Reconstructing the causal structure of physical systems from observational data constitutes a fundamental inverse problem. Here we show that the reconstruction dimension—defined as an upper bound on the number of recoverable components—is determined by the group-representation structure of the observation spaces and reconstruction maps. This formulation provides an explicit and operational characterization of reconstructability and reconstruction dimension, extending ideas that are often understood only intuitively in equivariant representation theory. As a concrete example, we demonstrate the reconstruction of the local velocity-gradient tensor from orientational measurements of particles suspended in flows, where the observation and velocity-gradient tensor spaces form SO(3) representations with constrained equivariant maps between them. Using an SO(3)-equivariant neural network (implemented with e3nn), we show that the reconstructable subspaces predicted by the representation decomposition are qualitatively consistent with those found in practice. Our formulation shows that the representation structure constrains reconstructability by determining an upper bound sector by sector, while our numerical results suggest that the actual saturation of the bound depends on the physics and data geometry. Beyond providing a useful theoretical framework, this work also connects the abstract representation-theoretic structure to concrete inverse reconstruction problems in fluid physics.

We construct a family of exactly solvable relativistic kinetic theories in $1+1$ dimensions whose hydrodynamic sector continuously interpolates between Fick's and Cattaneo's laws of diffusion. The interpolation is controlled by a single parameter $a\in [0,1]$, which tunes the microscopic scattering dynamics from infinitely soft but infinitely frequent scatterings ($a=0$), reproducing standard diffusion, to maximally hard but finite-rate scatterings ($a=1$), yielding hyperbolic Cattaneo-type transport. For intermediate values of $a$, the dynamics combines frequent weak scatterings with rare strong randomizing events, providing a concrete microscopic realization of mixed diffusive-telegraphic behavior. Remarkably, the full quasinormal mode spectrum can be obtained analytically for all $a$. This allows us to track explicitly how purely diffusive modes continuously deform into damped propagating modes as the collision structure is varied.

In conventional generative adversarial networks (GANs), the discriminator typically employs a sigmoid activation to map features to probabilities. However, this activation suffers from the vanishing-gradient problem, which can lead to training instability and mode collapse. This work reformulates the final-layer activation of the discriminator as cumulative distribution functions (CDFs) of random variables, thereby introducing a learnable noise-scale parameter. We show analytically that, for CDF families with bounded reversed hazard rates in the negative tail, a noise-scale value smaller than unity scales the gradient of both the saturating and nonsaturating generator losses by a factor proportional to its reciprocal. Rather than fully resolving the vanishing-gradient problem, this mechanism provides more informative gradient signals to the generator when the discriminator is close to its optimum. Experiments on a two-dimensional Gaussian mixture and on MNIST show that the proposed CDF-based activation effectively improves mode coverage and training stability. Meanwhile, experiments on CIFAR-10 using a deep convolutional GAN (DCGAN) indicate that, when gradient flow is already stabilized by architectural features, the choice of final-layer activation plays a more limited role. An ablation study on MNIST further distinguishes the benefits of the proposed method from that of conventional noise regularization techniques. These results demonstrate that the proposed CDF-based activation also contributes a meaningful scheme for stabilizing adversarial training.

Fluctuations can drive otherwise continuous phase transitions to first order through the Brazovskii mechanism. We study how these fluctuation-induced transitions are modified in active systems by introducing nonequilibrium spatiotemporally correlated noise. We show that, while the transition remains fluctuation-induced first order, activity systematically suppresses these fluctuation effects, shifting the transition to higher temperatures and rendering it increasingly weakly first order. As a result, ordering is enhanced without inducing a spinodal instability of the isotropic phase, as confirmed by direct numerical simulations. In the strong-activity limit, fluctuation effects disappear and mean-field behavior is recovered. Our results identify activity as a generic control parameter for tuning the strength of fluctuation-induced first-order transitions.

Living systems often function with regulatory interactions, but the question of how activity, stochasticity, and regulations work together for achieving different goals still remains puzzling. We propose a stochastic model of an active tracking particle with information processing, where the entropy production and information flow are discussed, with the generalized fluctuation theorem serving as a benchmark for verifying the probability setups. Based on the model, the system performance, in terms of the first passage steps, the total energy consumption, and the thermal efficiency, is analyzed in the variable space of measurement error and control field, leading to discussions on optimal controls of the system. Not only elucidating the basic concepts involved in a stochastic active system with information processing, this prototypical model could also inspire more elaborated modelings of natural smart organisms and industrial designs of controllable active systems with desired physical performances in the future.

