We develop a reweighting framework to quantify the free energy difference between two equilibrium states of a strongly coupled open system at fixed temperature. For an open system described by the Hamiltonian of mean force (HMF), we show that the equilibrium free energy difference between two canonical endpoints can be written as exponential averages of the HMF shift, divided by an explicit factor built from the chi-squared divergence between the initial and final system marginals. These relations hold at the endpoint level and, under an explicit asymptotic-equilibration postulate, admit trajectory representations for protocols whose evolved system marginal reaches the prescribed final canonical endpoint. In this trajectory representation, the dynamics provide a route for generating samples from the final canonical endpoint. In the frozen-driving regime with a noninteracting reference, the equalities reduce to FEP-like expressions involving an environment functional and an explicit overlap diagnostic, with the Zwanzig formula recovered as a limiting case. We validate the approach on an open system coupled to an environment and evolved under overdamped Langevin dynamics, where conventional Zwanzig FEP suffers from poor phase-space overlap and slow numerical convergence. The finite-sampling tests show that the overlap factor can be reconstructed from the same samples entering the estimator, making the overlap burden directly observable. A multistage coupling ladder then decomposes this burden into local factors and provides direct comparison with recursive FEP, BAR, and MBAR.

A quenching phenomenon that emerges in coupled oscillators, namely, amplitude death (AD), has been widely accepted. The present paper analytically deals with AD in two identical reaction-diffusion systems with periodic boundary or zero-flux boundary conditions that are coupled by a diffusive connection, namely, the static connection or the delay connection. The main results of the present paper are to guarantee the following facts analytically. For reaction-diffusion systems with Turing instability, neither the static connection nor the delay connection induces AD. For reaction-diffusion systems with wave instability, the static connection cannot induce AD, but the delay connection can induce AD. These facts do not depend on the number of state variables in the reaction-diffusion system. Some numerical examples with the extended Brusselator model having three state variables demonstrate these facts.

Abnormal propagation of electrical excitation waves underlies the development of many cardiac arrhythmias. Optogenetics offers a powerful means to precisely manipulate cardiac excitation dynamics. Previous optogenetic control strategies have primarily relied on projecting light patterns that directly mimic wave activity in the studied excitable medium. In this study, we propose a geometry-guided strategy based on synthetic Archimedean spiral line illumination. We demonstrate that this method not only enables effective synchronization of excitation patterns, but also provides a systematic way to study the influence of illumination frequency and wavelength of the projected pattern on synchronization. Our computational analysis is performed in both two- and three-dimensional media using the Bär reaction-diffusion model. We examine both depolarizing and hyperpolarizing modes of optogenetic control, which have previously received very limited attention. Depolarizing illumination achieves synchronization by inducing new wave fronts, whereas hyperpolarizing illumination operates through the formation of dynamic repolarization barriers. Importantly, both mechanisms remain robust under realistic conditions, including optical attenuation and pathological fibrotic remodeling. In summary, this work introduces a biophysically grounded, geometry-driven optogenetic control paradigm for the synchronization and suppression of electrical turbulence in excitable media, laying the foundation for potential future applications in cardiac tissue.

