We present a hydrodynamical description of spherical void evolution in modified gravity (MG), extending the standard General Relativity (GR) and dynamical dark energy treatment by encoding gravity modifications into effective couplings that enter the Euler and Poisson equations. This yields a compact non-linear evolution equation for the Eulerian density contrast, controlled by a time- and density-dependent effective gravitational strength, and provides a direct map between model functions and void observables. We apply the framework to the luminal Galileon class of models, where derivative self-interactions generate Vainshtein screening and might lead to a breakdown of the physical branch in sufficiently underdense regions. Exploiting this feature, we apply the void-informed viability requirement that translates into bounds on the theory parameter space and, equivalently, on the minimum attainable void depth as a function of redshift. For viable parameters of a concrete model, we quantify the impact of MG on isolated void evolution, the Lagrangian to Eulerian mapping, and the shell-crossing threshold. Relative to GR, we find a clear hierarchy of MG effects, with ${\cal O}(10\%)$ modifications in the gravitational couplings, percent-level shifts in the void density evolution, and sub-percent deviations in both the mapping and the shell-crossing thresholds. Moreover, within the adopted parametrization, we show analytically that voids always lie in an unscreened regime on the physical branch. Overall, the formalism provides a self-consistent route to predict void dynamics and consistency constraints in a broad class of MG models.

The local equilibration time $τ_{\rm eq}$ of quantum many-body systems is conjectured to be bounded below by the Planckian time $\hbar /T$. We formalize this conjecture by defining $τ_{\rm eq}$ as the time scale at which a hydrodynamic description emerges for conserved densities. Drawing on analytic properties of real time thermal correlators, we establish a rigorous lower bound $τ_{\rm eq} \geq α\hbar /T$ on the onset of hydrodynamic behavior in a `regulated' thermal two-point function. The dimensionless coefficient $α$ depends only on dimensionality and the type of hydrodynamic or diffusive behavior that emerges, and is independent of the thermalization mechanism or other microscopic details. This bound applies universally to local quantum many-body systems, with or without a quasiparticle description, including in the presence of inelastic scattering.

Let $P$ be a set of $n$ points in the plane, not all on a line, each colored \emph{red} or \emph{blue}. The classical Motzkin--Rabin theorem guarantees the existence of a \emph{monochromatic} line. Motivated by the seminal work of Green and Tao (2013) on the Sylvester-Gallai theorem, we investigate the quantitative and structural properties of monochromatic geometric objects, such as lines, circles, and conics. We first show that if no line contains more than three points, then for all sufficiently large $n$ there are at least $n^{2}/24 - O(1)$ monochromatic lines. We then show a converse of a theorem of Jamison (1986): Given $n\ge 6$ blue points and $n$ red points, if the blue points lie on a conic and every line through two blue points contains a red point, then all red points are collinear. We also settle the smallest nontrivial case of a conjecture of Milićević (2018) by showing that if we have $5$ blue points with no three collinear and $5$ red points, if the blue points lie on a conic and every line through two blue points contains a red point, then all $10$ points lie on a cubic curve. Further, we analyze the random setting and show that, for any non-collinear set of $n\ge 10$ points independently colored red or blue, the expected number of monochromatic lines is minimized by the \emph{near-pencil} configuration. Finally, we examine monochromatic circles and conics, and exhibit several natural families in which no such monochromatic objects exist.

The theory of open quantum systems served as a tool to prepare entanglement at the beginning stage of quantum technology and more recently provides an important tool for state preparation. Dynamics given by time dependent Lindbladians are Markovian and lead to decoherence, decay of correlation and convergence to equilibrium. In contrast Non-Markovian evolutions can outperform their Markovian counterparts by enhancing memory. In this letter we compare the trajectories of Markovian and Non-Markovian evolutions starting from a fixed initial value. It turns out that under mild assumptions every trajectory can be obtained from a family of time dependent Lindbladians. Hence Non-Markovianity is invisible if single trajectories are concerned.

