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DOE OSTI2024

How to Partition a Quantum Observable

We present a partition of quantum observables in an open quantum system that is inherited from the division of the underlying Hilbert space or configuration space. It is shown that this partition leads to the definition of an inhomogeneous continuity equation for generic, non-local observables. This formalism is employed to describe the local evolution of the von Neumann entropy of a system of independent quantum particles out of equilibrium. Crucially, we find that all local fluctuations in the entropy are governed by an entropy current operator, implying that the production of entanglement entropy is not measured by this partitioned entropy. For systems linearly perturbed from equilibrium, it is shown that this entropy current is equivalent to a heat current, provided that the system-reservoir coupling is partitioned symmetrically. Finally, we show that any other partition of the coupling leads directly to a divergence of the von Neumann entropy. Thus, we conclude that Hilbert-space partitioning is the only partition of the von Neumann entropy that is consistent with the laws of thermodynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

A general flame aerosol route to high-entropy nanoceramics

High-entropy ceramics are an emerging class of materials with fascinating characteristics. However, elemental immiscibility and crystal complexity limit the development of a general synthesis strategy, and common methods yield bulk materials. Here, we introduce a transformative non-equilibrium flame aerosol technique for synthesizing high-entropy nanoceramics. This scalable, one-step process enables the production of high-entropy oxide nanoceramics with an unprecedented diversity of crystal structures, including fluorite-phase materials that integrate up to 22 distinct cation elements. The method’s capacity for entropic stabilization and grain refinement significantly improves the thermal stability of these nanostructures. In a representative application, a Pt-(MgCoNiCuZn)O high-entropy single-atom catalyst showed superior activity and long-term stability, maintaining constant CO 2 conversion over 670 h and dramatically outperforming conventional catalysts. Finally, the general approach opens a vast composition and structure space for the creation of high-entropy oxide nanomaterials for application across diverse fields, including catalysis, energy storage, sensing, and thermal management.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Multisite Proton–Coupled Electron Transfer at a Keggin-Type Polyoxotungstate

Proton−coupled electron transfer (PCET) governs many redox transformations, but is thermodynamically constrained when proton and electron transfer occur at a single site. Here, we introduce a new multisite PCET (MSPCET) platform, based on the Keggin-type polyoxotungstate, [VW 12 O 40 ] 3− (VW 12 ). Pairing VW 12 with either Brønsted bases or acids yields reagent pairs with tunable effective bond dissociation free energies (BDFE eff ) over 15 kcal mol −1 , enabling both oxidative and reductive H atom transfer reactions. Kinetic studies on the oxidative pathway by using 2,4,6- t Bu 3 PhOH as a model hydrogen atom (H atom) donor reveal a product-like, entropy-dominated concerted proton−electron transfer (CPET) pathway from a preorganized hydrogen-bonded complex. By contrast, reductive H atom transfer reactions exhibit larger ΔH ‡ values, measurable kinetic isotope effects, and balanced Brønsted slope, consistent with synchronous CPET-type mechanism. Extension to N−H, O−H, and C−H substrates demonstrates the versatility of the VW 12 MS-PCET platform for tunable (de)hydrogenation.

Charge transfer↗

DOE OSTI2025

The Path towards Plasma Facing Components: A Review of State-of-the-art in W-Based Refractory High-Entropy Alloys

Developing advanced materials for plasma-facing components (PFCs) in fusion reactors is a crucial aspect for achieving sustained energy production. Tungsten (W) - based refractory high-entropy alloys (RHEAs) have emerged as promising candidates due to their superior radiation tolerance and high-temperature strength. This review paper will focus on recent advancements in W-based RHEA research, particularly emphasizing the key role of modelling using machine learning (ML) in the stage of discovery by predicting properties for each composition and expediting the identification of optimal RHEA compositions with desired properties. Additionally, the application of additive manufacturing (AM) techniques for fabricating W-based RHEAs is explored, highlighting their advantages for rapid prototyping and multi-compositional sample production in a high throughput manner. The review critically evaluates the current understanding of mechanical properties relevant to PFC applications, including high-temperature strength and ductility. Furthermore, the radiation tolerance of W-based RHEAs under irradiated conditions is discussed. Finally, the validity of current AM-manufactured W-based RHEAs as PFC materials is assessed, and key challenges and opportunities for future research are identified. This review aims to provide a comprehensive overview of W-based RHEAs for fusion applications and their potential to guide the development and validation of advanced refractory high entropy alloys.

