We present the macroscopic dynamics of ferroelectric smectic $C$, smectic $C_F$, liquid crystals reported recently experimentally by two groups. In this fluid and tilted smectic phase, the macroscopic polarization, $\mathbf{P}$, is tilted with respect to the layer normal, thus giving rise to $C_{1h}$ overall symmetry for this phase in the spatially homogeneous limit. A combination of linear irreversible thermodynamics and symmetry arguments is used to derive the resulting dynamic equations applicable at sufficiently low frequencies and sufficiently long wavelengths. Compared to nonpolar smectic $C$ phases, we find two static cross-coupling terms between compression of the layering and bending of the layers, which do not lead to elastic forces but to elastic stresses. In addition, a number of static cross-coupling terms is elucidated, which can exist in smectic $C_F$ but not in the ferroelectric $A_F$ phase because of the polar in-plane preferred direction in smectic $C_F$. Due to the fact that the magnitude of the polarization is a slowly relaxing variable, the velocities of the first and second sound both reflect the monoclinic symmetry of the ground state, thus rendering all sound velocities to be biaxial. We also analyze reversible cross-coupling terms between elongational flow and electric fields as well as temperature and concentration gradients, which lend themselves to experimental detection. Such cross-coupling terms have apparently never been considered before for monoclinic symmetry since they are absent without the presence of a polar direction and thus do not exist in nonpolar smectic $C$ phases. Among the dissipative cross-coupling terms characteristic of smectic $C_F$, we find that bending of the layers can couple to temperature gradients. We also address the question how the linear $\mathbf{P}·\mathbf{E}$ coupling in the energy alters the macroscopic response behavior when compared to usual nonpolar smectic $C$ phases.

When a ribbon or tube is twisted far enough it forms buckles and wrinkles. Its new geometry can be strikingly ordered or hopelessly disordered. Here we study this process in a tube with hybrid boundary conditions: one end a cylinder and the other end crimped flat like a ribbon, so that the sample resembles a toothpaste tube. The resulting irregular structures and mechanical responses can be dramatically different from those of a ribbon. However, when we form two creases in the tube prior to twisting, we obtain an ordered structure composed of repeating triangular facets oriented at varying angles and a more elastic torque response, reminiscent of the creased helicoid structure of a twisted ribbon. We measure how the torque and structural evolution depend on parameters such as material thickness and the twist angle. When only part of the tube is precreased, the ordered structures are confined to this segment. Surprisingly, in some tubes made from thicker sheets, an ordered structure forms without precreasing. This study provides insights into controlling the buckling of thin shells, offering a potential pathway for designing ordered structures in soft materials.

Electron heat flux is an important and often dominant mechanism of energy transport in a variety of collisional plasmas in a confined fusion or astrophysical context. While nonlocal conductive heat transport, driven by strong temperature gradients, has been investigated extensively in previous literature, nonlocal regimes of the current-driven heat flow and friction have not received the same attention. In this Letter, a first-principles reduced kinetic method is applied to study nonlocal effects on current-driven transport. In addition to nonlocality due to sharp gradients, sufficiently large currents are found to significantly enhance current-driven heat flux due to a novel nonlocal mechanism, with this enhancement being increasingly prevalent for higher effective ionizations $Z^{*}$. Introducing the dimensionless number $N_u\equiv |{\mathit{u}}_e-{\mathit{u}}_i|/v_{\text{th},e}$, these enhancements occur for even relatively weak flows $N_u\gtrsim 1/100$, analogously to standard nonlocal effects becoming significant for Knudsen numbers $N_K\gtrsim 1/100$.

