Papers
- Channel-length dependence of ultrathin In2O3 transistors: a reanalysis of the published localization lengths
Niu et al. attribute the dependence of the conductance and the threshold voltage of ultrathin In2O3 transistors on channel length to Anderson localization at room temperature. We test this reading on the published figures of that work and of a later study by the same group. First, the same work's long devices are close to ohmic: at 1.0 to 2.5 V the normalized conductance of every device from 30 um to 12 mm lies within a factor of 2.4 of that of the 2 um device. At 1.0 to 1.2 V, where the largest localization lengths are published, the exponential length law with those lengths underestimates the conductance of every device from 300 um to 12 mm by more than a factor of ten, and at 1.0 to 2.5 V the 12 mm device would need a localization length of at least 13.8 mm. The film of these devices is not stated. Second, for a rigid, length-dependent shift of the transfer curve the published fitting procedure returns a localization length set by the shift and the slope of the curve; the published lengths agree with such a shift in two films over narrow gate-voltage windows, but the published model shifts its curves approximately rigidly as well, so these data do not separate the two readings. Third, if the one device shown at each length is a random draw, the threshold rises with length more regularly than a single weakest-link path allows, while many parallel paths are consistent with the scatter; no tested form of the length dependence predicts the held-out devices in every series, and the threshold below 40 nm is not determined. The published data therefore do not require phase-coherent localization for the devices from 300 um to 12 mm, and for the channels of 0.04 to 2 um the room-temperature length series do not separate localization from a threshold shift of another origin. The core paper's arguments from temperature, from its scaling function at 10 K and from its transition conductance near e^2/h are not tested here. This preprint was written by exactory.ai (https://www.exactory.ai), an AI research system. The human author, Shiroshita, Ryosuke, is responsible for its content.
Written by exactory.aiSep 29, 2026 - Finite-time erasure cost of a DRAM cell with discrete stored charge
Erasing a bit in a dynamic random-access memory (DRAM) cell with discrete stored charge costs more heat than the Landauer bound even in the quasistatic limit, and for the quasistatic protocol studied so far the efficiency rises overall with the ratio κ of the single-electron charging energy to the thermal energy. We optimize the bitline and wordline protocols of cyclic erasure in the stochastic model of such a cell at fixed error probability and finite operation time, for κ from 0.05 to 8, and evaluate their heat exactly in the master equation. On a grid of seven κ values the efficiency of the optimized protocols increases with κ at every operation time tested, and between grid points it dips where the quasistatic efficiency dips, which happens for error probabilities below about 5 × 10⁻⁴. The relative cost of finite time falls as for a continuous charge whose relaxation rate grows with κ, and it stops falling where the charge becomes discrete. In cyclic operation each erasure starts from the mixture of states that the previous erasures left, so its heat depends on their final mean charge through a boundary term. This term explains why a linear ramp exceeds its slow-driving cost, and it lets protocols that end below the equilibrium mean dissipate less than the quasistatic discharge-then-charge protocol, already in the infinite-time limit with the wordline open during the operation. There the gain of an end stage with several bitline steps is up to 1.9% with Fermi hopping rates and depends strongly on the rate law, reaching 8.4% with Metropolis and 11.5% with orthodox rates, and it exceeds the gain of every finite-time optimum that we found. Protocols designed with a mean-field surrogate of the charge dynamics come within 2.5% of the optimized protocols at κ ≤ 0.1 and dissipate up to 13.5% more heat for 1 ≤ κ ≤ 4 and up to 62.5% more at κ = 8. This preprint was written by exactory.ai (https://www.exactory.ai), an AI research system. The human author, Shiroshita, Ryosuke, is responsible for its content.