The dissipation mechanisms in weakly collisional turbulent plasmas have been a longstanding topic of investigation. In recent years, one significant and promising development has been the use of the “scale-filtered” Vlasov-Maxwell equations to fully quantify the scale-by-scale energy balance, a feature that was absent when using fluid models for kinetic plasmas. In particular, this method reveals that the energy transfer in kinetic scales is fully accounted for by the scale-filtered pressure-strain interaction. Despite contemporary progress, the influence of electron-ion thermal disequilibrium on the kinetic-scale energy budget remains poorly understood. Using two-dimensional fully kinetic particle-in-cell simulations of decaying plasma turbulence, we systematically investigate the scale-filtered pressure-strain interaction and its components at sub-ion scales by varying the electron-ion temperature ratio. Our analysis focuses on the three components of the pressure-strain interaction: the normal and shear components of total deformation $Pi-D$, and pressure dilatation. Our results demonstrate that the scale-filtered pressure-strain interaction is dominated by scale-filtered $Pi-D$ across the kinetic range, with the shear component consistently providing the dominant contribution. We find that the scale-filtered normal and shear contributions of $Pi-D$ exhibit persistent anticorrelation and opposite signs across all kinetic scales. We also discover that the amplitude of both anisotropic components, i.e., $Pi-D$ for each species, scales directly with their temperature and inversely with the temperature of the other species, whereas the scale-filtered pressure dilatation remains negligible compared to the $Pi-D$ terms but shows enhanced compressibility effects as plasma temperatures decrease. We discuss the implications of these findings in thermally nonequilibrated plasmas, such as in the turbulent magnetosheath and solar wind, and find that pressure-strain interaction could explain the scale-by-scale energy cascade rate in the solar wind at 1 AU.

Directed transport is a characteristic feature of numerous biological systems in response to signals such as nutrient and chemical gradients. These signals often depend on time owing to the high complexity of interactions in these systems. In this study, we focus on the steady-state behavior of polymeric systems responding to such time-dependent signals. We model them as ideal Rouse polymers submerged in a nonequilibrium bath, which is described by a spatially and temporally varying self-propulsion wave field. Through a coarse-graining analysis, we show that these polymers display rich emergent response to the temporal stimuli as a function of their length and topology. In particular, long polymers and structures with ring and star topologies ride the wave, displaying a positive drift in the direction of the wave, whereas shorter polymers and fully connected structures drift against the wave signal. We confirm these analytical predictions with robust numerical simulations, showing that the response of polymeric systems to temporal stimuli can be controlled by the topology or the length of the polymer.

Investigating the dynamical behavior of complex systems from data poses formidable challenges in the field of nonlinear science. This paper proposes a delayed-feedback echo state network ( df-ESN) model specifically designed for modeling and analyzing complex systems from data. The df-ESN introduces the delayed feedback of the reservoir state to reflect the finite transmission speed of signals among reservoir units. The delayed feedback term links the current reservoir state to its value $m$ steps ago, thereby significantly enhancing the memory capacity. By adopting the Lyapunov-Krasovskii stability method, we establish delay-dependent stability criteria to ensure the global echo state property (ESP). Furthermore, the definition of local echo state property (local ESP) is proposed to weaken the restrictive constraints imposed by the conventional ESP condition. The df-ESN also offers a strategy to determine the optimal parameters in the delayed feedback mechanism via a grid search technique, thus overcoming the challenges of determining optimal reservoir parameters in the ESN. This work provides a comprehensive theoretical understanding for the memory capability, local/global echo state property, and the impact of the noise on the model performance. Various nonlinear dynamical problems are conducted to verify the effectiveness of df-ESN, including chaotic time series prediction, high-dimensional spatiotemporal system analysis, bifurcation diagram reconstruction, and basin of attraction prediction. Moreover, df-ESN is used to study the model-free dynamical analysis of double soliton solutions of the nonlinear Schrödinger equation. The results underscore the capability of the proposed df-ESN as a model-free strategy for analyzing the complex systems, and they contribute to a deeper understanding of the underlying theoretical aspects of the model.

We study the tail-overlap interaction of a well-separated pair of dissipative solitons in systems with slow saturable gain. Gain saturation introduces nonlocal terms in the soliton field equation that depend on the total energy and therefore invalidate the standard methods used to study overlap interactions. We solve this problem by making the overlap interactions local in a doubled phase space and use this approach to calculate the drift velocities of interacting Swift–Hohenberg solitons. We derive explicit equations of motion for the soliton position with both fixed and saturable gain for reflection-symmetric and asymmetric solitons. We show that gain saturation significantly affects the drift velocity of the pair as a whole, while relative drift is insensitive to this effect. Consequently, the interactions of reflection-symmetric solitons with fixed and saturable gain are identical, while gain saturation increases the overall drift velocity of a pair of asymmetric solitons by an exponentially large factor. The theoretical equations of motion are exact in the limit of large separations and are verified by comparison with numerical simulations of the field equation.

