Papers

Continuous-time quantum walks on a lattice spread ballistically and converge to a limiting distribution for the rescaled position. On the hard-wall half line the boundary reflects the walker but does not change the bulk dispersion, so the ballistic front remains set by the maximal group velocity. We ask how close one can get to this front when the initial state is constrained to occupy only the first $M$ sites. We show that optimizing the moment-generating function of the limiting-velocity distribution over this finite-support class reduces to the principal eigenvalue of an explicit $M\times M$ Hermitian matrix, which yields the optimal state by direct diagonalization. For large $M$, a near-front scaling limit produces a continuum description that controls the entire peak region. In particular, the maximal mean drift approaches the front with an inverse-square deficit in $M$ and a constant prefactor $\pi^2/4$. Numerical results verify both the finite-$M$ spectral formulation and the predicted scaling.

Predicting the thermodynamic properties of an alloy requires sampling its configurations across many chemical conditions and recovering free energies on a common absolute scale. Markov chain Monte Carlo (MCMC) is the standard tool, but it requires separate simulations at different conditions, and auxiliary free-energy methods such as thermodynamic integration are used to place results on a common absolute scale. Modern discrete neural samplers typically use reverse KL divergence as the objective and can be mode-seeking or biased. We present Free energy Offering Generative Sampler (FrOGS), a hybrid discrete neural sampler that couples an autoregressive model to a continuous-time Markov chain (CTMC) to be trained jointly under a single shared loss. FrOGS draws i.i.d. configurations, returns an unbiased estimate of the partition function, and gives consistent estimates of thermodynamic observables. We train a single model across a wide range of chemical conditions to produce estimates on a common absolute free-energy scale. FrOGS matches exact finite-size results on the 2D Ising model and reference phase diagrams for AgPd and CuAu, without mode collapse. We additionally compare to SEGAL, a published autoregressive baseline, and find that only FrOGS recovers the stability range of the CuAu$_3$ phase.

One-dimensional quantum–classical hybrid walks are introduced by combining quantum and classical steps under periodic and random protocols. Exact diffusion coefficients are derived for both protocols throughout the diffusive regime. The exact results show how diffusion depends on the average frequency and temporal arrangement of classical steps. As the average frequency approaches zero, both diffusion coefficients diverge inversely with the frequency. At matched average frequencies, the ratio of the diffusion coefficients for the random and periodic protocols approaches two. A finite-mode approximation is also developed and tested against the exact diffusion coefficient for the random protocol. The exact results for the one-dimensional model provide a foundation for future studies of more general quantum–classical hybrid walks.

Understanding how individual protection and population density influence epidemic spreading remains a central challenge in epidemiology. While classical compartmental models successfully describe the temporal evolution of epidemics, they do not explicitly account for the microscopic motion and spatial organisation of individuals. Here, we investigate contagion dynamics using an agent-based model of Active Brownian Particles (ABPs), where self-propelled agents interact through local contact and a prescribed fraction of the population is protected. By systematically varying the protected-agent fraction and the population density, we identify two distinct contagion regimes separated by a crossover protection of approximately $30\%$. Below this threshold, the maximum contagion rate follows the universal scaling $\nu_{\mathrm{max}}\propto\phi^{1/2}$, indicating that disease transmission is governed primarily by frequency of encounters. Above the threshold, universal scaling is lost and protection becomes the dominant mechanism controlling epidemic spreading, with the strongest suppression occurring in low-density populations. These results demonstrate that microscopic active-matter models provide a powerful framework for investigating epidemic dynamics beyond the assumptions of well-mixed population models and reveal how spatial organisation and individual protection jointly determine contagion dynamics.