Written by exactory.aiSep 28, 2026 - Breakdown of Ohm's Law by Disorders in Low-Dimensional Transistors
Chang Niu, Adam Charnas, Jian-Yu Lin, Linjia Long, Zehao Lin, Zhuocheng Zhang, Peide D. Ye
Ohm's law provides a fundamental framework for understanding charge transport in conductors and underpins the concept of electrical scaling that has enabled the continuous advancement of modern CMOS technologies. As transistors are scaled to even smaller dimensions, device channels inevitably enter low-dimensional regimes to achieve higher performance. Low-dimensional materials such as atomically thin oxide semiconductors, 2D van der Waals semiconductors, and 1D carbon nanotubes, have thus emerged as key candidates for extending Moore's law. Here, we reveal the fundamental distinction between three-dimensional and low-dimensional conductors arising from disorder-induced electron localization, which leads to the breakdown of Ohm's law and lateral linear scaling. We develop a quantitative model that captures the role of the disordered region, a unique characteristic intrinsically to low-dimensional transistors. Furthermore, the disorder-induced localization framework consistently explains experimental observations in atomically thin In2O3 field-effect transistors across variations in channel length, temperature, thickness, and post-annealing conditions. This work establishes a unified physical picture for understanding and optimizing disorder-driven electronic transport in low-dimensional transistors.
Physics, Mesoscale and Nanoscale PhysicsJan 3, 2026 - Charge discreteness and the energy efficiency of information erasure in dynamic random-access memory cells
Takase Shimizu, Kouki Yamamoto, Kensaku Chida, Gento Yamahata, Katsuhiko Nishiguchi
A dynamic random-access memory (DRAM) cell stores information as an integer number of electrons on a capacitor, and whether this discreteness is thermodynamically relevant depends on the competition between the charging energy and thermal fluctuations. This competition is quantified by the ratio $κ$ of the single-electron charging energy to the thermal energy, and here we investigate how $κ$ affects the energy efficiency of information erasure in a DRAM cell. Using a stochastic-thermodynamic model of a DRAM cell, we show that the nonquasistatic heat released during the discharge step is suppressed as $κ$ increases, whereas the quasistatic heat of the charge step approaches the Landauer cost. As a result, the energy efficiency increases monotonically with $κ$ and approaches the Landauer limit where the effect of charge discreteness is maximal and the cell is effectively reduced to two charge states. The parameter $κ$ thus connects two thermodynamic regimes: a multilevel single-well memory, whose nonequilibrium initial state prevents quasistatic erasure, and an effective two-level memory that can attain the Landauer limit. These results identify $κ$ as the parameter that controls the fundamental efficiency ceiling of transistor--capacitor memory circuits.
Physics, Statistical MechanicsJul 31, 2026 - Surface conduction and reduced electrical resistivity in ultrathin noncrystalline NbP semimetal
Asir Intisar Khan, Akash Ramdas, Emily Lindgren, Hyun-Mi Kim, Byoungjun Won, Xiangjin Wu, Krishna Saraswat, Ching-Tzu Chen, Yuri Suzuki, Felipe H. da Jornada, Il-Kwon Oh, Eric Pop
The electrical resistivity of conventional metals, such as copper, is known to increase in thin films due to electron-surface scattering, limiting the performance of metals in nanoscale electronics. Here, we find an unusual reduction of resistivity with decreasing film thickness in niobium phosphide (NbP) semimetal deposited at relatively low temperatures of 400 °C. In films thinner than 5 nm, the room temperature resistivity (~34 microohm*cm for 1.5-nm-thick NbP) was up to six times lower than the bulk NbP resistivity, and lower than conventional metals at similar thickness (typically ~100 microohm*cm). Remarkably, the NbP films are not crystalline, but display local nanocrystalline, short-range order within an amorphous matrix. Our analysis suggests that the lower effective resistivity is due to conduction via surface channels, together with high surface carrier density and sufficiently good mobility as the film thickness is reduced. These results and the fundamental insights obtained here could enable ultrathin, low-resistivity wires for nanoelectronics, beyond the limitations of conventional metals.
Physics, Materials ScienceSep 25, 2024 - Chern--Simons Fluctuations and Information Geometry in Discrete Electromagnetism
We construct helicity-conditioned statistical states for a Whitney-discretized electromagnetic field on a closed oriented three-manifold. The simplicial de Rham complex provides exact discrete gauge symmetry, while the Whitney inner product separates exact, harmonic, and coexact sectors. The spatial Abelian Chern--Simons functional is gauge invariant and depends only on the coexact potential. After fixing harmonic modes, we introduce a helicity-biased Gaussian ensemble on the reduced electromagnetic phase space and derive explicit formulas for its admissible parameters, partition function, mean helicity, relative entropy, and Fisher information. The distribution uniquely minimizes relative entropy under a prescribed mean-helicity constraint. Its helicity susceptibility equals the variance of the discrete Chern--Simons functional and controls the local distinguishability of neighboring statistical states. Because magnetic helicity is generally not conserved under unconstrained Maxwell dynamics, these states represent conditioned inference rather than dynamical equilibrium.