We discuss some properties of the distance functions on Riemannian manifolds and we relate their behavior to the geometry of the manifolds. This leads to alternative proofs of some "classical" theorems connecting curvature and topology.

We outline an approach to obtain direct $L^2$ estimates not requiring interpolation for so-called linearized partial sums operators associated with expansions in Walsh functions. We focus specifically on a simpler case of dyadic partial sums but also outline a second approach to proving bounds on general linearized partial sums.

This paper describes progress achieved in early investigations of the orbital motion and light curve of comet C/2026 A1 (MAPS), the third ground-based discovery of a Kreutz sungrazer in the 21st century. The highly unusual trait of the comet that has so far been ascertained is its extraordinarily long orbital period. The most recent orbital computations make it increasingly likely that the object is a fragment of one of the comets observed by Ammianus Marcellinus in AD 363, thereby strengthening evidence in support of the contact-binary hypothesis of the Kreutz system. In this context, the comet is the only second-generation fragment of Aristotle's comet that we are aware of to appear after the 12th century. It does not look like a major fragment, but rather like an outlying fragment of a much larger sungrazer. In 363 it apparently separated from a parent different from the lineage of comet Pereyra. The light curve of comet MAPS has so far been fairly smooth, without outbursts. To reach the brightness of comet Ikeya-Seki, the comet would have to follow an r^(-17) law in the coming weeks, which is unlikely.

LLM-based agents show promise for automating penetration testing, yet reported performance varies widely across systems and benchmarks. We analyze 28 LLM-based penetration testing systems and evaluate five representative implementations across three benchmarks of increasing complexity. Our analysis reveals two distinct failure modes: Type A failures stem from capability gaps (missing tools, inadequate prompts) that engineering readily addresses, while Type B failures persist regardless of tooling due to planning and state management limitations. We show that Type B failures share a root cause that is largely invariant to the underlying LLM: agents lack real-time task difficulty estimation. As a result, agents misallocate effort, over-commit to low-value branches, and exhaust context before completing attack chains. Based on this insight, we present Excalibur, a penetration testing agent that couples strong tooling with difficulty-aware planning. A Tool and Skill Layer eliminates Type A failures through typed interfaces and retrieval-augmented knowledge. A Task Difficulty Assessment (TDA) mechanism addresses Type B failures by estimating tractability through four measurable dimensions (horizon estimation, evidence confidence, context load, and historical success) and uses these estimates to guide exploration-exploitation decisions within an Evidence-Guided Attack Tree Search (EGATS) framework. Excalibur achieves up to 91% task completion on CTF benchmarks with frontier models (39 to 49% relative improvement over baselines) and compromises 4 of 5 hosts on the GOAD Active Directory environment versus 2 by prior systems. These results show that difficulty-aware planning yields consistent end-to-end gains across models and addresses a limitation that model scaling alone does not eliminate.

This paper presents a method to assess the pointing and image motion performance of optical payloads in the presence of image displacement (shift), smear, and jitter. The method assumes the motion is a stationary random process over an image exposure interval. Displacement, smear, and jitter covariances are computed from the solution to a Lyapunov differential equation. These covariances parameterize statistical image motion modulation transfer functions (MTFs), and they can be used to verify pointing and image motion MTF requirements. The method in the present paper extends a previous method to include smear, as well as displacement, and hence jitter. The approach in the present paper also leads, as a special case, to a more efficient method to compute the displacement covariance than the previous method. Numerical examples illustrate the proposed method.