Hatler, Caleb [University of Wisconsin-Madison]↗

DOE OSTI2026

Characterization of High-Entropy Alloys for Accelerator Beam Window Applications

Particle production targets and accelerator beam windows receive millions of high-energy/intensity beam pulses throughout their service lifetime. For next-generation multi-MW accelerators, it is necessary for beam windows to be able to withstand higher levels of thermal shock and radiation damage, while also having good high-temperature mechanical properties. Novel High-Entropy Alloys (HEAs) that form a single-phase microstructure, have nanoscale precipitates, and are made from low-Z elements are good candidates for beam window materials. This is due to their high-temperature strength and high resistance to radiation-induced swelling and hardening, as well as their beam transparency, allowing for maximized particle production and a longer service lifetime.

Kidwell, Tristan [U. Chicago (main)] (ORCID:000900↗

DOE OSTI2024

QCD evolution of entanglement entropy

Entanglement entropy has emerged as a novel tool for probing nonperturbative quantum chromodynamics (QCD) phenomena, such as color confinement in protons. While recent studies have demonstrated its significant capability in describing hadron production in deep inelastic scatterings, the QCD evolution of entanglement entropy remains unexplored. Here, in this work, we investigate the differential rapidity-dependent entanglement entropy within the proton and its connection to final-state hadrons, aiming to elucidate its QCD evolution. Our analysis reveals a strong agreement between the rapidity dependence of von Neumann entropy, obtained from QCD evolution equations, and the corresponding experimental data on hadron entropy. These findings provide compelling evidence for the emergence of a maximally entangled state, offering new insights into the nonperturbative structure of protons.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Particle Creation from Entanglement Entropy

We investigate how entanglement entropy can drive particle creation, deriving explicit relations between entropy and the radiated particle spectrum, the total number of particles, and the total energy. Particle production is computed for scenarios that include accelerated motion, black hole evaporation, and beta decay, validating against known results while also extending them. We focus primarily on the low-entropy limit (analogous to nonrelativistic motion), but also examine cases of significant particle production arising from harmonic cycles. The results establish an explicit operational link between information flow and matter creation, providing a concrete demonstration of “it from bit”.

Good, Michael R. R. [Nazarbayev University, Astana↗

DOE OSTI2025

Entanglement as a Probe of Hadronization

Recently, it was discovered that the proton structure at high energies exhibits maximal entanglement. This leads to a simple relation between the proton’s parton distributions and the entropy of hadrons produced in high-energy inelastic interactions, which has been experimentally confirmed. In this Letter, we extend this approach to the production of jets. Here, the maximal entanglement predicts a relation between the jet fragmentation function and the entropy of hadrons produced in jet fragmentation. We test this relation using the ATLAS Collaboration data on jet production at the Large Hadron Collider, and find a good agreement between the prediction based on maximal entanglement within the jet and the data. This study represents the first use of a quantum entanglement framework in an experimental study of the hadronization process, offering a new perspective on the transition from perturbative to nonperturbative QCD. Our results open the door to a more comprehensive understanding of the quantum nature of hadronization.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Toward Efficient Entropic Recycling by Mastering Ring–Chain Kinetics

Traditional chemical recycling approaches for condensation polymers suffer compounding energy losses and CO 2 emissions across multiple polymerization and depolymerization cycles. Entropic recycling can address these energy losses by entrapping free energy within the deconstruction products. Entropic recycling involves depolymerization to macrocyclic monomers, but such processes have not been feasible due to the high dilutions typically required to generate macrocyclic compounds. Here, we leverage selective catalysis to allow entropic recycling at concentrations 20–2000× higher than typical for macrocyclization reactions. We find that Ru-based olefin metathesis catalysts containing bulky iodine ligands significantly bias the ring–chain kinetic product distribution during ring-closing metathesis (RCM) toward the formation of oligomeric cycloalkenes. Further improvements in reaction concentration and macrocycle yield are obtained by using high catalyst loadings and by predisposing the alkene substrates to undergo favorable macrocyclization. These RCM optimizations translate effectively to cyclodepolymerization (CDP) of an olefin-containing polymer, with RCM and CDP affording similar macrocycle product distributions under identical reaction conditions. Macrocycle polymerization by entropy-driven ring-opening metathesis provides much higher molecular weight polymers than condensation polymerization of linear analogues, reducing the time to achieve high molecular weight from hours to minutes and enabling polymerization at room temperature. Finally, our findings re-emphasize the importance of energy consumption during a polymer’s lifecycle and provide a framework for the design of efficient entropic recycling systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Preparation and Photocatalytic Hydrogen Production of TiO 2 /(AlMnCoNiZn) 3 O 4 Nanocomposites