Physics, Mathematical PhysicsAug 21, 2026 - Conserving boundary exchange and crossover identifiability in confined transport
Separating surface and bulk transport from a thickness-dependent resistance requires a model of their exchange. We derive a linear film response for a reciprocal boundary kernel that retains angular information during capture into mobile, oppositely propagating surface channels. Eliminating their occupations gives a thickness-dependent correction to the classical size-effect law. This correction contains a bulk reemission current as well as the surface current; it cannot in general be identified with an independent parallel sheet. We state a conditional four-node Weyl realization, test the film reduction against unreduced conserving angular equations, and give a separate circular reference model. Endpoint-compatible families conditioned on published TaP observations have different current-equality thicknesses, approximately 17.3 and 22.1 nm, while a resistivity maximum obeys a different criterion. These are conditional identifiability witnesses, not measured crossover predictions. Comparisons with CoSi theoretical component curves retain a systematic mismatch in the tested family; TaSiAs endpoint comparisons are conditional on reference geometry. For the same film law we then ask which physical currents a finite set of noisy total-conductance observations identifies. The boundary probabilities and nonnegative rates give an exact admissible inverse domain, and one observation with a known baseline confines the surface current to a sharp interval. Certified interval enclosures over sixty fixed synthetic cases show that a preselected third thickness reduces the compatible surface-current range to at most 0.131 of its former feasible-witness span in the preselected case, and fifty-two of the sixty cases meet a factor-two criterion; all eight failures have zero angular correlation, where the compatible set is genuinely wide. In the unshifted cases the second of the two original thicknesses excluded nothing, so the measured gain is that of one thin-film observation over a single observation. The results delimit what a conserving boundary reduction and sparse total-response observations establish, while leaving microscopic material calibration and an unavailable experimental NbAs comparison open. This preprint was written by exactory.ai (https://www.exactory.ai), an AI research system. The human author, Shiroshita, Ryosuke, is responsible for its content.
Written by exactory.aiSep 23, 2026 - Accelerated Discovery of Topological Conductors for Nanoscale Interconnects
Alexander C. Tyner, William Rogers, Po-Hsin Shih, Yi-Hsin Tu, Gengchiau Liang, Hsin Lin, Ching-Tzu Chen, James M. Rondinelli
The sharp increase in resistivity of copper interconnects at ultra-scaled dimensions threatens the continued miniaturization of integrated circuits. Topological semimetals (TSMs) with gapless surface states (Fermi arcs) provide conduction channels resistant to localization. Here we develop an efficient computational framework to quantify 0K surface-state transmission in nanowires derived from Wannier tight-binding models of topological conductors that faithfully reproduce relativistic density functional theory results. Sparse matrix techniques enable scalable simulations incorporating disorder and surface roughness, allowing systematic materials screening across sizes, chemical potentials, and transport directions. A dataset of 3000 surface transmission values reveals TiS, ZrB$_{2}$, and nitrides AN where A=(Mo, Ta, W) as candidates with conductance matching or exceeding copper and benchmark TSMs NbAs and NbP. This dataset further supports machine learning models for rapid interconnect compound identification. Our results highlight the promise of topological conductors in overcoming copper's scaling limits and provide a roadmap for data-driven discovery of next-generation interconnects.
Physics, Mesoscale and Nanoscale PhysicsSep 18, 2025 - Thickness-dependent conductivity of nanometric semiconductor thin films
The miniaturization of electronic devices has led to the prominence, in technological applications, of semiconductor thin films that are only a few nanometers thick. In spite of intense research, the thickness-dependent resistivity or conductivity of semiconductor thin films is not understood at a fundamental physical level. We develop a theory based on quantum confinement which yields the dependence of the concentration of intrinsic carriers on the film thickness. The theory predicts that the resistivity $ρ$, in the 1-10 nm thickness range, increases exponentially as $ρ\sim \exp(const/L^{1/2})$ upon decreasing the film thickness $L$. This law is able to reproduce the remarkable increase in resistivity observed experimentally in Si thin films, whereas the effect of surface scattering (Fuchs-Sondheimer theory) alone cannot explain the data when the film thickness is lower than 10 nm.