Among others, chirality is a property of organometallic molecules whose main feature is that the spatial superposition is exclusively observed through a specular plane. A specular plane is a physical kind of subspace onto which chiral objects can already be superposed. That is, chirality corresponds to a specular plane for the superposition principle; i.e., a mirrorlike operation. The chirality was a collateral finding; meanwhile, the different order synchronization was analyzed. Such a fact motivated us to revisit the problem to investigate the conditions on which the chirality phenomenon emerges during the chaos synchrony. This contribution is not one more contraption to the chaos synchronization, but the search of veiled phenomenon in synchronized chaotic systems. Thus, we show that chirality in chaos synchrony can be derived via nonlinear functions derived from the group transformations, which span algebraic subspaces. Specifically, the Lie algebraic subspaces allow us to unveil the chirality on the chaos synchrony throughout a continuously differentiable maps. The master-salve configuration is realized for chaotic continuous systems to document that chirality is a completely different phenomenon in chaos synchrony.

We study the transition between layer-localized and delocalized regimes in a general contact-based contagion model on multiplex networks. Using the inverse participation ratio, we characterize how activity shifts from being confined to a single layer to spreading across the entire system. Through a first-order perturbative analysis of the leading eigenvector of the supracontact probability matrix, we derive an analytical expression for the fictive coupling $p^{*}$ that marks the crossover between the two regimes. This result reproduces and explains previously observed numerical scalings and extends them to a broad class of contact-based processes beyond the susceptible-infected-susceptible model. We also obtain an analytical expression for the IPR of the nondominant layer in the localized regime, confirming its power-law dependence on the coupling with exponent $\alpha =4$. Finally, we study the transition between nondominant and dominant layers as a function of the intralayer activity parameter $\gamma$. Our analytical findings are supported by dynamical simulations that highlight distinct susceptibility patterns across regimes. Altogether, this work provides a unified spectral framework for understanding localization and dominance transitions in multiplex contagion dynamics.

We study opinion dynamics with higher-order interactions, motivated by the fact that social influence often takes place in groups rather than only through pairwise contacts. We introduce a noisy majority-rule model on annealed hypergraphs with heterogeneous group sizes and investigate how the distribution of interaction sizes affects collective ordering and relaxation. Using analytical theory and Monte Carlo simulations, we show that group-size heterogeneity strongly shapes both the transition between ordered and mixed states and the associated timescales. In particular, broader and heavier-tailed distributions make ordering more robust by enhancing the effect of rare large-group events. They also modify the finite-size scaling of relaxation, producing a crossover from the standard logarithmic behavior to faster ordering in sufficiently broad ensembles. In the pure majority-rule limit, we further show that the exit probability near coexistence obeys a universal error-function scaling form controlled by a single structural parameter. Our results demonstrate that the full distribution of group sizes is a key determinant of nonequilibrium ordering in higher-order opinion dynamics.

In a series of magnetized-liner-inertial-fusion experiments performed at the Z pulsed power facility of Sandia National Laboratories, beryllium liners filled with deuterium gas densities between 0.7 to 1.4 mg/cc and a tracer amount of krypton were imploded. At the collapse of the cylindrical implosion, electron temperatures in the $2–4\mathrm{keV}$ range and deuterium ion number densities of $\sim {10}^{23}{\mathrm{cm}}^{-3}$ were expected. Spatially resolved krypton K-shell line emission was recorded with a time-integrated transmission crystal x-ray spectrometer. The spatially resolved data showed $n=2\to 1$ line emission from Be-, Li-, and He-like krypton ions and are characteristic of the highest electron temperatures achieved in the thermonuclear plasma. Detailed modeling of krypton atomic and radiation physics demonstrated that the spectrum is electron temperature dependent, thus allowing for axial temperature distributions to be extracted from the data. Additionally, the electron density (as well as the ion density) of the deuterium compressed plasma was estimated from the relative distribution of narrowband intensity between regions along the $z$ axis. The measurement of axially resolved temperature and density distributions enabled an assessment of thermal transport along the axis of the burning plasma, showing that it proceeded at a much faster rate than local cooling by bremsstrahlung emission. Furthermore, from the pressure distribution, the rate of residual kinetic energy associated with axial plasma flow was evaluated as well.