Recent separated reactant experiments for thin-shell ($6\mu \mathrm{m}$) shock-driven implosions on OMEGA have demonstrated significant mix from a buried deuterated layer of the shell into the hot spot. Time resolved ${\mathrm{D}}^3\text{He-p}$ reaction history data demonstrate a $(50\pm 20)\mathrm{ps}$ shift earlier in peak nuclear emission for separated reactant experiments relative to control, in contrast to past experimental data for thicker, $20\mu \mathrm{m}$ shells with no laser burn through that show a $75\mathrm{ps}$ delay due to the time required for hydrodynamic instabilities to develop. This contrast suggests that the mix mechanism was not hydrodynamic. Ion kinetic simulations utilizing fall line analyses show much closer agreement with mix yield and temperature than diffusion models, predicting a ${\mathrm{D}}^3\text{He-p}$ mix yield of $1.7\times {10}^9$ as compared to the experimental value of $9.3(\pm 2.1)\times {10}^8$. This is three orders of magnitude closer than the fall line analysis from a hydrodynamic simulation with an inline diffusive mix model, which suggests minimal mix and ${\mathrm{D}}^3\text{He-p}$ yields of $5\times {10}^5$. This makes kinetic mechanisms the only feasible explanation for the mix seen, demonstrating impact of a non-standard mix mechanism. An analytical model of this kinetic mix mechanism suggests that it can remain significant in situations when the shell expands significantly to low densities, and diffusive models predict negligible mix. Kinetic mix will impact multiple types of high energy density, laser-driven fusion experiments including high-adiabat direct drive cryoexperiments, nuclear cross section experiments, and thin-shell polar direct drive experiments used to tune heat conduction models.

Information-theoretic quantities have received significant attention as system-independent measures of correlations in many-body quantum systems, e.g., as universal order parameters of synchronization. In this work, we present a method to determine the macroscopic behavior of the steady-state multipartite mutual information between $N$ interacting units undergoing Markovian evolution that is invariant under unit permutations. Using this approach, we extend a conclusion previously drawn for classical systems that either the extensive scaling of mutual information is not possible for systems relaxing to fixed points of the mean-field dynamics, or such scaling is not robust to perturbations of system dynamics. In contrast, robust extensive scaling occurs for a system relaxing to time-dependent attractors, e.g., limit cycles. We illustrate the applicability of our method on the driven-dissipative Lipkin-Meshkov-Glick model.

Nonequilibrium dynamics are present in many aspects of our lives, ranging from microscopic physical systems to the functioning of the brain. What characterizes stochastic models of nonequilibrium processes is the breaking of the fluctuation-dissipation relations as well as the existence of nonstatic stable states, or phases. A prototypical example is a dynamical phase characterized by a limit cycle—the order parameter of finite magnitude rotating or oscillating at a fixed frequency. Consequently, birhythmicity, where two stable limit cycles coexist, is a natural extension of the simpler single limit cycle phase. Both the abundance of real systems exhibiting such states and their relevance for building our understanding of nonequilibrium phases and phase transitions are strong motivations to build and study models of such behavior. Field-theoretic tools can be used to provide insights into either phase and the transition between them. In this work, we explore a simple linear model of a single limit cycle phase with phase-amplitude coupling. We demonstrate how such nonequilibrium coupling affects the fluctuation spectrum of the theory. We then extend this model to include a continuous transition to a two-cycle phase. We give various results, such as the appearance of a critical exceptional point, the destruction of the transition, the enhancement of noise for the phase, and the presence of Kardar-Parisi-Zhang(KPZ) dynamics. Finally, we qualitatively demonstrate these results with numerics and discuss future directions.

We observe that the time-averaged continuous Price equation is identical to the positive momentum virial theorem, and we discuss the applications and implications of this connection. We also introduce ecological models using a maternal effect, which can describe arbitrary population size cycles and trait evolution across spatially separated populations. The virial theorem sheds light on the time-averaged behavior of these models.