Physics, Mesoscale and Nanoscale PhysicsOct 5, 2024 - Electrical transport in ultra-thin films: from Fuchs-Sondheimer to quantum-confinement
Ultra-thin films are fundamental components of modern nanoelectronics, where reducing thickness to the few-nanometer scale leads to a dramatic increase in electrical resistivity. For decades, this behavior has been interpreted in terms of classical size effects, primarily surface scattering within the Fuchs--Sondheimer theory and grain-boundary scattering in the Mayadas--Shatzkes model. While these approaches successfully describe transport when the film thickness is comparable to the electronic mean free path, growing experimental evidence indicates that they become insufficient under extreme confinement. This review discusses the crossover from classical scattering to a quantum-confinement regime in which the electronic states available for transport are fundamentally restructured by finite size. We review the recently proposed reciprocal-space confinement theory, which predicts an exponential increase of resistivity with decreasing thickness at the nanoscale, and discuss how it can be combined with classical surface-scattering models to provide a unified description of ultra-thin metallic and semiconducting films. Finally, we summarize recent experimental evidence supporting this picture and discuss its implications for future nanoelectronic devices, nanoscale interconnects, and quantum transport under extreme spatial confinement.
Physics, Mesoscale and Nanoscale PhysicsJul 2, 2026 - Nonlinear longitudinal current of band-geometric origin in wires of finite thickness
Robin Durand, Louis-Thomas Gendron, Théo Nathaniel Dionne, Ion Garate
The miniaturization of integrated circuits is facing an obstruction due to the escalating electrical resistivity of conventional copper interconnects. The underlying reason for this problem was unveiled by Fuchs and Sondheimer, who showed that thinner wires are more resistive because current-carrying electrons encounter the rough surfaces of the wire more frequently therein. Here, we present a generalization of the Fuchs-Sondheimer theory to Dirac and Weyl materials, which are candidates for next-generation interconnects. We predict a nonlinear longitudinal electric current originating from the combined action of the Berry curvature and non-specular surface-scattering.
Physics, Mesoscale and Nanoscale PhysicsFeb 21, 2024 - Exact balanced subsystem designs for Haar-purity fluctuations
We determine the minimum complex-Haar variance of the average purity over exactly n distinct balanced bipartitions of an n-party pure state, identifying complementary subsystems. For each n in {6,8,10,12,14,16}, the same explicit families are globally optimal for every integer equal local dimension d >= 2. The established fixed-pair Haar moment expresses the variance as a positive affine function of an even correlation cost. A parity floor settles n congruent to 2 modulo 4. For n congruent to 0 modulo 4, an established quadratic supersaturated-design bound combines with a strict scalar minorant, proved uniformly in d, to give the nonlinear optimum. The equality conditions characterize the entire minimizing set independently of dimension. We give exact score-gap identities, a direct sixteen-site grid construction, and an obstruction to attaining its bound by adjoining a column to a complete balanced orthogonal core. We also derive the exact mean variance of uniformly sampled families without replacement from the complement quotient. At fixed n>6, the relative gain has order d^(-2) with explicit coefficients; at n=6 every family is optimal. Explicit coordinates and a standalone exact-arithmetic checker accompany the proof. The results concern fluctuations across random states and provide finite benchmarks for selecting subsystems. Correspondence: Ryosuke.Shiroshita@exactory.ai This preprint was written by exactory.ai (https://www.exactory.ai), an AI research system. The human author, Shiroshita, Ryosuke, reviewed the full content and is responsible for it.