Quantum-induced stochastic dynamics arises when a quantum system, strongly decohered by its coupling to a quantum environment, evolves as a genuine classical stochastic process. Depending on the environment's quantum state, the environment can act as a dynamic bath, capable of simultaneously exchanging heat and performing work. We formulate a thermodynamic framework for this semiclassical regime, defining heat, work, and entropy production. We derive a modified Second Law that accounts for nonequilibrium quantum features, such as squeezing. The framework is exemplified by an optomechanical setup, where we characterize the thermodynamics of the nonstationary noise induced by the cavity field.

The emergence of quantum chaos in a system of trapped interacting bosons with externally impressed rotation is studied through spectral form factor (SFF) and power spectrum using exact diagonalization. Two distinct interaction regimes are considered: the moderate, when the interaction energy is small compared to the trap energy, and the strong, when the interaction energy is comparable to the trap energy. In the moderate interaction regime, the SFF for the nonrotating case exhibits a dip-plateau structure with an absence of linear ramp, indicating integrable behavior, while for the single-vortex state the SFF exhibits a discernible linear ramp consistent with pseudo-integrable behavior. In the strong interaction regime, the nonrotating case exhibits emergence of a linear ramp with small time span in SFF, indicating that the system has moved further towards chaotic regime but continues to be pseudo-integrable. For the single-vortex and the multivortex states in a strong interaction regime, the span of the linear ramp in SFF increases progressively with rotation, indicating the system has moved into a strong chaotic regime consistent with Gaussian orthogonal ensemble. The power spectrum results with the exponent lying in the interval $1\lesssim \alpha \lesssim 2$ are consistent with the SFF findings. An understanding of the observed crossover from integrable to quantum chaos is presented in terms of the macroscopic occupation of a single-particle quantum state—the Bose-Einstein condensation—and its depletion driven by interaction and rotation.

We generalize the Hunt-Crossley (HC) model to the case compatible with external potential fields, attributing to a small dimensionless parameter, and employ the perturbation method to derive the perturbation and asymptotic solutions of the coefficient of restitution. The numerical results reveal that the perturbation solution decreases with the impact velocity for higher velocities and asymptotically approaches the case without any external force, while dropping into a critical sticking velocity for lower velocities. Finally, we analyze the dissipative properties of the bouncing ball system and demonstrate that a localized dispersive structure consistent with experiments appears after mapping the chaotic phase diagram to the perturbation solution. The proposed model and its solutions may be applied to study other collision-related nonlinear dynamic systems.

The presence of chaos in classical Hamiltonian systems is witnessed by its maximal Lyapunov exponent, that quantifies the instability of motion through the exponential growth of indicators such as the trace of the stability matrix or the out-of-time-ordered correlator. On the other hand, integrable dynamics near unstable fixed points, which are in turn characterized by a stability exponent, can also induce such exponential growth. Following the paradigm of integrability breaking as driven by nonlinear resonances that hallmarks the genesis of chaos, the integrability-chaos transition is universally described by a periodic perturbation applied to a generic pendulum. Remarkably, this means that within the corresponding separatrix dynamics, which is an unavoidable a consequence of the resonance scenario, both instability exponents must play a role as both dynamical regimes coexist. We report here the universality of the transition from instability to Lyapunov exponents, thus completing the resonance scenario at the level of indicators based on exponential growth. To achieve this goal we obtain an analytical expression for the time evolution near separatrices, which enables us to derive an analytical expression for the exponent that characterizes chaos and its transition from local instability to global chaos. We support our claim for the universality of this mechanism by studying two paradigmatic examples of the integrability-to-chaos transition, namely, the kicked rotor and the kicked Bose-Hubbard dimer.

The dynamical behavior of water in magnesium perchlorate aqueous solutions is investigated through molecular dynamics simulations using the TIP4P/2005 water model and the recently extended Madrid-2019 force field. This study is motivated by the recent radar detection of liquid water underneath the Martian South Pole. We explore the supercooled regime for salt concentrations up to 24.4 wt %. In the region of mild supercooling we analyze the water oxygen self-intermediate scattering functions. Our results show that the relaxation dynamics of water is well described by the mode coupling structural relaxation in this region. Upon further cooling, a fragile-to-strong crossover is observed for all investigated concentrations. Below the crossover, activated processes maintain the ergodicity. Notably, the addition of magnesium perchlorate induces a downward shift in both the mode coupling temperature and the fragile-to-strong crossover temperature. This combined effect extends the range of existence of the supercooled liquid regime to lower temperatures compared to bulk water. These findings support the hypothesis that perchlorate aqueous solutions can persist in a thermodynamically metastable liquid state at the low-temperature conditions of the Martian subsurface.