A central challenge in movement ecology is to describe ecologically meaningful residence sites from raw tracking data due to heterogeneous sampling frequency and uncertain site boundaries. Here, we develop a greedy nearest-neighbor clustering approach with local reassignment and polygon-based site construction that generates timestamped sequences of site visits for each tracked individual, and apply it to nine years of GPS data from two sympatric raven species in the Dead Sea region—the Fan-tailed Raven (Corvus rhipidurus) and the Brown-necked Raven (C. ruficollis). Using the resulting visitation sequences, we quantify recursion patterns using the non-Markovian individual mobility model (IMM), which captures the balance between novel-site discovery $\beta$ and preferential return $\alpha$. The inferred dynamics are consistent with IMM predictions and reveal clear interspecific differences: Brown-necked Ravens continue to discover new sites at a higher rate (lower $\beta$), whereas Fan-tailed Ravens show a steeper concentration of visits among top-ranked sites. Entropy analyses further separate the species, with Brown-necked Ravens exhibiting higher site entropy and higher conditional entropy of site-to-site transitions. Together, these results provide a robust framework for describing interspecific differences in movement strategies that can be used to infer memory from GPS data and suggest distinct space-use strategies in two closely related sympatric species.

Information engines convert information into extractable work through measurements and feedback. We realize an engine that employs information to compress a gas of self-propelled bristle bots. Its work per measurement, $\bar{W}$, is controlled by the size of the detection region $\Delta x$ and the probability $p_1$ that this region is vacant. In thermal systems, $\bar{W}$ follows the universal form $-p_1 \ln p_1$, whereas the active engine shows a qualitatively modified relation. As particle density increases, the maximum of $\bar{W}(\Delta x)$ switches between two distinct operating regimes. Notably, this transition is also found in the solutions that maximize power output for finite-time cycles with dynamics affected by dry friction. We attribute this nonequilibrium feature to the accumulation of active particles near the boundaries.

We study bilinear order-parameter correlations in a general class of sign problem-free systems that are described by what we call Fluctuating Gaussian States (FGS) with anti-unitary symmetries, where the weight of each Gaussian measurement in the space-time path integral is positive-definite. Supported by Monte Carlo simulations on fluctuating Gaussian fermionic and bosonic examples, we argue that such systems generally exhibit two types of broken-symmetry phases: a saddle point phase and a non-local contraction phase, with the competition between the two determined by the stability of the fluctuation saddle point of FGS. Due to the Fermi liquid instability in fermionic FGS with anti-unitary symmetries, we also discuss the possibility of representing fermionic FGS with a particular Projected Entangled-Pair State (PEPS) ansatz, which we argue a certain construction provides an efficient description for the saddle point phase, but not for the non-local contraction phase. Finally, we discuss the potential implication of our result in non-equilibrium systems and stabilizing a target bilinear order.

Prethermalization describes long-lived intermediate regimes that precede equilibrium and can dominate experimentally accessible dynamics. Here, we show that a separation of spectral energy scales, despite giving rise to a hierarchy of dynamical timescales, does not by itself guarantee the appearance of a prethermal plateau. Under the same Hamiltonian, some observables may exhibit prethermal behavior, while others relax directly toward equilibrium. We uncover the mechanism governing this selectivity, showing that the emergence of a prethermal plateau depends not only on the Hamiltonian, but also on the observable and the initial state. Our results apply broadly to systems close to a fully permutation-symmetric limit and are illustrated with a long-range interacting spin model. We further prove that the Loschmidt echo provides a lower bound on the prethermal lifetime of any bounded observable whenever the prethermal and exact dynamics are unitary.

Additive functionals $\overline{J}_t=\frac{1}{t}\int_0^tU(X_s)\circ dX_s$ of Stratonovich-type recently attracted much attention in the context of inference of thermodynamic properties of complex systems from observations $U$ of individual fluctuating paths $(X_s)_{0\le s\le t}$, whereby $X_0$ is initiated from some general measure. Concentration results on $\overline{J}_t$, albeit desirable, are virtually nonexistent. They turn out to be significantly more challenging to prove than for classical Lebesgue-type functionals $\overline{\rho}_t=\frac{1}{t}\int_0^t V(X_s)ds$ because the tilt deforms the full second-order structure of the Feynman-Kac generator instead of contributing an additive potential. This renders the generator generally non-self-adjoint even under detailed balance. We overcome this by working with a symmetrized Dirichlet form with a new effective potential that now couples the observable to the non-equilibrium character of the dynamics. We prove concentration inequalities for $\overline{J}_t$ for any bounded, sufficiently smooth vector-valued function $U$ of a general geometrically ergodic diffusion process $X_s$, including explicit sub-gamma and Bernstein-type inequalities, and we obtain explicit upper bounds on ${\rm Var}(\overline{J}_t)$. Strikingly, under detailed balance the concentration of $\overline{J}_t$ is distinctively sub-Gaussian at all times and all deviations, with a variance proxy fixed by the noise alone and independent of the spectral gap, which has no analog for $\overline{\rho}_t$.