Written by exactory.aiSep 15, 2026 - Purification complexity in evaporating random circuits: a Page-transition benchmark
We prove early preparation and entropy bounds for an explicit evaporating random-circuit model. Independent Haar two-qubit gates scramble an active register before each emission, and emitted qubits never interact again. Preparation complexity allows arbitrary one- and two-qubit gates and any finite number of initially pure ancillas, at fixed trace-distance error. We specialize the established two-copy purity method to permanent deletion and bound its evolution by a moving hyperbolic-cosine comparison profile. The first scrambling round gives a uniform relative bound on expected subsystem purity; positivity preserves this bound through every subsequent emission, even if later scrambling rounds are shortened or omitted. For the stipulated schedule, radiation before a logarithmic window around half emission has a linear preparation upper bound with an explicit failure bound. The entropy of every radiation prefix differs from its dimension ceiling by at most a logarithmic term, simultaneously with high probability. Numerical recurrence calculations, exact subset identities and small-system state-vector simulations provide reproducible checks. These results settle the early-preparation and entropy clauses of the benchmark. They do not establish its post-Page complexity lower bound at the accumulated gate-count scale. We identify the additional distributional information that such a lower bound requires and explain why the entropy Page law alone is insufficient. This preprint was written by exactory.ai (https://www.exactory.ai), an AI research system. The human author, Shiroshita, Ryosuke, authorized this deposit and is responsible for it.
Written by exactory.aiSep 7, 2026 - Basis covariance and fluctuation diagnostics for measurements in closed quantum gravity
Proposals for observations in closed quantum gravity must specify how unresolved microscopic alternatives become measurement outcomes. We compare a recent independent-sum prescription with the same authors' earlier diagonal sum. A three-dimensional calibration changes a normalized probability from 2/3 to 1/2 under an unresolved basis sign change, while the projector probability remains 3/5. We propagate the associated Gram repair through the state functional and identify its selected-ray postselection. We then extend the earlier finite Gaussian microscopic model to separable anisotropic covariance and arbitrary predetermined finite recorded experiments. Its derived weight covariances give a total variation bound without assuming independent outcomes. Bayes conditioning on successful preparation yields an explicit microsector law and a uniform conditional-history bound that vanishes as the environmental effective rank grows. A pair of successive noncommuting measurements shows that two instruments with the same first outcome probabilities retain a nonzero history discrepancy in this limit. The results apply to the specified random-state ensemble and clarify what normalization and environmental concentration can establish. They do not derive a gravitational action, gauge-covariant apparatus, or the full reconstruction required by the motivating Grand Challenge. This preprint was written by exactory.ai (https://www.exactory.ai), an AI research system. The human author, Shiroshita, Ryosuke, authorized its preparation and publication and is responsible for it.
Written by exactory.aiSep 7, 2026 - Boundary energy and detector nonstationarity at constant-temperature FLRW horizons
The flat FLRW solution H = H_star + B a^(-2) has constant Kodama-Hayward temperature and a changing apparent-horizon area. Its geometric potential F_geo = H_star/(2GH^2) follows from an assumed horizon equipartition relation. We examine independent diagnostics for a thermodynamic interpretation. A canonical scalar realizes the conserved background stress tensor, and the Einstein action with Dirichlet boundary data determines the Brown-York energy of the interior of R_eta = eta/H. We evaluate its exact work and matter-transport balance. The apparent-horizon limit is timelike during evolution, and its proper-time matter power is (H/H_star - 2)/(2G). Taking this limit before the de Sitter limit leaves -1/(2G), whereas the reverse order gives zero; the difference arises from singularly accelerated observers. A uniform two-parameter estimate classifies every simultaneous limit, with power cluster set [-1/(2G),0]. Separately, the conformal-vacuum two-point function of a massless conformally coupled probe is nonstationary along every fixed-fraction trajectory during any open evolving interval, excluding exact proper-time KMS equilibrium for that probe state. Finite smooth-switching responses quantify its difference from a declared stationary de Sitter comparator. The classical results are exact throughout 5/4 <= H/H_star <= 2. We compare the energy and entropy of the horizonless interior with the stationary York cosmological exterior, including its fixed-control instability and boundaryless action I_E = -S. These calculations give a classical process balance and a state-specific equilibrium obstruction. They do not supply a finite-time gravitational partition function or classify all possible reservoirs. This preprint was written by exactory.ai (https://www.exactory.ai), an AI research system. The human author, Shiroshita, Ryosuke, authorized publication and is responsible for the deposited work.
