analyze the dielectric spectra observed for dilute electrolytic cells in low-frequency regions from two perspectives: space-charge polarization and diffuse double layers on the electrodes. The difference between the two polarization phenomena is characterized by the effective dielectric constant and the kinetic parameter introduced in the Poisson-Nernst-Planck model. The analytical results indicate that the generation of space-charge polarization is attributed to the kinetic process of mobile ions replacing solvent molecules on the electrode surface. This is an experimental confirmation of the formation process of macroscopic dipole moment due to space-charge polarization and its practical contribution to the dielectric constant of material.

We investigate, using a recently developed model of liquid state theory describing the rheology of dense granular flows, how a yield stress appears in granular matter at the yielding transition. Our model allows us to predict an analytical equation of the corresponding dynamical yield surface, which is compared to the usual models of solid fracture. In particular, this yield surface interpolates between the typical failure behaviors of soft and hard materials. This work also underlines the central role played by the effective friction coefficient at the yielding transition.

Accurate modeling of warm and hot dense matter is challenging in part due to the multitude of excited states that must be considered. Here, we present a variational framework that models these excited states. In this framework an excited state is defined by a set of effective one-electron occupation factors, and the corresponding energy is defined by the effective one-body energy with an exchange and correlation term. The variational framework is applied to an atom-in-plasma model (a generalization of the so-called average atom model). Comparisons with a density functional theory based average atom model generally reveal good agreement in the calculated pressure, but our model also gives access to the excitation energies and charge state distributions.

Molecular dynamical simulations are performed to investigate the scaling of the transverse sound speed in two-dimensional (2D) and 3D Yukawa fluids. From the calculated diagnostics of the radial distribution function, the mean-squared displacement, and the Pearson correlation coefficient, the approximate isomorphic curves for 2D and 3D liquidlike Yukawa systems are obtained. It is found that the structure and dynamics of 2D and 3D liquidlike Yukawa systems exhibit the isomorphic property under the conditions of the same relative coupling parameter $\mathrm{\Gamma }/{\mathrm{\Gamma }}_{\mathrm{m}}=\mathrm{const}$. It is demonstrated that the reduced transverse sound speed, i.e., the ratio of the transverse sound speed to the thermal speed, is an isomorph invariant, which is a quasiuniversal function of $\mathrm{\Gamma }/{\mathrm{\Gamma }}_{\mathrm{m}}$. The obtained isomorph invariant of the reduced transverse sound speed can be useful to estimate the transverse sound speed, or determine the coupling strength, with applications to dusty (complex) plasma or colloidal systems.

In this paper a system consisting of two electron spins has been prepared initially in a singlet state using the chemical compass model is considered. It is assumed that each electron spin interacts symmetrically and/or asymmetrically with its respective private nuclear environment in the presence of an external magnetic field. We discussed the effect of the interaction parameters and the external magnetic field on some quantifiers of quantum correlations as entanglement, coherence, Bell inequality, as well as the steerability inequality. It is shown that within a certain range of external magnetic fields, the quantum coherence and entanglement behave similarly. The Bell and the steerable inequalities predicted a similar behavior for symmetric and asymmetric interactions. Moreover, as one increases the external magnetic field, the lower bounds of both inequalities have improved. The usefulness of using the spin state as quantum channel to teleport a two-qubit system has examined where the Bell inequality could be above its classical bounds by controlling the interaction parameters. It is shown that by tuning the coupling parameters the fidelity of the teleported state exceeds the classical bounds, as well as the long-lived stationary fidelity could be achieved during the interaction time.

Topology plays a fundamental role in our understanding of many-body physics, from vortices and solitons in classical field theory to phases and excitations in quantum matter. Topological phenomena are intimately connected to the distribution of information content that, differently from ordinary matter, is now governed by nonlocal degrees of freedom. However, a precise characterization of how topological effects govern the complexity of a many-body state, i.e., its partition function, is presently unclear. In this paper, we show how topology and complexity are directly intertwined concepts in the context of classical statistical mechanics. We concretely present a theory that shows how the Kolmogorov complexity of a classical partition function sampling carries unique, distinctive features depending on the presence of topological excitations in the system. We confront two-dimensional Ising, Heisenberg, and XY models on several topologies and study the corresponding samplings as high-dimensional manifolds in configuration space, quantifying their complexity via the intrinsic dimension. While for the Ising and Heisenberg models the intrinsic dimension is independent of the real-space topology, for the XY model it depends crucially on temperature: across the Berezkinskii-Kosterlitz-Thouless (BKT) transition, complexity becomes topology dependent. In the BKT phase, it displays a characteristic dependence on the homology of the real-space manifold, and, for $g$-torii, it follows a scaling that is solely genus dependent. We argue that this behavior is intimately connected to the emergence of an order parameter in data space, the conditional connectivity, which displays scaling behavior. Our approach paves the way for an understanding of topological phenomena emergent from many-body interactions from the perspective of Kolmogorov complexity.