Emerging IoT applications are transitioning from battery-powered to grid-powered nodes. DRP, a contention-based data dissemination protocol, was developed for these applications. Traditional contention-based protocols resolve collisions through control packet exchanges, significantly reducing goodput. DRP mitigates this issue by employing a distributed delay timer mechanism that assigns transmission-start delays based on the average link quality between a sender and its children, prioritizing highly connected nodes for early transmission. However, our in-field experiments reveal that DRP is unable to accommodate real-world link quality fluctuations, leading to overlapping transmissions from multiple senders. This overlap triggers CSMA's random back-off delays, ultimately degrading the goodput performance. To address these shortcomings, we first conduct a theoretical analysis that characterizes the design requirements induced by real-world link quality fluctuations and DRP's passive acknowledgments. Guided by this analysis, we design EDRP, which integrates two novel components: (i) Link-Quality Aware CSMA (LQ-CSMA) and (ii) a Machine Learning-based Block Size Selection (ML-BSS) algorithm for rateless codes. LQ-CSMA dynamically restricts the back-off delay range based on real-time link quality estimates, ensuring that nodes with stronger connectivity experience shorter delays. ML-BSS algorithm predicts future link quality conditions and optimally adjusts the block size for rateless coding, reducing overhead and enhancing goodput. In-field evaluations of EDRP demonstrate an average goodput improvement of 39.43\% than the competing protocols.

Let $f\colon X \to \mathbb{A}^1_t$ be an affine flat morphism of finite type, and let $V = f^{-1}(0)$. Then, we obtain a morphism of log schemes $f\colon (X|V) \to (\mathbb{A}^1_t|0)$. In this article, we develop algorithmic tools to study the log-geometric properties of $f$ by means of a presentation \[Γ(X,\mathcal{O}_X) = \Bbbk[t,x_1,\ldots,x_n]/(f_1,\ldots,f_r).\] We obtain similar tools for projective flat morphisms when the homogeneous coordinate ring is given by generators and relations. We provide an implementation of our algorithms in Macaulay2. In a slightly different direction, we give some results on the sheaf $\mathcal{LS}_V$ of log smooth structures on a toroidal crossing scheme $(V,\mathcal{P},\barρ)$.

While ground-state preparation is expected to be a primary application of quantum computers, it is also an essential subroutine for many fault-tolerant algorithms. In early fault-tolerant regimes, logical measurements remain costly, motivating adaptive, shot-frugal state-preparation strategies that efficiently utilize each measurement. We introduce the Shadow Enhanced Greedy Quantum Eigensolver (SEGQE) as a greedy, shadow-assisted framework for measurement-efficient ground-state preparation. SEGQE uses classical shadows to evaluate, in parallel and entirely in classical post-processing, the energy reduction induced by large collections of local candidate gates, greedily selecting at each step the gate with the largest estimated energy decrease. We derive rigorous worst-case per-iteration sample-complexity bounds for SEGQE, exhibiting logarithmic dependence on the number of candidate gates. Numerical benchmarks on finite transverse-field Ising models and ensembles of random local Hamiltonians demonstrate convergence in a number of iterations that scales approximately linearly with system size, while maintaining high-fidelity ground-state approximations and competitive energy estimates. Together, our empirical scaling laws and rigorous per-iteration guarantees establish SEGQE as a measurement-efficient state-preparation primitive well suited to early fault-tolerant quantum computing architectures.

This paper is about spherical maximal functions with general dilation sets acting on functions in weighted $L^p(|x|^α)$ spaces. Aside from endpoint cases, a complete description of the allowable ranges of $p$, $α$ is given in terms of the Legendre--Assouad function of the dilation set. This settles, up to endpoints, an open problem of Duoandikoetxea and Seijo.

We study an adiabatic variant of the variational quantum eigensolver (VQE) in which VQE is performed iteratively for a sequence of Hamiltonians along an adiabatic path. We derive the conditions under which gradient-based optimization successfully prepares the adiabatic ground states. These conditions show that the barren plateau problem and local optima can be avoided. Additionally, we propose using energy-standard-deviation measurements at runtime to certify eigenstate accuracy and verify convergence to the global optimum.