Photocatalytic water splitting is a promising strategy for addressing the global energy crisis and environmental pollution. In this study, spinel-type high-entropy oxide (HEO) nanoparticles, (AlMnCoNiZn) 3 O 4 , were successfully synthesized via a solution combustion method. TiO 2 /(AlMnCoNiZn) 3 O 4 nanocomposites with varying molar ratios were subsequently fabricated through solid-state sintering, and their photocatalytic water-splitting performance was systematically investigated. The hydrogen production rate initially increased and then decreased with increasing TiO 2 content. The optimal nanocomposite achieved a hydrogen evolution rate of 1450 μmol·h −1 ·g −1 under simulated sunlight irradiation, which is 2.2 times higher than that of pure TiO 2 nanoparticles. In addition, the TiO 2 /(AlMnCoNiZn) 3 O 4 nanocomposites exhibited significantly improved photocorrosion resistance compared with TiO 2 nanoparticles. After 12 h irradiation under a 500-W high-pressure mercury lamp, the hydrogen production rates of the nanocomposites and pure TiO 2 retained 79.3% and 5.47% of their initial values, respectively. These results demonstrate the important role of (AlMnCoNiZn) 3 O 4 and other HEOs in enhancing the photocatalytic performance of nanoheterojunction catalysts. Lastly, this work broadens the potential applications of (AlMnCoNiZn) 3 O 4 and related HEO materials in the field of photocatalysis.

Heterojunction↗

DOE OSTI2025

The algebraic structure of gravitational scrambling

We introduce a new algebraic framework to describe gravitational scrambling, including the semiclassical limit of any out-of-time-order correlation function that is built out of operator insertions separated by approximately the scrambling time. In two dimensions, the scrambling algebra, which we call a modular-twisted product, is defined in terms of two copies of the Leutheusser-Liu half-sided modular inclusion of von Neumann algebras; these describe early- and late-time operators respectively. In limits where the separation between insertions is taken to be either significantly greater or smaller than the scrambling time, the modular-twisted product reduces, respectively, to free- and tensor-product algebras that were previously studied in [arXiv:2209.10454]. In a sense, the modular-twisted product interpolates between these two products. Including the Hamiltonian in the scrambling algebra leads to a Type II$_\infty$ von Neumann algebra with finite renormalized entropies that interpolate between single-QES and multi-QES phases. We also describe how to generalize the modular-twisted product algebra to higher dimensions, including spatially localized boundary excitations.

FOS: Physical sciences↗

DOE OSTI2024

General synthesis of high-entropy single-atom nanocages for electrosynthesis of ammonia from nitrate

Given the growing emphasis on energy efficiency, environmental sustainability, and agricultural demand, there’s a pressing need for decentralized and scalable ammonia production. Converting nitrate ions electrochemically, which are commonly found in industrial wastewater and polluted groundwater, into ammonia offers a viable approach for both wastewater treatment and ammonia production yet limited by low producibility and scalability. Here we report a versatile and scalable solution-phase synthesis of high-entropy single-atom nanocages (HESA NCs) in which Fe and other five metals-Co, Cu, Zn, Cd, and In-are isolated via cyano-bridges and coordinated with C and N, respectively. Incorporating and isolating the five metals into the matrix of Fe resulted in Fe-C5 active sites with a minimized symmetry of lattice as well as facilitated water dissociation and thus hydrogenation process. As a result, the Fe-HESA NCs exhibited a high selectivity toward NH3 from the electrocatalytic reduction of nitrate with a Faradaic efficiency of 93.4% while maintaining a high yield rate of 81.4 m h -1 mg -1 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Selective depolymerization of polyolefin copolymer via high-entropy alloy catalyzed pyrolysis in a double-layered ultrafast heating reactor

Chemical recycling of polyolefin copolymers (PCPs) is essential for mitigating plastic pollution, yet achieving selective depolymerization into C 2 –C 3 monomers at high productivity remains challenging. Here, we introduce a double-layered ultrafast heating reactor (DUHR) that integrates Joule heating with a high-entropy alloy (HEA) catalyst composed of near-equimolar Co, Cu, Fe, Mn, and Ni. We achieve highly selective depolymerization of PCP into ethylene and propylene, yielding a 70% non-condensable fraction. Significant aromatic fractions form via radical-driven pathways—a behavior distinct from conventional externally heated pyrolyzers—highlighting DUHR's ability to generate reactive species and modulate reaction pathways. Furthermore, these findings demonstrate an effective strategy for chemical recycling of real-world plastic waste for polyolefin circularity and sustainable resource recovery.