Thermodynamic uncertainty relations reveal a fundamental trade-off between the precision of a trajectory observable and entropy production, where the uncertainty of the observable is quantified by its variance. In information theory, Shannon entropy is a common measure of uncertainty. However, a clear quantitative relationship between the Shannon entropy of an observable and the entropy production in stochastic thermodynamics remains to be established. In this study, we show that an uncertainty relation can be formulated in terms of the Shannon entropy of an observable and the entropy production. We introduce symmetry entropy, an entropy measure that quantifies the symmetry of the observable distribution, and demonstrate that a greater asymmetry in the observable distribution requires higher entropy production. Specifically, we establish that the sum of the entropy production and the symmetry entropy cannot be less than $ln2$. As a corollary, we also prove that the sum of the entropy production and the Shannon entropy of the observable is no less than $ln2$. As an application, we demonstrate our relation in the diffusion decision model, revealing a fundamental trade-off between decision accuracy and entropy production in stochastic decision-making processes.

Reservoir computing has emerged as a powerful framework for predicting critical transitions in dynamical systems. In this work, we employ parallel parameter-aware reservoir computing to predict the dynamics of multilayer networks with distinct coupling mechanisms. We consider a two-layer multiplex network in which the first layer oscillators are coupled with attractive coupling, which promotes in-phase synchronization, while the second layer oscillators are coupled with repulsive coupling, encouraging anti-phase synchronization and oscillation death. With sufficiently strong interlayer coupling, collective emergent phenomena can be transferred from one layer to another. Notably, we also observe that interlayer coupling can induce oscillation death simultaneously in both layers. Using a parallel parameter-aware reservoir computing scheme, we accurately predict the critical parameter values at which the transfer of dynamical phenomenon occurs. We use two reservoirs designated to learn the dynamics of each layer in a two-layer multiplex network. Our findings provide valuable insight into the role of reservoir computing in forecasting transitions in multilayer networks.

The Stuart-Landau oscillator generalized to $D>2$ dimensions has $\mathrm{SO}(D$) rotational symmetry. We study the collective dynamics of a system of $K$ such oscillators of dimensions $D=3$ and 4, with coupling chosen to either preserve or break rotational symmetry. This leads to emergent dynamical phenomena that do not have analogs in the well-studied case of $D=2$. Further, the larger number of internal parameters allows for the exploration of different forms of heterogeneity among the individual oscillators. When rotational symmetry is preserved there can be various forms of synchronization as well as multistability and partial amplitude death, namely, the quenching of oscillations within a subset of variables that asymptote to the same constant value. The oscillatory dynamics in these cases are characterized by phase locking and phase drift. When the coupling breaks rotational symmetry we observe partial synchronization (when a subset of the variables coincide and oscillate) and partial oscillation death (when a subset of variables asymptote to different stationary values), as well as the coexistence of these different partial quenching phenomena.

Effective clearance of amyloid-$\beta$ ($\mathrm{A}\beta$) from the brain is essential for preventing neurodegenerative diseases such as Alzheimer's. A significant portion of this clearance occurs through the blood-brain barrier (BBB) via receptor-mediated transport. However, current models fail to capture the complex kinetics and spatial heterogeneity of receptors at the BBB. In this study, we derive a boundary condition that accounts for finite receptor kinetics, receptor density, and bidirectional transport across the BBB. Specifically, we develop a nonlinear homogenized boundary condition that ensures mass conservation and incorporates receptor-mediated Michaelis-Menten kinetics. We then implement this boundary condition in a cylindrical geometry representing a capillary surrounded by brain tissue. After verifying that the model matches an analytical steady-state solution that we derive and that it yields realistic blood $\mathrm{A}\beta$ concentrations, we explore how realistic variations in parameter values drive changes in both steady-state $\mathrm{A}\beta$ concentration and transient dynamics. Simulations and analytical results reveal that $\mathrm{A}\beta$ concentrations in the brain are sensitive to receptor number ratios, while concentrations in the blood are primarily affected by the blood clearance rate. Additionally, we use the model to investigate $\mathrm{A}\beta$ clearance during sequential sleep cycles and due to a pathological phenomenon, spreading depolarization. This work presents a biophysically consistent boundary condition for $\mathrm{A}\beta$ transport across the BBB, offering a powerful tool for studying brain waste clearance under both physiological and pathological conditions.