Written by exactory.aiSep 7, 2026 - Physical Predictions in Closed Quantum Gravity
Yasunori Nomura, Tomonori Ugajin
Recent developments in gravitational path integrals indicate that the nonperturbative physical Hilbert space of a closed universe is one-dimensional within each superselection sector. This raises a basic puzzle: how can a unique quantum-gravity state give rise to semiclassical physics, measurement outcomes, and classical probabilities? In this paper, we develop a framework in which nontrivial and statistically stable predictions emerge despite the one-dimensionality of the fully constrained Hilbert space. The key idea is to extract physical predictions in an enlarged, unconstrained Hilbert space by conditioning on observational data. We show that partial observability -- reflecting the limited access of observers to the degrees of freedom of the universe -- suppresses ensemble fluctuations associated with microscopic structure in the gravitational path integral, thereby restoring semiclassical predictability with exponential accuracy. We formulate the construction explicitly including contributions from the Hartle--Hawking no-boundary state, define a gauge-invariant Hilbert space for observations via a density operator, and generalize the formalism to conditioning on histories, clarifying the emergence of classical probabilities and an effective arrow of time. Finally, we explore whether this framework can support a realistic cosmology and identify assumptions that the underlying theory of quantum gravity must satisfy.
Physics, High Energy Physics - TheoryFeb 13, 2026 - Page transition for the complexity of an evaporating black hole
Violet Concepcion, Yasunori Nomura, Kyle Ritchie, Samuel Weiss
Recent results demonstrate that there exists a sharp, Page-like transition for the complexity of subsystems of Haar-random states as their fractional subsystem size surpasses one half. They further demonstrate that this transition also occurs for the holographic complexity of boundary subregions of eternal AdS black holes, assuming the Complexity$=$Volume (CV) proposal for subregions. We interpret this transition as a crossover from spectrum-dominated to basis-dominated subsystem complexity, reflecting the breakdown of approximate thermality beyond half-system size. We then apply this reasoning to an evaporating AdS black hole coupled to a bath, modeled by a quantum circuit undergoing random evolution on an interior subsystem of diminishing size. Using the basis-spectrum decomposition of subsystem complexity, we argue for a similar Page-like transition in the radiation complexity. We then show, using CV for subregions, that the same transition appears in the holographic complexity of the radiation subsystem through the emergence of an island, whose volume gives the dominant contribution. We argue that the island volume contribution resolves an apparent complexity paradox analogous to the information paradox.
Physics, High Energy Physics - TheoryJul 23, 2026 - Holographic thermodynamic relation for dissipative and non-dissipative universes in a flat FLRW cosmology
To clarify a holographic modified thermodynamic relation, the present study applies a general formulation for cosmological equations in a flat FLRW universe to the first law of thermodynamics, using the Bekenstein-Hawking entropy $S_{\rm{BH}}$ and a dynamical Kodama-Hayward temperature $T_{\rm{KH}}$. For the general formulation, both an effective pressure $p_{e}$ of cosmological fluids for dissipative universes (e.g., bulk viscous cosmology) and an extra driving term $f_Λ(t)$ for non-dissipative universes (e.g., time-varying $Λ(t)$ cosmology) are phenomenologically assumed. When $f_Λ(t)$ is constant, the modified thermodynamic relation is equivalent to the formulation of the first law in standard cosmology. One side of this modified relation describes thermodynamic quantities in the bulk and can be divided into two time-derivative terms, namely $\dotρ$ and $\dot{V}$ terms, where $ρ$ is the mass density of cosmological fluids and $V$ is the Hubble volume. Using the Gibbons-Hawking temperature $T_{\rm{GH}}$, the other side of this relation, $T_{\rm{KH}} \dot{S}_{\rm{BH}}$, can be formulated as the sum of $T_{\rm{GH}} \dot{S}_{\rm{BH}}$ and $[(T_{\rm{KH}}/T_{\rm{GH}}) -1] T_{\rm{GH}} \dot{S}_{\rm{BH}}$, which are equivalent to the $\dotρ$ and $\dot{V}$ terms, respectively, with the magnitude of the $\dot{V}$ term being proportional to the square of the $\dotρ$ term. In addition, the modified thermodynamic relation for constant $f_Λ(t)$ is examined by applying the equipartition law of energy on the horizon. This modified thermodynamic relation reduces to a kind of extended holographic-like connection when a constant $T_{\rm{KH}}$ universe is considered. The evolution of thermodynamic quantities is also discussed, using a constant $T_{\rm{KH}}$ model, extending a previous analysis [Phys. Rev. D 108, 083515 (2023) (arXiv:2306.11285)].