We consider a minimalist model of polar chiral active matter: overdamped, self-propelled agents coupled through a localized Kuramoto-Sakaguchi interaction, which causes alignment. Intrinsic frustration drawn from a broad distribution constitutes a temperature for the ensemble. In the comoving frame of the local order parameter, the agent dynamics reduce exactly to the Adler equation, placing each agent in a tilted washboard potential: trapped agents are phase-synchronized, and we demonstrate thereby that synchronization (phase rigidity) is maintained by information supercurrents; agents that are running in this potential form a resistive bath. The model is therefore formally isomorphic to a disordered, resistively shunted Josephson array, and a Monte Carlo sweep over the frequency dispersion empirically recovers the disorder-broadened Adler-Ohmic crossover of the ensemble-averaged slip velocity. Lifting the dynamics from $S^1$ to $S^2$, the polar alignment torque (the Kuramoto term) is geometrically equivalent to the Gilbert-damping term of the Landau-Lifshitz-Gilbert equation; the mapping establishes an effortless azimuthal precession, yielding a Goldstone-mode dispersion that carries an effective inertia $\propto R^2$, where $R$ is the local order parameter. This furnishes a microscopic basis for the spin-wave transport assumed in inertial-spin models of flocking. Within its regime of validity, i.e., dry, polar, chiral agents under marginal synchronization with sufficient frustration, the model is well-described as a dissipative spintronic fluid.

The transmembrane voltage, $V_{i=0}$, which is the potential drop required to nullify the electrical current ($i=0$), is a key characteristic of water desalination and energy harvesting systems that utilize macroscopically large nanoporous membranes, as well as for physiological ion channels subjected to asymmetric salt concentrations. To date, existing analytical expressions for $V_{i=0}$ have been limited to simple scenarios under simplifying assumptions. In this work, we derive two expressions for $V_{i=0}$. First, we consider the much simpler scenario of two species. Then, we can consider an electrolyte composed of an arbitrary number of species. The difference in the models is that the latter solution utilizes an ad hoc assumption of a linear concentration profile, while the former solution does not require such an ad hoc assumption. However, to derive a closed-form solution, another assumption is needed. In both models, we explicitly assume that the system is locally electroneutral. We show that both electroneutral models display remarkable correspondence with the numerical simulations of the one-dimensional Poisson-Nernst-Planck equations that do not assume electroneutrality. We show how the interplay between diffusion coefficients and ionic valencies significantly varies the system response and why it is essential to account for all system parameters. Importantly, we show that the new models can be reduced to several known models. Ultimately, this model can be used to improve experimental interpretation of ion transport measurements.

This work establishes a direct connection between semiclassical Thomas-Fermi theory and Tsallis statistics. The kinetic energy term of the Thomas-Fermi framework is shown to be associated with the Tsallis entropy $S_q$, while the particle interactions play the role of internal energy $U$, allowing the Thomas-Fermi-Lenz functional to be interpreted as a free-energy functional within a generalized thermostatistical setting. Accordingly, the minimization of the energy functional is equivalent to a maximum-entropy principle. The entropic index $q$ is found to depend on spatial dimension: $q=(d+2)/d$ in the nonrelativistic case, $q=(d+1)/d$ in the ultrarelativistic limit, and $q=3$ under strong magnetic fields. A time-dependent hydrodynamic formulation leads to a nonlinear diffusion equation consistent with a nonlinear Fokker-Planck description. An anomalous diffusion characterized by a universal subdiffusive regime, independent of the spatial dimension, was identified. The time-dependent and time-independent results reveal a correspondence between Thomas-Fermi theory and Tsallis statistics, indicating that the former can be viewed as a generalized thermostatistics; Tsallis statistics is not assumed, it emerges from Thomas-Fermi theory.