We conducted a comprehensive statistical analysis of the breakdown-voltage variations in helium near its critical point (5.2 K) using Weibull distribution analysis and Shannon entropy evaluation. Through detailed measurements at temperatures ranging from 5.1 to 5.5 K and densities from 5 to $115\mathrm{kg}/{\mathrm{m}}^3$, we discovered two significant phenomena. First, in the liquidlike region above the critical density, we identified two distinct breakdown mechanisms with different Weibull shape parameters: a high-variability mode associated with bubble-mediated breakdown and a low-variability mode resembling gas-phase breakdown. The contribution of the bubble-mediated mode increases systematically with density, emerging at pressures 0.01–0.02 MPa above the critical pressure line. Second, the statistical variation in breakdown voltages shows a notable reduction near the critical density ($\approx 69.6\mathrm{kg}/{\mathrm{m}}^3$), particularly at temperatures close to the critical point. This reduction in the statistical spread was consistently observed through both the Weibull distribution analysis and Shannon entropy evaluation, with the latter providing a distribution-independent measure of voltage variations applicable across all fluid states from gaslike to liquidlike regions. The reduced statistical variation near the critical point presents an intriguing contrast with the enhanced density fluctuation characteristic of this region, suggesting a complex interplay between the fluid structure and breakdown mechanisms. These findings reveal previously unknown aspects of the breakdown phenomena in highly fluctuating fluids and provide insights into the relationship between fluid structure and electrical breakdown characteristics.

We present a multiscale simulation framework that couples the finite-element method with molecular dynamics. Bypassing traditional equations of state (EOS) by using in-line atomistic simulations, the method offers the advantage of incorporating detailed microscale physics not easily represented with coarse-grained models. Coupling consistency with the continuum code is ensured through the use of lifting and restriction operators, in line with heterogeneous multiscale methods. The concurrent continuum-atomistic framework is validated through comparison with experimental results and conventional EOS models, and demonstrated in a shock-driven hydrodynamic flow simulation under extreme conditions. We further evaluate the framework's usability by comparing it to state-of-the-art EOS models of deuterium. A computational performance study reveals that the atomistic EOS evaluation is a feasible alternative to conventional approaches, and demonstrates a weak scaling of 99% efficiency. These results highlight the framework's potential for large-scale multiscale modeling across a broad range of materials and conditions.

We investigate a phase transition from linear to nonlinear information processing in echo state networks, a widely used framework in reservoir computing. The network consists of randomly connected recurrent nodes perturbed by a noise and the output is obtained through linear regression on the network states. By varying the standard deviation of the input weights, we systematically control the nonlinearity of the network. For small input standard deviations, the network operates in an approximately linear regime, resulting in limited information processing capacity. However, beyond a critical threshold, the capacity increases rapidly, and this increase becomes sharper as the network size grows. Our results indicate the presence of a discontinuous transition in the limit of infinitely many nodes. This transition is fundamentally different from the conventional order-to-chaos transition in neural networks, which typically leads to a loss of long-term predictability and a decline in the information processing capacity. Furthermore, we establish a scaling law relating the critical nonlinearity to the noise intensity, which implies that the critical nonlinearity vanishes in the absence of noise.

The far-from-equilibrium nature of active particles forms clusters with excessive dynamics, which can be suppressed by external physical fields in various applications. These application scenarios often require clusters with specific scales and numbers. To discover how to regulate these properties, we investigate the characteristics of clusters formed by aligning self-propelled particles in a Gaussian potential. This potential traps particles into static clusters (SCs) around the equivalent potential trough. During the process of formation, we use the order parameters defined on the connection graph to distinguish both the stability of these clusters and the number of static ones. We find that both increasing self-propulsion velocity and local density of the active particles lead to their partial or complete escape. This finding inspires a regulation strategy of both the scale and number of SCs by adjusting the potential parameters. The resulting SCs are endowed with diverse spanning scales, from giant clusters to wreath-like slender structures. Our results open new perspectives on controlling motility-induced phase separation and multitask manipulation for active particle systems.