Driven by scientific and industry ambition, HPC and AI applications such as operational Numerical Weather Prediction (NWP) require processing and storing ever-increasing data volumes as fast as possible. Whilst POSIX distributed file systems and NVMe SSDs are currently a common HPC storage configuration providing I/O to applications, new storage solutions have proliferated or gained traction over the last decade with potential to address performance limitations POSIX file systems manifest at scale for certain I/O workloads. This work has primarily aimed to assess the suitability and performance of two object storage systems -namely DAOS and Ceph- for the ECMWF's operational NWP as well as for HPC and AI applications in general. New software-level adapters have been developed which enable the ECMWF's NWP to leverage these systems, and extensive I/O benchmarking has been conducted on a few computer systems, comparing the performance delivered by the evaluated object stores to that of equivalent Lustre file system deployments on the same hardware. Challenges of porting to object storage and its benefits with respect to the traditional POSIX I/O approach have been discussed and, where possible, domain-agnostic performance analysis has been conducted, leading to insight also of relevance to I/O practitioners and the broader HPC community. DAOS and Ceph have both demonstrated excellent performance, but DAOS stood out relative to Ceph and Lustre, providing superior scalability and flexibility for applications to perform I/O at scale as desired. This sets a promising outlook for DAOS and object storage, which might see greater adoption at HPC centres in the years to come, although not necessarily implying a shift away from POSIX-like I/O.

Regulatory limits on Maximum Permissible Exposure (MPE) require handheld devices to reduce transmit power when operated near the user's body. Current proximity sensors provide only binary detection, triggering conservative power back-off that degrades link quality. If the device could measure its distance from the body, transmit power could be adjusted proportionally, improving throughput while maintaining compliance. This paper develops a device-centric integrated sensing and communication (ISAC) method for the device to measure this distance. The uplink communication waveform is exploited for sensing, and the natural motion of the user's hand creates a virtual aperture that provides the angular resolution necessary for localization. Virtual aperture processing requires precise knowledge of the device trajectory, which in this scenario is opportunistic and unknown. One can exploit onboard inertial sensors to estimate the device trajectory; however, the inertial sensors accuracy is not sufficient. To address this, we develop an autofocus algorithm based on extended Kalman filtering that jointly tracks the trajectory and compensates residual errors using phase observations from strong scatterers. The Bayesian Cramér-Rao bound for localization is derived under correlated inertial errors. Numerical results at 28GHz demonstrate centimeter-level accuracy with realistic sensor parameters.

Stabilizer states hold a special place in quantum information science due to their connection with quantum error correction and quantum circuit simulation. In the context of classical simulations of many-body physics, they are an example of states that can be both highly entangled and efficiently represented and transformed under Clifford operators. Recently, Clifford operators have been discussed in the context of fermionic quantum computation through their extension, the Majorana Clifford group. Here, we document the phase-sensitive form of the corresponding Majorana stabilizer states, as well as the algorithms for computing their amplitudes, their inner products, and update rules for transforming Majorana stabilizer states under Majorana Clifford gates.

Cryo-electron microscopy (cryo-EM) has emerged as a powerful technique for resolving the three-dimensional structures of macromolecules. A key challenge in cryo-EM is characterizing continuous heterogeneity, where molecules adopt a continuum of conformational states. Covariance-based methods offer a principled approach to modeling structural variability. However, estimating the covariance matrix efficiently remains a challenging computational task. In this paper, we present SOLVAR (Stochastic Optimization for Low-rank Variability Analysis), which leverages a low-rank assumption on the covariance matrix to provide a tractable estimator for its principal components, despite the apparently prohibitive large size of the covariance matrix. Under this low-rank assumption, our estimator can be formulated as an optimization problem that can be solved quickly and accurately. Moreover, our framework enables refinement of the poses of the input particle images, a capability absent from most heterogeneity-analysis methods, and all covariance-based methods. Numerical experiments on both synthetic and experimental datasets demonstrate that the algorithm accurately captures dominant components of variability while maintaining computational efficiency. SOLVAR achieves state-of-the-art performance across multiple datasets in a recent heterogeneity benchmark. The code of the algorithm is freely available at https://github.com/RoeyYadgar/SOLVAR.