Sensory adaptation provides a concrete setting in which low-order system identification can fail qualitatively. We show that one fixed higher-order adaptive system composed entirely of real first-order relaxation modes can be reduced to opposite sides of the second-order pole boundary: low-frequency moment matching gives $\rho_{\rm moment}=4.50$, whereas finite-window fitting gives $\rho_{\rm window}=3.31$, and the inferred pole class changes further with sampling protocol. Thus the real-versus-complex classification of a reduced model is not itself reduction invariant. We then use the general two-state spectrum to connect stochastic identifiability to adaptation: for nontrivial coupling and one-state observation, cross diffusion drops out of the scalar spectrum when the hidden state has no self-relaxation. In the adaptive model, this condition is precisely the integral-memory limit that produces exact adaptation, while leaky memory restores spectral sensitivity. For the exact-adaptation model, the Gaussian path-space irreversibility nevertheless depends on the hidden cross-diffusion channel. Hence $\{H,S_x\}$ does not determine the irreversibility rate. Independently, for a specified all-even reduced two-state drift with $\rho<4$, the drift-only lower bound is $\sigma \ge \tau_x^{-1}(4/\rho-1)$. Published E.~coli and C.~elegans responses provide biological examples of these limits. The distinction established here between transfer-function invariants, reduction-dependent properties, and hidden-state quantities provides a concrete framework for evaluating the limitations of low-dimensional models of adaptive biological dynamics.

Optimal transport describes the most efficient way to move mass between two distributions, given a cost matrix for moving mass between each pair of locations. Entropic optimal transport, solved via the Sinkhorn algorithm, is a widely used regularized version of this problem. Its inverse problem asks the opposite question: given an observed transport plan, what cost matrix produced it? This is difficult because the cost is identifiable only up to an additive gauge freedom. Here we show that this freedom can be fixed exactly by a single double-centering operation applied to the observed plan, yielding the true cost matrix in closed form, with no iterative optimization required. When a modest number of true cost entries are known, the same approach lets us jointly estimate the temperature parameter controlling the entropic regularization, together with a diagnostic for the reliability of this estimate. We further show that the method is not specific to the entropic optimal transport, but extends to a broader class of transport models defined by an invertible relation between cost and plan.

We present a unifying description of dynamical phase transitions in the unitary evolution of an isolated quantum particle and the dissipative relaxation of a classical Brownian particle, based on a dynamical generat- ing function. In the semiclassical and weak-noise limits, Fisher zeros of this function condense in the complex- time plane and reach the corresponding physical axes, producing dynamical phase transitions through a competition between return trajectories. This establishes a direct connection between quantum and classical (finite-time) dynamical phase transitions, where the semiclassical limit plays the role of the thermodynamic limit. In particular, the established link naturally provides a classical version of the Loschmidt amplitude and shows how dynamical quantum phase transitions, typically associated with isolated many-body systems, can arise in a single-particle quantum system. The dynamical phases are distinguished by a unifying, trajectory- based order parameter, realized as a classical correlation function and a sequential quantum weak value.