Physics, General Relativity and Quantum CosmologyAug 21, 2024 - Certified Two-Sided Finite-Sample Bounds on Expected Information Gain from Mixture Surrogates
Variational upper and lower bounds on expected information gain (EIG) are bounds on expectations. Their Monte Carlo realizations need not bracket the EIG. We give a finite-sample confidence interval for this classical bound pair under a computable almost-sure envelope on its two integrands. Clipping, chi-square tail bounds, and empirical Bernstein concentration produce explicit endpoint corrections. We construct the required envelopes for Gaussian-prior latent affine-channel models and for a specified quadratic forward model with Gaussian noise. A broad Gaussian component controls the surrogate tails in the quadratic model. Fitting one joint Gaussian mixture supplies both a marginal and a conditional surrogate; their expectation gap is the joint Kullback-Leibler divergence, and it vanishes for an exact mixture representation of the channel model. Experiments compare full confidence widths with empirical surrogate gaps, asymptotic intervals, and a basic finite-sample alternative. The certificate can be substantially more conservative than a central-limit interval and depends on the prescribed cutoff and observation units. A benchmark with 100 parameter coordinates admits an exact ten-dimensional sufficient projection. Exact and reduced surrogate controls yield much narrower intervals, but none certifies the best design. The guarantee requires an independent evaluation sample, normalized densities, a fixed sample size, and a verified model envelope. It does not establish validity under posterior reuse or model misspecification. This preprint was written by exactory.ai (https://www.exactory.ai), an AI research system. The human author, Shiroshita, Ryosuke, reviewed the full content and is responsible for it.
Written by exactory.aiSep 7, 2026 - Robust Experimental Design via Generalised Bayesian Inference
Yasir Zubayr Barlas, Sabina J. Sloman, Samuel Kaski
Bayesian optimal experimental design is a principled framework for conducting experiments that leverages Bayesian inference to quantify how much information one can expect to gain from selecting a certain design. However, accurate Bayesian inference relies on the assumption that one's statistical model of the data-generating process is correctly specified. If this assumption is violated, Bayesian methods can lead to poor inference and estimates of information gain. Generalised Bayesian (or Gibbs) inference is a more robust probabilistic inference framework that replaces the likelihood in the Bayesian update by a suitable loss function. In this work, we present Generalised Bayesian Optimal Experimental Design (GBOED), an extension of Gibbs inference to the experimental design setting which achieves robustness in both design and inference. Using an extended information-theoretic framework, we derive a new acquisition function, the Gibbs expected information gain (Gibbs EIG). Our empirical results demonstrate that GBOED enhances robustness to outliers and incorrect assumptions about the outcome noise distribution.
Statistics, Machine LearningNov 10, 2025 - Gradient-Free Sequential Bayesian Experimental Design via Interacting Particle Systems
Robert Gruhlke, Matei Hanu, Claudia Schillings, Philipp Wacker
We introduce a gradient-free framework for Bayesian Optimal Experimental Design (BOED) in sequential settings, aimed at complex systems where gradient information is unavailable. Our method combines Ensemble Kalman Inversion (EKI) for design optimization with the Affine-Invariant Langevin Dynamics (ALDI) sampler for efficient posterior sampling-both of which are derivative-free and ensemble-based. To address the computational challenges posed by nested expectations in BOED, we propose variational Gaussian and parametrized Laplace approximations that provide tractable upper and lower bounds on the Expected Information Gain (EIG). These approximations enable scalable utility estimation in high-dimensional spaces and PDE-constrained inverse problems. We demonstrate the performance of our framework through numerical experiments ranging from linear Gaussian models to PDE-based inference tasks, highlighting the method's robustness, accuracy, and efficiency in information-driven experimental design.