Chemical recycling↗

DOE OSTI2024

High-Power Targetry R&D for Next-Generation Accelerator Target Facilities

Beam-intercepting devices such as beam windows and particle-production targets are critical components of accelerator target facilities for High Energy Physics (HEP) experiments. The high-power, pulsed structure of the particle beams used for these experiments leads to thermal shock and high-cycle fatigue in addition to radiation damage resulting from the accumulated particle fluence. This can lead to degradation of the target system s mechanical and thermal properties; considerably reducing their lifetimes and presenting substantial challenges to reliable operation of multi-MW class facilities. Recently several major accelerator facilities have been forced to operate at reduced power levels due to target survivability concerns. Furthermore, at Fermilab it is planned to increase the neutrino production beam power up to 2.4 MW in coming years. Therefore, timely R&D on the irradiated behavior of target system materials is critical to efficient operation of accelerator facilities and full utilization of recent accelerator power upgrades for HEP research. This talk will begin with an overview of high-power targetry, and the significant challenges presented by beam power increases expected for future HEP experiments. We will then cover several past materials irradiation studies that have been completed by the High-Power Targetry R&D group at Fermilab and its collaborators on common accelerator and target materials such as graphite, beryllium, titanium, and tungsten. Finally, we will conclude with a discussion of two novel materials investigations under way within the group; high-entropy alloys for beam window applications, and electrospun nanofibers to serve as particle production targets.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Quantum magic and computational complexity in the neutrino sector

We consider the quantum magic in systems of dense neutrinos undergoing coherent flavor transformations, relevant for supernova and neutron-star binary mergers. Mapping the three-flavor-neutrino system to qutrits, the evolution of quantum magic is explored in the single scattering angle limit for a selection of initial tensor-product pure states for 𝑁 𝜈 ≤ 8 neutrinos. For |𝜈𝑒⟩ ⊗𝑁𝜈 initial states, the magic, as measured by the 𝛼 = 2 stabilizer Renyi entropy ℳ 2 , is found to decrease with radial distance from the neutrino sphere, reaching a value that lies below the maximum for tensor-product qutrit states. Further, the asymptotic magic per neutrino, ℳ 2 /𝑁 𝜈 , decreases with increasing 𝑁 𝜈 . In contrast, the magic evolving from states containing all three flavors reaches values only possible with entanglement, with the asymptotic ℳ 2 /𝑁 𝜈 increasing with 𝑁 𝜈 . These results highlight the connection between the complexity in simulating quantum physical systems and the parameters of the Standard Model.

computational complexity↗

DOE OSTI2024

Efficient simulation of low-temperature physics in one-dimensional gapless systems

Here, we discuss the computational efficiency of the finite-temperature simulation with minimally entangled typical thermal states (METTS). To argue that METTS can be efficiently represented as matrix product states, we present an analytic upper bound for the average entanglement Rényi entropy of METTS for a Rényi index 0 < q ≤ 1. In particular, for one-dimensional (1D) gapless systems described by conformal field theories, the upper bound scales as O⁡(cN 0 ⁢log⁡β) where c is the central charge and N is the system size. Furthermore, we numerically find that the average Rényi entropy exhibits a universal behavior characterized by the central charge and is roughly given by half of the analytic upper bound. Based on these results, we show that METTS can provide a speedup compared to employing the purification method to analyze thermal equilibrium states at low temperatures in 1D gapless systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

A Quantum Computational Determination of the Weak Mixing Angle in the Standard Model

The weak mixing angle $s_W$ is a fundamental constant in the Standard Model (SM) and measured at the $Z$ boson mass to be $\widehat{s}^2_W(m_Z) = 0.23129 \pm 0.00004$ in the $\overline{\rm MS}$ renormalization scheme, where $m_Z=91.2\ \text{GeV}$. On the other hand, non-stabilizerness - the magic - characterizes the computational advantage of a quantum system over classical computers. We consider the production of magic from stabilizer initial states, which carry zero magic, in the 2-to-2 scattering of charged leptons in the SM at the tree level, which is mediated by the photon and the $Z$ boson. Using the second order stabilizer Rényi entropy, and averaging over all 60 initial stabilizer states and the scattering angle, we compute and minimize the magic production as a function of $s^2_W$ in the Møller scattering $e^-e^-\to e^-e^-$, which is free of kinematic thresholds. At the centre-of-mass energy $\sqrt{s}=m_Z$, there is a unique minimum in magic production at $\mathbf{s}^{2}_W(m_Z)=0.2317$, which agrees with the measured $\widehat{s}^2_W(m_Z)$ at the sub-percent level. At higher energies, the magic-minimizing $\mathbf{s}^{2}_W$ continues to agree with the empirical value at the percent level or better, up to 10 TeV. The finding suggests the electroweak sector of the SM tends to generate minimal quantum resources from the computational viewpoint.

Liu, Qiaofeng [Northwestern U.]↗

DOE OSTI2025

A Quantum Computational Determination of the Weak Mixing Angle in the Standard Model

Liu, Qiaofeng [Northwestern U.]↗