Spectroscopic measurements of single-particle spectral functions provide crucial insight into strongly correlated quantum matter by resolving the energy and spatial structure of elementary excitations. Here we introduce a spectroscopic protocol for single-charge injection with simultaneous spatial and energy resolution in a Rydberg tweezer array, effectively emulating scanning tunneling microscopy. By combining this protocol with single-atom-resolved imaging, we go beyond conventional spectroscopy by not only measuring the single-particle spectral function but also directly imaging the microscopic structure of the excitations underlying spectral resonances in frustrated $tJ$ Hamiltonians. We reveal resonances associated with the formation of bound magnetic polarons -- composite quasiparticles consisting of a mobile hole bound to a magnon -- and directly extract their binding energy, spatial extent, and spin character. Finally, by exploiting the spatial tunability of our platform, we measure the local density of states across different lattice geometries. Our work establishes Rydberg tweezer arrays as a powerful platform for spectroscopic studies of strongly correlated models, offering microscopic control and direct real-space access to emergent quasiparticles in engineered quantum matter.

New exotic particles with MeV masses, such as axion-like particles or light dark matter, can be emitted from core-collapse supernovae (SNe) with semi-relativistic velocities. Due to their speed dispersion, they would arrive at Earth as an extended packet with a time spread that can be as large as tens of millennia for typical detectors. It has been argued in the literature that the superposition of packets from all galactic SNe would give rise to a smooth and stationary diffuse flux that could be observable on terrestrial experiments. In this article, we critically examine this hypothesis by carrying out a numerical simulation of the galactic history of SN explosions. We show that, although the particle packets do overlap, due to the short observational time window, each of them only contributes with a very narrow range of energies and with an intensity that depends on the SN distance. As a consequence, the energy dependence of the resulting flux is extremely sensitive to the stochastic nature of the SN population and far from smooth. This has profound implications for the expected signature in terrestrial experiments, which displays a spectral shape that is not properly described by the smooth approximation. We develop a numerical tool to compute this stochastic galactic flux for generic semi-relativistic particles, which also allows us to explore sub-MeV particles, where the smooth diffuse flux approach does not hold. To test this framework, we revisit existing bounds on axion-like particles and fermionic dark matter, finding weaker constraints than previously reported.

Polymer electrolytes are critical for safe, high-energy-density solid-state batteries, yet discovering candidates that balance high ionic conductivity with high transference numbers remains a significant challenge. In this work, we develop a high-throughput screening platform that utilizes molecular dynamics simulations to navigate a chemical space of 1.7 million hypothetical polymer electrolyte candidates. Data from previous literature is used to warm-start batch Bayesian optimization for iteratively selecting new polymer electrolytes to evaluate. We iteratively identified, evaluated and analyzed 767 homopolymers as potential candidates. Our results reveal several candidates with transport properties exceeding the benchmark polyethylene oxide (PEO)/LiTFSI system. Crucially, our optimization campaigns for ionic conductivity and Li-diffusivity demonstrate that branched architectures and ketone functional groups significantly enhance ion-hopping mechanisms within the polymer matrix. We provide an in-depth mechanistic comparison of Li vs. Na cation transport and offer our open-source framework to accelerate the discovery of liquid, gel, and multi-cation electrolyte systems.