The $N$-queens problem asks for the number $Q\left(N\right)$ of ways to place $N$ mutually nonattacking queens on an $N\times N$ chessboard. Simkin [M. Simkin, Adv. Math. 427, 109127 (2023)] proved $Q\left(N\right)\sim {(N/e^{\gamma })}^N$, and subsequent work [P. Nobel, A. Agrawal, and S. Boyd, Optim. Lett. 17, 1229 (2023)] refined the constant to $\gamma =1.94400\left(1\right)$, settling the asymptotic behavior of this classical combinatorial problem. In this work, we pursue a thermodynamic-integration route in an unrestricted lattice-gas ensemble. We map the $N$-queens problem to a lattice gas with pairwise repulsive interactions along shared rows, columns, and diagonals, and we perform extensive Monte Carlo simulations for $N=8-1024$ with ${10}^8$ sweeps per temperature point. The specific heat per queen $C_v/N$ converges to a size-independent function with a broad, nondivergent maximum at $T^{*}\approx 0.235\mathrm{J}$, associated with a defect-proliferation crossover. This convergence, combined with the trivially exact high-temperature entropy $S\left(\infty \right)/N=\frac{1}{N}ln\left(\genfrac{}{}{0pt}{}{N^2}{N}\right)$, enables a thermodynamic integration of $C_v/T$ that extracts the ground-state entropy and yields ${\gamma }_{\mathrm{MC}}=1.946\pm 0.003$ at $N=1024$, within $0.1\%$ of the precise combinatorial value. The Simkin-Nobel value enters only as a benchmark; the thermodynamic route requires no prior knowledge of $Q\left(N\right)$. We further present a transfer-matrix-based tensor-network formulation that encodes the nonattacking constraints into a rank-9 site tensor with 17 nonzero elements, providing a complementary exact-enumeration route.

Symmetry-breaking order at low temperatures is often accompanied by slow relaxation dynamics, due to diverging free-energy barriers arising from interfaces between different ordered states. Here we extend this correspondence to classical topological order, where the ordered states are locally indistinguishable, so there is no notion of interfaces between them. We study the relaxation dynamics of the three-dimensional (3D) classical ${\mathbb{Z}}_2$ lattice gauge theory (LGT) as a canonical example. We prove a lower bound on the mixing time in the deconfined phase, $t_{\text{mix}}=exp\left[\mathrm{\Omega }\left(L\right)\right]$, where $L$ is the linear system size. This bound applies even in the presence of perturbations that explicitly break the one-form symmetry between different long-lived states. This perturbation destroys the energy barriers between ordered states, but we show that entropic effects nevertheless lead to diverging free-energy barriers at nonzero temperature. Our proof establishes the LGT as a robust finite-temperature classical memory. We further prove that entropic effects lead to an emergent one-form symmetry, via a notion that we make precise. We argue that the exponential mixing time follows from universal properties of the deconfined phase, and numerically corroborate this expectation by exploring mixing timescales at the Higgs and confinement transitions out of the deconfined phase. These transitions are found to exhibit markedly different dynamic scaling, even though both have the static critical exponents of the 3D Ising model. We expect this entropic mechanism for memory and emergent symmetry to also bring insight into self-correcting quantum memories.

At finite temperature, an attractive pair potential does not by itself define a bond between two particles. Specifically, two particles initialized near a potential minimum can remain localized over one observation window and escape over another; therefore, bonding is an observation-time-dependent localization problem. Here, we treat bonding as finite-time localization and ask when thermal fluctuations delocalize this state. We measure localization by a fluctuation-derived stiffness, $k_{\mathrm{eff}}=1/\left(\beta \langle u^2\rangle \right)$, where $\langle u^2\rangle$ is the variance of the particle separation. For isotropic particle–particle and one-dimensional particle–wall interactions, we derive a nonequilibrium theory based on the finite-time escape problem that yields the nonequilibrium probability density function for the separation coordinate, drawing on ideas from Becker-Döring theory, and thus $k_{\mathrm{eff}}$ as a function of temperature and observation time ${\tau }_{\mathrm{obs}}$. We find that as temperature increases or as the sampled region grows, the configuration-space volume outside the well dominates the fluctuations and $k_{\mathrm{eff}}$ drops rapidly, signaling the melting of finite-time bonds at a temperature $T^{*}$. Langevin simulations show the same loss of stiffness for particle–particle and particle–wall potentials, and the theory captures this behavior without any adjustable parameters. The temperature $T^{*}$ marks finite-time escape from the localized state and therefore depends on the observation window. Although the nonequilibrium probability density function is obtained exactly, evaluating $k_{\mathrm{eff}}$ from its moments requires numerical quadrature. To provide a simplified analytical representation of this behavior, we introduce a constrained Boltzmann distribution restricted to a finite region of configuration space of size $R_{\mathrm{eq}}$, where $R_{\mathrm{eq}}$ is determined from the nonequilibrium theory. We show that both the nonequilibrium theory and constrained Boltzmann-like representation quantitatively capture the melting of finite-time bonds, with the latter providing an approximate coarse-grained description of bond interactions.