We study linear instabilities and pattern formation in a spatially extended Selkov model for glycolysis with diffusion and chemotactic interactions between two species. Linear stability analysis reveals two distinct bifurcations: a zero-wavevector, finite-frequency Hopf bifurcation leading to spatially homogeneous oscillations, and a finite-wavevector Turing instability with a saddle-node bifurcation leading to stationary inhomogeneous patterns. The selected wavevector, $k_c$, depends sensitively on the nature and strength of chemotaxis and varies nonmonotonically with the chemotaxis parameters, allowing re-entrant transitions between homogeneous and patterned states. For sufficiently strong chemotaxis, when the two species mutually attract or mutually repel each other, an unusual instability emerges in which the preferred wavevector diverges as a finite threshold in chemotactic strength is approached. We complement the linear analysis with extensive direct numerical simulations (DNS) of the nonlinear partial differential equations in two dimensions. The DNS confirm the predicted instabilities and their nonmonotonic and re-entrant character, and also reveal spatially uniform oscillatory states for suitable parameters. The stationary patterns include spots and, unexpectedly, stable stripes. We further uncover transitions between spot and stripe morphologies controlled by chemotactic strength and diffusivity ratios. The stability of the striped states is consistent with linear amplitude equations, whereas the spot-stripe transition is attributed to nonlinear effects beyond linear stability. Our results demonstrate that chemotaxis can act as a nonmonotonic control parameter for instability selection, wavelength selection, re-entrant pattern formation, and nonlinear pattern morphology in reaction-diffusion systems.

We investigate pattern formation in generic two-species reaction-diffusion systems with mutual chemotaxis. We show that tuning the chemotaxis strength can give rise to striking nonmonotonic variation of patterns, opening the possibility of re-entrant transitions between patterned and spatially uniform steady states. In certain regimes, chemotaxis also induces additional heretofore unexplored instabilities. Furthermore, varying the strength of chemotaxis can drive morphological transitions between spot and stripe patterns.

Exchange-dominated magnons in nanometer-thick ferromagnets extend to the terahertz regime through thickness quantization of perpendicular standing spin-wave (PSSW) modes. While interfacial spin-orbit torques (SOTs) have been shown to enable the excitation of such modes, the microscopic origin of the interfacial driving torque remains unclear. In particular, the coexistence of spin and orbital currents complicates the understanding. Here, we develop and use an atomistic framework that explicitly resolves interfacial symmetries and separates spin and orbital torque contributions. Exploiting a trilayer geometry for a thin ferromagnet sandwiched between non-magnetic layers, where the symmetry-controlled polarity of the interfacial torque produces mode-selective magnon excitation as observed in the recent experiment of Salikhov et al. Nature Phys. 19, 529 (2023), we disentangle the different interfacial torque contributions. By decomposing the torque into magnetization-even (field-like) and magnetization-odd components, we identify the field-like torque as the dominant contribution responsible for the excitation. Crucially, isolating orbital and spin contributions reveals that the interfacial orbital torque provides the primary channel for the efficient excitation of exchange-dominated THz magnons in thin ferromagnets. Our results establish a microscopic basis for symmetry-engineered control of confined terahertz spin dynamics in magnetic multilayers.

This paper presents a computational study of language competition dynamics on Erdős–Rényi random networks, extending the foundational Abrams–Strogatz model through two novel contributions: (i) a dynamic edge-weighting mechanism that reinforces social ties between co-minority speakers by an additive increment $\Delta$, and (ii) a probabilistic agent-based framework governing language switching via a weighted majority rule. Phase boundaries separating the dominance and coexistence regimes are identified across a two-dimensional parameter space $(p, \Delta)$, where $p$ denotes the network connectivity probability. We further characterise anomalous persistence zones within predicted dominance regions, attributing them to the formation of isolated minority speaker clusters. Scaling study across network sizes $N \in \{50, 100, 250, 500, 1000\}$ reveal that average cluster size decreases with $N$ and that phase boundaries diffuse with increasing stochastic noise. Finally, we discuss extensions to a tripartite bilingual model and heterogeneous prestige/volatility to more faithfully capture real sociolinguistic contact scenarios.

We discuss an information-geometric framework for characterizing quantum states in non-equilibrium dynamics. Using the transverse-field Ising chain model as a laboratory, we investigate the quantum Fisher information metric with particular emphasis on the mixed metric component $g_{ht}$ and related geometric observables, where $h$ is a controllable post-quench Hamiltonian parameter and $t$ is real time. The framework treats $h$ and $t$ as coordinates of an extended information manifold $(h,t)$. The geometric observables characterize the speed of evolution on the manifold and the alignment between the temporal and parameter-deformation directions. Correlations between these geometric quantities and two widely used measures of non-equilibrium dynamics, the entanglement entropy and the Loschmidt echo, are analyzed.