We investigate the azimuthal dependence of H I and O VI-bearing gas in the circumgalactic medium (CGM) of 113 isolated galaxies in the redshift range 0.12 < z < 0.75, including 91 new measurements from the MUSE Quasar-fields Blind Emitters Survey (MUSEQuBES). The H I covering fraction (k_HI) within the virial radius (Rvir) of low-mass (7 < log10(M*/Msun)< 9) galaxies, for a threshold column density of log10(N(HI)/cm^-2) = 14.5, exhibits an enhancement along both the disk plane (azimuthal angle phi < 20 degree) and in the polar direction (phi > 70 degree). In contrast, such a bimodal distribution is not observed for higher mass galaxies (9 < log10(M*/Msun) < 11.3). Similarly, the O VI covering fraction (k_OVI), for a threshold of log10(N(OVI)/cm^-2) = 14.0, shows a tentative enhancement along both the projected major and minor axes for low-mass galaxies. In contrast, O VI-bearing gas around higher- mass galaxies appears more uniformly distributed, with no significant azimuthal dependence. Finally, using the halo circular-velocity-normalized pixel-velocity two-point correlation function (TPCF), we find that O VI absorbers are kinematically narrower along the disk plane compared to the polar directions of the host galaxies with similar stellar mass distributions. The observed isotropic distribution of O VI in high-mass halos suggests that its spatial distribution is governed by global halo properties; however, the O VI kinematics retain memory of the site of origin.

The win ratio (WR) statistic is increasingly used to evaluate treatment effects based on prioritized composite endpoints, yet existing Bayesian adaptive designs are not directly applicable because the WR is a summary statistic derived from pairwise comparisons and does not correspond to a unique data-generating mechanism. We propose a Bayesian model-assisted adaptive design for randomized phase II clinical trials based on the WR statistic, referred to as the BMW design. The proposed design uses the joint asymptotic distribution of WR test statistics across interim and final analyses to compute posterior probabilities without specifying the underlying outcome distribution. The BMW design allows flexible interim monitoring with early stopping for futility or superiority and is extended to jointly evaluate efficacy and toxicity using a graphical testing procedure that controls the family-wise error rate (FWER). Simulation studies demonstrate that the BMW design maintains valid type I error and FWER control, achieves power comparable to conventional methods, and substantially reduces expected sample size. An R Shiny application is provided to facilitate practical implementation.

We present BMC4TimeSec, an end-to-end tool for verifying Timed Security Protocols (TSP) based on SMT-based bounded model checking and multi-agent modelling in the form of Timed Interpreted Systems (TIS) and Timed Interleaved Interpreted Systems (TIIS). In BMC4TimeSec, TSP executions implement the TIS/TIIS environment (join actions, interleaving, delays, lifetimes), and knowledge automata implement the agents (evolution of participant knowledge, including the intruder). The code is publicly available on \href{https://github.com/agazbrzezny/BMC4TimeSec}{GitHub}, as is a \href{https://youtu.be/aNybKz6HwdA}{video} demonstration.

The simple harmonic oscillator has a well-known normalizable, positive energy, bound state spectrum. We show that degenerate with each such positive energy eigenvalue there is a non-normalizable positive energy eigenstate whose eigenfunction is orthogonal to that of the standard energy eigenfunction. This class of states is not built on the vacuum that $a$ annihilates, but is instead built on the vacuum that $a^{\dagger} a$ annihilates. These non-normalizable but nonetheless stationary energy eigenstates are accompanied by yet another set of non-normalizable states, states whose wave functions however are not stationary but instead grow linearly in time. With these states not being energy eigenstates, the eigenbasis of the Hamiltonian is incomplete; with the full Hilbert space containing states that are not energy eigenstates. Thus each energy eigenvalue of the harmonic oscillator is an exceptional point at which the Hamiltonian becomes of non-diagonalizable, and thus manifestly non-Hermitian, Jordan-block form. Such non-Hermitian structures occur for Hamiltonians that have an antilinear $PT$ symmetry. As is characteristic of such systems, one can construct a probability conserving inner product that despite the linear in time growth is nonetheless time independent, and not only that, it leads to states with zero norm. In addition, as is again characteristic of $PT$ symmetry, these non-normalizable states can be made normalizable by a continuation into a so-called Stokes wedge domain in the complex plane. In this domain one has a completely consistent quantum theory, one that lives alongside the standard normalizable energy eigenspectrum sector. This thus not quite so simple harmonic oscillator provides an explicit realization of our general contention that antilinearity is more basic to quantum theory than Hermiticity.