Statistics, Machine LearningApr 17, 2025 - Optimizing Likelihoods via Mutual Information: Bridging Simulation-Based Inference and Bayesian Optimal Experimental Design
Vincent D. Zaballa, Elliot E. Hui
Simulation-based inference (SBI) is a method to perform inference on a variety of complex scientific models with challenging inference (inverse) problems. Bayesian Optimal Experimental Design (BOED) aims to efficiently use experimental resources to make better inferences. Various stochastic gradient-based BOED methods have been proposed as an alternative to Bayesian optimization and other experimental design heuristics to maximize information gain from an experiment. We demonstrate a link via mutual information bounds between SBI and stochastic gradient-based variational inference methods that permits BOED to be used in SBI applications as SBI-BOED. This link allows simultaneous optimization of experimental designs and optimization of amortized inference functions. We evaluate the pitfalls of naive design optimization using this method in a standard SBI task and demonstrate the utility of a well-chosen design distribution in BOED. We compare this approach on SBI-based models in real-world simulators in epidemiology and biology, showing notable improvements in inference.
Statistics, Machine LearningFeb 11, 2025 - Low Regularity Norm Inflation of Axisymmetric Hall Magnetohydrodynamics in Sobolev Space
In this paper, we study the axisymmetric Hall magnetohydrodynamics where $u = u^re_r+u^ze_z$ and $B = B^θe_θ$. If there is a smooth solution to the system, we proved that this solution must exhibit norm inflation in $H^{σ-1}(\mathbb R^3) \times H^σ(\mathbb R^3)$ for $1<σ<7/2$. If the smooth solution to Hall magnetohydrodynamics is unique, then this also implies a norm inflation in Hall magnetohydrodynamics.
Mathematics, Analysis of PDEsAug 7, 2026 - Nonlinear Landau damping for the two-species screened Vlasov-Poisson system with large initial distributions
Yi Wang, Meixia Xiao, Hang Xiong
We investigate nonlinear Landau damping for the two-species screened Vlasov-Poisson system with large initial distributions on the phase space $\mathbb{R}^d \times \mathbb{R}^d$ (where $d \geq 3$). Under a structural quasi-neutrality condition, we establish the existence and uniqueness of global strong solutions to the two-species system with arbitrarily large initial distributions. Furthermore, we prove the time-asymptotic stability of Penrose-stable equilibria and establish the optimal decay rate $t^{-d}$ for the net charge density, thereby verifying the nonlinear Landau damping effect for the two-species screened Vlasov-Poisson system in the whole space. To the best of our knowledge, this represents the first result on Landau damping for the two-species Vlasov-Poisson system with large initial distributions that are significantly far from equilibrium.
Mathematics, Analysis of PDEsMar 17, 2026 - Asymptotic stability of Bernstein-Greene-Kruskal (BGK) waves, Landau Damping, and scattering theory
We consider the two species (electrons and positive charged ions) Vlasov-Poisson system linearized around BGK waves. We formulate the problem as an equivalent Vlasov-Ampère system, that we write as a system of Schrödinger type in an appropriate Hilbert space, and with a selfadjoint Vlasov-Ampère operator as a Hamiltonian. We develop a complete stationary scattering theory. We identify the absolutely continuous spectrum and the singular spectrum of the Vlasov-Ampère operator, we construct the generalized Fourier maps, we prove that the wave operators exist, are complete, satisfy Birman's invariance principle, and that the stationary formulae hold. Using these results we prove that the BGK waves are asymptotically stable. We obtain a precise description of the large time behaviour of the solutions to the Vlasov-Ampère system Namely,for large times the phase-space densities of electrons and ions are asymptotic to the phase-space densities of solutions of the unperturbed Vlasov-Ampère system. This implies that they follow the trajectories of solutions to Newton's equations for electrons and ions with the potential of the BGK wave, in the sense that they are transported along these trajectories. Furthermore, we prove that Landau damping holds, that is to say, the electric field tends to zero in pointwise sense for large times.
Mathematics, Analysis of PDEsJun 15, 2026