We study an information engine operating in an active bath, where a Brownian particle confined in a harmonic trap undergoes feedback-driven displacement cycles. Unlike thermal environments, active baths exhibit temporally correlated fluctuations, introducing memory effects that challenge conventional feedback strategies. Extending the framework of stochastic thermodynamics to account for such memory, we analyze a feedback protocol that periodically shifts the potential minimum based on noisy measurements of the particle's position. We show that conventional feedback schemes, optimized for memoryless thermal baths, can degrade performance in active media due to the disruption of bath-particle memory by abrupt resetting. To overcome this degradation, we introduce a class of memory-preserving feedback protocols that partially retain the covariance between the particle's displacement and active noise, thereby exploiting the temporal persistence of active fluctuations. Through asymptotic analysis, we show how the feedback gain—which quantifies the strength of positional shifts—nontrivially shapes the engine's work and power profiles. In particular, we demonstrate that in active media, intermediate gains outperform full-shift resetting. Our results reveal the critical interplay between bath memory, measurement noise, and feedback gain, offering guiding principles for designing high-performance information engines in nonequilibrium environments.

We study the zero-temperature Glauber dynamics of homogeneous Ising ferromagnets on hypercubes, as their dimension $d$ varies. By hypercube, we mean the $d$-dimensional hypercubic graph with $2^d$ vertices, where each vertex is connected to $d$ neighbors. We investigate the asymptotic ($d\to \infty$ and time $t\to \infty$) behavior of various quantities on hypercubes, such as the final magnetization, the probability for the system to enter a ground state, etc. Our numerical studies are carried out using a uniformly random initial state but with the constraint that the initial magnetization is zero. The final states can be divided into three categories: ground states, frozen states, and blinker states. We use the notion of a $k$-core to describe the geometry of the frozen states and give an exponential lower bound for the number of frozen states in terms of $d$. Blinker states—which exist only in even $d$—are final states containing at least one blinker (a permanently flipping spin). Blinkers states can have rich local structures; we give explicit constructions for configurations that contain blinkers and prove that the lowest possible dimension for blinker configurations is $d=8$. We also study the "nature versus nurture" problem on hypercubes, asking how much the final state depends on the information contained in the initial configuration, and how much depends on the realization of the dynamical evolution. Finally, we provide several conjectures and suggest some open problems based on the numerical results.

We show that norm-conserving spin models driven by temporally hyperuniform noise exhibit a sharp ergodicity-breaking transition in the absence of interactions. In the nonergodic phase, the dynamics freeze into configurations determined by the initial condition. Our analysis demonstrates that such interaction-free ergodicity breaking arises generically whenever a global constraint is imposed and the driving noise is class-I hyperuniform, the strongest form in Torquato's classification. The transition can also be interpreted as a condensation of fluctuations into the zero-frequency mode, reminiscent of Bose–Einstein condensation in an ideal gas.

In this paper, we present an application of the variational quantum simulation (VQS) framework to capture finite temperature open system dynamics on near-term quantum hardware. By embedding the generalized amplitude damping channel into the VQS algorithm, we model energy exchange with a thermal bath through its Lindblad representation and thereby simulate realistic dissipative effects. To explore a wide range of activation behaviors, we introduce a nonadditive relaxation time model using a generalized form of the Arrhenius law, based on the phenomenological parameter $q$. We compare our method on driven qubit systems subject to both static and composite time-dependent fields, comparing population evolution and trace distance errors against reference numerical solutions. Our results demonstrate that (1) VQS accurately maps the effective nonunitary generator under GAD, (2) smoother drive envelopes induced by nonaddtive parameters suppress high-frequency components and yield lower simulation errors, and (3) the variational manifold exhibits dynamical selectivity, maintaining mapping fidelity even as the reference numerical solution's sensitivity to $q$ increases.