Fixed points of the 2d renormalization group flow are known to correspond to tree level string vacua. We discuss how the renormalization group (or "sigma model") approach can be extended to the string loop level. The central role of the condition of renormalizability of the generating functional for string amplitudes with respect to both "local" and "modular" infinities is emphasized. Several one-loop and two-loop examples of renormalization are considered. It is found that in order to ensure the renormalizability of the generating functional one is to use an "extended" (Schottky-type) parametrization of the moduli space. An approach to resummation of the string perturbative expansion based on operators of insertion of topological fixtures is suggested.

Radially symmetric non-BPS 't Hooft-Polyakov monopoles and dyons are constructed as resurgent transseries: infinite sums of exponentially decaying terms, each multiplied by a factorially divergent fluctuation factor. All higher exponential terms are explicitly expressed in terms of the leading order solutions. In the BPS limit all fluctuation terms truncate.

Experimental particle physics seeks to understand the universe by probing its fundamental particles and forces and exploring how they govern the large-scale processes that shape cosmic evolution. This whitepaper presents a vision for how Artificial Intelligence (AI) can accelerate discovery in this field. We outline grand challenges that must be addressed to enable transformative breakthroughs and describe how current and planned experimental facilities can implement this vision to advance our understanding of the vast and complex physical world from the smallest to the largest scales. We show how facilities currently under construction, such as the HL-LHC, DUNE and soon EIC, can both benefit from and serve as proving grounds for this vision, while also enabling a longer-term goal for how future experiments -- like FCC-ee at CERN, IceCube-Gen2, a Muon Collider in the U.S., and smaller to mid-scale projects -- can be fully AI-native. We describe how a truly national-scale collaboration, jointly managed across large funding partners, and involving both DOE laboratories and universities, can make this happen.

To advance the understanding of microstructural evolution behavior in Mg-rare earth alloys, the effect of yttrium (Y) addition on static recrystallization and grain growth in Mg alloys was systematically investigated in extruded Mg-1wt.%Y and Mg-7wt.%Y alloys. Y addition was found to significantly retard the microstructural evolution, primarily due to its solute drag effect arising from Y segregation at grain boundaries. The relative intensity of solute drag effects from different alloying elements in Mg alloys was further assessed from both thermodynamic and kinetic perspectives, considering their grain boundary segregation tendencies and diffusivities. Additionally, static recrystallization in Mg-Y alloys was observed to proceed via a two-stage behavior characterized with two distinct JMAK exponents, indicating the heterogeneous nucleation of recrystallized grains. Abnormal grain growth (AGG) behavior was observed in these Mg-Y alloys. Overall, this study highlights the critical role of Y segregation at grain boundaries in controlling recrystallization and grain growth kinetics in Mg-Y alloys. This provides new insights into the design of thermally stable Mg alloys with refined microstructures.

Functional inequalities such as the Poincaré and log-Sobolev inequalities quantify convergence to equilibrium in continuous-time Markov chains by linking generator properties to variance and entropy decay. However, many applications, including multiscale and non-reversible dynamics, require analysing probability measures that are not at equilibrium, where the classical theory tied to steady states no longer applies. We introduce generalised versions of these inequalities for arbitrary positive measures on a finite state space, retaining key structural properties of their classical counterparts. In particular, we prove continuity of the associated constants with respect to the reference measure and establish explicit positive lower bounds. As an application, we derive quantitative coarse-graining error estimates for non-reversible Markov chains, both with and without explicit scale separation, and propose a quantitative criterion for assessing the quality of coarse-graining maps.