Radiofrequency-heated, high-$\beta$, magnetized hydrogen plasmas in the Princeton field-reversed-configuration-2 device, with its magnetic-field-parallel radial boundary formed by eight discrete room-temperature coaxial copper rings, display constant density for times exceeding 150 ms. When the copper rings are cooled to LN2 temperature, the line-average plasma density decreases, in a few ms, from its initial peak value by a factor exceeding 5. Providing a single ms-duration hydrogen gas puff at the discharge's boundary, 3 to 70 ms after the density decay, returns the plasma density to its original high value at which it remains for 10s to 100s of ms. Commencing at the brief gas puff, the amplitudes of rotational modes and low-frequency turbulence in the plasma decrease by more than a factor of 10 and remain low throughout the constant plasma-density phase.

We study the segregation of motile semiflexible filaments from a background of similar but nonmotile filaments. Our Langevin dynamics simulations reveal a wide range of emergent structures governed by filament flexibility and activity, i.e., self-propulsion strength. The system segregates at low activities, while at high activities it undergoes remixing. This is a characteristic feature of semiflexible active filaments which is not seen in rigid active particle systems. We show that collision-induced softening of single filaments is the dominant mode for this remixing. We provide a scaling argument for the lowering of the active polymer stiffness and show that it agrees well with the lowering of the segregation order parameter. We expect that our studies will shed light on the spatial organization of biofilaments within the cell, on the plasma membrane, and beyond, and help in the design of novel biomaterials whose structure can be tuned via the properties of the active or the passive filaments.

Subcritical transition to turbulence, in which the laminar state is linearly stable yet finite-amplitude perturbations develop into turbulence, is ubiquitous but predicting it from the structure of the governing equations remains difficult. We demonstrate such a framework using a shell model of turbulence, in which external forcing breaks the phase symmetry of the governing equations. This symmetry breaking suppresses the linear instability of the laminar state, while the energy cascade and spectrum of the developed turbulent state are preserved. A complementary single-triad model admits an exact elliptic neutral stability curve, revealing that the stabilization depends only on the breaking strength and not on the nonlinear coupling coefficients. Since the phase symmetry of the shell model corresponds to Galilean invariance in the Navier-Stokes equations, this mechanism may offer a new perspective on subcritical transition in fluid systems.

We study the ferromagnetic Ising model on a two-dimensional transition lattice that continuously interpolates between the Lieb and kagome lattices via a geometric deformation parameterized by the angle $\theta$. The exchange couplings follow a distance-dependent decay controlled by an exponent $n$, enabling us to disentangle the interplay between geometry and interaction range. Using extensive Monte Carlo simulations and Binder cumulant analysis, we map the phase diagram $T_c\left(\theta \right)$ and show that the critical temperature increases monotonically as the lattice acquires higher effective connectivity. In the large-$n$ limit, the system approaches a nearest-neighbor regime in which the Monte Carlo critical temperatures converge to the known exact values of the Lieb and kagome limits. Finite-size scaling and data collapse confirm that the entire interpolation belongs to the two-dimensional Ising universality class. Beyond demonstrating the robustness of the critical behavior across the Lieb-kagome transition, the present framework suggests natural extensions. The continuous geometric interpolation between the nonfrustrated Lieb lattice and the frustrated kagome lattice offers a suitable platform to explore antiferromagnetic interactions, where the interplay between frustration and long-range couplings may induce nontrivial ordering.