We investigate driven dynamics across critical and exceptional points in the one- and two-dimensional imbalanced-pairing Kitaev models using both the wave-function normalization approach and the biorthogonal framework. For a positive pairing imbalance parameter, the quasiparticle spectrum remains real, and a pairing imbalance neither shifts the equilibrium phase boundaries nor generates imaginary eigenenergies. In this regime, the defect density follows the conventional Kibble–Zurek scaling in one dimension and the extended Kibble–Zurek scaling, arising from a gapless manifold, in two dimensions within both frameworks. The corresponding scaling exponents are therefore governed by those of the Hermitian transition. For a negative pairing imbalance parameter, time-reversal symmetry is broken, the quasiparticle spectrum develops complex eigenvalues, and the gap closes at exceptional points. For ramps ending at an exceptional point, the defect density follows the modified Kibble–Zurek scaling in the wave-function normalization approach, whereas it obeys the conventional Kibble–Zurek scaling in the biorthogonal framework. When the ramp traverses the time-reversal-symmetry-broken region, a finite density of defects remains even in the adiabatic limit, leading to defect freezing in both frameworks. Although this frozen background indicates a breakdown of adiabaticity, the excess defects generated on top of this background continue to obey the conventional Kibble–Zurek scaling in one dimension and the extended Kibble–Zurek scaling in two dimensions.

We develop a finite-temperature Gaussian-state formulation of quantum energy teleportation in the one-dimensional harmonic chain. For Gibbs states, the optimized measurement-feedback protocol reduces to thermal two-point functions. In the single-site protocol, the extracted energy is governed by a single correlator, which makes the thermodynamic and near-critical limits analytically tractable. At fixed finite temperature, the extracted energy is exponentially screened with distance and is controlled by a thermal correlation length for both critical and non-critical $\alpha$. In the zero-temperature critical limit taken after the thermodynamic limit, we derive the exact asymptotic law $E_{\mathrm{ext}}\sim d^{-4}$. Numerical results confirm both regimes and resolve the crossover responsible for the apparent drift of the effective decay exponent at intermediate distances. We also analyze squeezed Gaussian measurements and show that they modify the extraction prefactor: $p-$squeezing enhances the extracted energy, whereas $q-$squeezing suppresses it, without changing the large-distance scaling.

Ensuring a sustainable energy supply requires maintaining power-grid stability. Rotor dynamics are governed by the swing equation, which takes the form of a second-order Kuramoto model with a correlation between power and total coupling strength. Yet the microscopic mechanisms that nucleate and propagate synchronized clusters remain poorly understood. Using a minimal model motivated by empirical grid data and the \Adhoc potential method, we reveal two distinct seed cluster types and propagation pathways: a population-driven seed cluster at the center of the power distribution propagating to its tails by rotor accretion, and, for a symmetric distribution, coupling-driven seed clusters at its tails propagating inward to the center by cluster merger. These differences generate distinct order-parameter patterns, while inertia controls whether the seed clusters persist with distinct angular velocities. The same propagation pathways also govern recovery following external disturbances. We further confirm that the same selection–persistence rule holds in data-derived annealed representations of European power grids. Therefore, our results can inform strategies for sustaining stable power-grid operation. More generally, our pathway-based framework reframes synchronization by emphasizing the dynamics of cluster formation and recovery rather than relying solely on static criteria.

Transport in certain systems fails when diffusion cannot replenish or remove material from a boundary rapidly enough, causing the boundary concentration to reach a critical minimum or maximum. Motivated by experiments in electrochemical systems that demonstrate this diffusion-limited failure of charge transport, we determine dynamic current protocols that maximize charge transfer subject to a prescribed concentration constraint. The optimal protocol has a "bang-ride" structure: the maximum feasible current is used until the boundary concentration reaches its critical value, after which the current is progressively reduced to maintain that value. For semi-infinite domains, we derive the optimal currents analytically and obtain system-independent upper bounds on their improvement over constant-current operation. We also extend the framework to finite and multilayer domains and show that the same formulation applies to both charging and discharging.