In this study, we investigate the charging dynamics of a multiqubit quantum battery, characterized by the SU(2) algebra and driven by a finite-dimensional SU(1,1) bosonic charger. To enable systematic exploration of the parameter space, we develop and validate a neural-network surrogate model that replicates the exact quantum dynamics with high fidelity, yielding computational savings of up to 2 orders of magnitude compared with direct simulation. The dynamical blockade described below is the central physical result of this work, and the surrogate model is the computational means by which we characterize it across the full parameter space. Our framework reveals a many-body charging blockade: when the battery dimensions are comparable to the charger's excitation number, charging efficiency falls well below its kinematic limit despite ample energy remaining in the charger. We identify the physical underpinnings of this blockade as the saturation of the charger's emission rate, which confines the system to a low-excitation subspace before the battery can access its most absorptive states. This mechanism is intrinsic to finite chargers and absent in conventional infinite-mode models. This blockade is robust across a range of Bargmann indices and persists in a standard Dicke charger, confirming that it is a general feature of finite-dimensional charging rather than a property specific to the SU(1,1) algebra. We further show that a large number of charger excitations improves efficiency and reduces variance at the same time, whereas the blockade regime degrades both metrics together. These findings identify a many-body constraint on collective quantum charging and provide guidelines for designing high-performance quantum energy storage systems.

Diffusion with multipole-moment conservation gives rise to transport laws that generalize Fick's law and has attracted growing attention following experimental advances in strongly tilted optical lattices. It was recently shown that conserving complete multipole-moment groups leads to subdiffusive dynamics governed by a nonlinear diffusion equation, raising the question of whether hydrodynamic equations would also be nonlinear when the conservation law is imposed only at the subsystem level. Here we show that subsystem symmetries generically produce nonlinear hydrodynamic equations with shear-only transport, in which any localization present in the initial marginal distributions is preserved at long times by the conservation of those marginals. A linear regime emerges only as a limiting case for small fluctuations around a uniform background. We derive the deterministic and fluctuating parts of the hydrodynamic equations in arbitrary dimensions and obtain the corresponding maximum-entropy equilibrium distributions under constrained marginals. We also show that marginal-conserving diffusion provides a concrete hydrodynamic realization of partial multipole-moment conservation, and we offer an information-theoretic interpretation in which total correlation decays monotonically even when pairwise mutual information does not.

The complexity of many natural systems stems from the abundance of interactions that go beyond simple pairwise networks. While higher-order interactions (HOIs) are fundamental to the dynamics of complex networks, their role in shaping ecological communities through species dispersal remains poorly understood. Here, using chaotic tritrophic dynamics, we explore how synchronization emerges in networks characterized by both dyadic and three-body interactions. In random networks, HOIs reduce extreme asynchrony by promoting partial clustering, but never produce complete synchrony. By contrast, in globally connected networks, stronger HOIs drive the system from asynchronous states to full synchrony, with important consequences for community persistence. Employing the master stability function, we further demonstrate that global synchrony remains stable once a critical coupling threshold is crossed. Our findings reveal that HOI-mediated dispersal introduces topology dependence governed by the local triadic structure of the landscape network, which critically shapes the system's collective emergent dynamics.

Chimera states are one of the most intriguing phenomena in nonlinear dynamics, characterized by the coexistence of coherent and incoherent behavior in systems of coupled identical oscillators. Despite extensive studies and numerous observations in different settings, the development of reliable and systematic methods to classify chimera states and distinguish them from other dynamical patterns remains a challenging task. Existing approaches are often limited in scope and lack robustness. In this work we propose a method based on Fourier analysis combined with statistical classification to identify chimera behavior. The method is applied to a system of topological signals coupled via the Dirac operator, where it successfully captures the rich dynamical regimes exhibited by the model. We demonstrate that the proposed approach is robust with respect to variations in network topology and system parameters. Beyond the specific model considered, the framework provides a general and automated tool for distinguishing different dynamical regimes in complex systems.