We study a one-dimensional fractional $U(1)$ Ginzburg–Landau model whose quadratic part has Fourier multiplier $|k|^\sigma$, focusing on the marginal case $\sigma=1$. This dispersion yields logarithmic spin-wave fluctuations, suggesting BKT-like behavior despite the one-dimensional setting. We sample the equilibrium Gibbs measure using stochastic Gross–Pitaevskii dynamics and analyze correlation functions, dimensionless ratios, effective exponents, and twist responses. The correlation function shows a low-temperature algebraic branch with a temperature-dependent exponent, while the high-temperature regime exhibits a nonlocal-kernel-induced tail consistent with $C(r)\sim r^{-2}$. The correlation and Binder ratios are nearly size independent at low temperature and collapse with the BKT-type variable $(T-T_{\rm BKT})(\log L)^2$; finite-size effects set in around $T\simeq0.35\text{--}0.4$, consistent with $T_{\rm BKT}\simeq0.35$. Unlike the two-dimensional XY model, twist responses do not yield a finite helicity modulus: the ordinary linear-response quantity grows with system size, whereas the cusp twist response scales as $L^{-\eta(T)}$, like the squared zero-mode order parameter. Thus, the transition is BKT-like in correlation scaling, but lacks a universal helicity-modulus jump.

Many physical systems evolve under periodic driving: the same control protocol is applied again and again, even though the state of the system itself need not return to where it started after each cycle. We derive a physics-independent lower bound on the entropy production of any periodic process modeled by the evolution of an initial distribution $p_0$ by a repeated application of the same map $G$. This is a strict strengthening of the second law of thermodynamics for periodic processes. It does not require that the single-period dynamics arise from a CTMC, satisfy (local) detailed balance, or be subject to other typical restrictions. We discuss its application to spins in the Curie-Weiss model and Deterministic Finite Automata, with possible extensions to other uniform computers.

Feedback can convert continuously monitored quantum jumps into a thermodynamic resource. We formulate full counting statistics for open quantum systems under unital jump feedback by incorporating the feedback maps into the tilted generator. The resulting trajectory ensemble determines both current fluctuations and the Fisher information of the measurement record. We show that feedback can enhance reservoir-parameter estimation and clock precision without necessarily changing average thermodynamic currents. This enhanced precision is not bounded by reservoir entropy production alone. By embedding the reduced dynamics in an enlarged measurement-feedback process, we derive a feedback-modified thermodynamic uncertainty relation in which the information entropy production of the feedback apparatus supplies the missing cost. A charge-monitored double quantum dot illustrates the framework: jump-conditioned feedback improves thermometry and chemical-potential sensing, and stabilizes a quantum clock defined by output-current ticks.

Cohesive granular materials derive their mechanical stability not only from the strength of individual interparticle bonds but also from the number of bonds forming the load-bearing network. However, these two effects are difficult to separate experimentally because conventional control parameters, such as liquid content, generally alter both simultaneously. Here, we use a mixed granular system composed of cohesive and noncohesive grains to control the cohesive bond number while keeping the bond strength approximately unchanged. We investigate the failure lifetime under repeated vibration and find that the number of cycles to failure, $N_f$, depends strongly on the mixing ratio $\alpha$. In a mean-field picture of random mixing, the fraction of cohesive contacts scales as $\alpha^2$, and $N_f$ increases approximately exponentially with $\alpha^2$. By contrast, although the lifetime tends to decrease with increasing vibration intensity $G$, its dependence on $G$ is comparatively weak over the present experimental range. Remarkably, although the Young's modulus is nearly independent of $\alpha$ above the rigidity threshold, the lifetime continues to increase strongly with $\alpha$. This demonstrates that mechanical rigidity and durability against repeated perturbations exhibit distinct dependences on the cohesive network. These results identify bond number as a key control parameter for the durability of cohesive granular materials.

We show that for any potential with a discrete energy spectrum, the well-known interpolation between ideal boson and fermion partition functions at discrete values of $\xi=-1/m$ yielded zero temperature ground state energies corresponding to $m$ fermions occupying a single quantum state. The grand canonical partition function in this case can be a result from genuine parastatistics.

Can an artificial intelligence (AI) generate a scientific hypothesis outside a human collaborator's active hypothesis space (AHS), and can human-AI research be organized to make such breakthroughs more likely? We document such a case while proving a theorem that connects two basic organizing mechanisms of statistical physics: collective behavior arising in zero field from competing interactions and that induced or controlled by an external field. A zero-field $O(n)$-vector open chain with arbitrary inhomogeneous nearest- and next-nearest-neighbor interaction functions $U_i(S_i\cdot{S}_{i+1})$ and $V_i(S_i\cdot{S}_{i+2})$ is microscopically, via a temperature-independent mapping at the Hamiltonian level, equivalent to a simpler $O(n)$ open chain with nearest-neighbor interaction $V_i(\boldsymbol\sigma_i\cdot\boldsymbol\sigma_{i+1})$ and axial single-spin potential $U_i(\sigma_i^z)$ for every integer $n\ge1$ and every system size $L\ge1$. The homogeneous linear specialization maps the foundational frustrated $J_1$-$J_2$ model onto the canonical $J$-$h$ field model—with $n=1,2,3$ being the Ising, XY, and Heisenberg classical spin models, respectively; the theorem resolved a longstanding challenge for $n=3$ published in 1990. Its proof was done with an AI-synthesized recursive Householder moving frame and understood via a human-recognized hidden reciprocity. An analogous theorem holds when the continuous $O(n)$ spins are replaced by the $q$-state Potts spins, implying a closed-form exact solution of the $J_1$-$J_2$ standard Potts open chain for every $q\ge2$ and every $L\ge1$. The emergence of these theorems from a human-AI co-development framework suggests that sustained AI involvement throughout a systematic research program may incubate autonomous scientific breakthroughs and make aspects of the discovery process experimentally testable.

Higher-gradient modifications of Newtonian gravity remove the point-mass singularity, but their Lagrangian dynamics is haunted by the Ostrogradsky instability. We show that the same field equations follow from the Second Law of thermodynamics applied to a self-gravitating fluid with a weakly nonlocal state space, and that on this route the instability is absent by construction: the potential obeys a first-order relaxation equation that is a gradient flow, whose Lyapunov function is the entropy density, and whose relaxation spectrum is negative definite at every wavenumber precisely when the entropy is concave. The derivation also yields the pressure tensor and the energy current, an exact identity that reproduces Newton's force law without further input, and a dissipation-free cross-coupling to the bulk viscous pressure that no variational principle can produce. Regularity constrains the Yukawa-type corrections by an amplitude sum rule, $\sum_i\alpha_i=-1$, so that laboratory tests of the inverse-square law bound the largest internal length below $4\times10^{-5}$~m, and identify the complex-root regime as a classically consistent Lee–Wick-like sector.

Determining exact joint eigenvalue densities is central to random matrix theory. We solve this long-standing problem for non-Hermitian matrices with transposition symmetry (complex symmetric and complex self-dual) at arbitrary matrix size. Up to a Vandermonde factor, they are scattering-state wave functions of the Calogero model, a line of particles interacting through an inverse-square potential, with the coupling strength set by the symmetry. In contrast to many previously known joint densities, the densities cannot be written as a gas of eigenvalues with pairwise interactions. We further compute the complex level spacing distributions and two-point spectral correlation functions, which carry power-law tails, absent in a Coulomb gas. Our results shed light on the interplay among random matrices, integrability, and symmetry.

The complex spectral statistics of non-Hermitian random matrices provide a standard diagnostic of dissipative quantum chaos. Yet an analytical understanding of how symmetry enriches these universal correlations remains limited. We establish an exact duality between the spectral statistics of Hermitian and non-Hermitian random matrices in the limit of large matrix size. This duality resolves a longstanding analytical problem by yielding the previously unknown eigenvalue pair-correlation functions for complex symmetric (class AI$^\dagger$) and complex self-dual matrices (class AII$^\dagger$), completing the analytical description of bulk pair correlations in the non-Hermitian threefold way. It further gives closed-form spectral densities near the origin for seven additional symmetry classes. Numerical tests in interacting and dissipative quantum models support the universality of these predictions beyond Gaussian ensembles. The duality suggests a deeper connection between chaos in closed and open quantum systems.