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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models

While projection-based reduced order models can reduce the dimension of full order solutions, the resulting reduced models may still contain terms that scale with the full order dimension. Hyper-reduction techniques are sampling-based methods that further reduce this computational complexity by approximating such terms with a much smaller dimension. The goal of this work is to introduce the points selection algorithm developed by Shin and Xiu as a hyper-reduction method. The selection algorithm was originally proposed as a stochastic collocation method for uncertainty quantification. Since the algorithm aims at maximizing a quantity $\mathcal{S}$ that measures both the column orthogonality and the determinant, we refer to the algorithm as S-OPT. Numerical examples are provided to demonstrate the performance of S-OPT and to compare its performance with a gappy proper orthogonal decomposition (POD) algorithm. Here, we found that using the S-OPT algorithm is shown to predict the full order solutions with higher accuracy than gappy POD especially when the number of sampling points is small, although we note that S-OPT shows slow asymptotic convergence with respect to the number of samples for some applications, e.g., Lagrangian hydrodynamics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A novel framework for increasing research transparency: Exploring the connection between diversity and innovation

A split sample/dual method research protocol is demonstrated to increase transparency while reducing the probability of false discovery. We apply the protocol to examine whether diversity in ownership teams increases or decreases the likelihood of a firm reporting a novel innovation using data from the 2018 United States Census Bureau’s Annual Business Survey. Transparency is increased in three ways: 1) all specification testing and identifying potentially productive models is done in an exploratory subsample that 2) preserves the validity of hypothesis test statistics fromde novoestimation in the holdout confirmatory sample with 3) all findings publicly documented in an earlier registered report and in this journal publication. Bayesian estimation procedures that leverage information from the exploratory stage included in the confirmatory stage estimation replace traditional frequentist null hypothesis significance testing. In addition to increasing statistical power by using information from the full sample, Bayesian methods directly estimate a probability distribution for the magnitude of an effect, allowing much richer inference. Estimated magnitudes of diversity along academic discipline, race, ethnicity, and foreign-born status dimensions are positively associated with innovation. A maximally diverse ownership team on these dimensions would be roughly six times more likely to report new-to-market innovation than a homophilic team.

Science & Technology - Other Topics↗
DOE OSTI2025

Accelerating Hamiltonian Monte Carlo for Bayesian inference in neural networks and neural operators

Hamiltonian Monte Carlo (HMC) is a powerful and accurate method to sample from the posterior distribution in Bayesian inference. However, HMC techniques are computationally demanding for Bayesian neural networks due to the high dimensionality of the network’s parameter space and the non-convexity of their posterior distributions. Therefore, various approximation techniques, such as variational inference (VI) or stochastic gradient MCMC, are often employed to infer the posterior distribution of the network parameters. Such approximations introduce inaccuracies in the inferred distributions, resulting in unreliable uncertainty estimates. In this work, we propose a hybrid approach that combines inexpensive VI and accurate HMC methods to efficiently and accurately quantify uncertainties in neural networks and neural operators. The proposed approach leverages an initial VI training on the full network. We examine the influence of individual parameters on the prediction uncertainty, which shows that a large proportion of the parameters do not contribute substantially to uncertainty in the network predictions. This information is then used to significantly reduce the dimension of the parameter space, and HMC is performed only for the subset of network parameters that strongly influence prediction uncertainties. This yields a framework for accelerating the full batch HMC for posterior inference in neural networks. We demonstrate the efficiency and accuracy of the proposed framework on deep neural networks and operator networks, showing that inference can be performed for large networks with tens to hundreds of thousands of parameters. Finally, we show that this method can effectively learn surrogates for complex physical systems by modeling the operator that maps from upstream conditions to wall-pressure data on a cone in hypersonic flow.

Bayesian inference↗
DOE OSTI2022

Langevin dynamics of generalized spins as SU( N ) coherent states

Classical models of spin systems traditionally retain only the dipole moments, but a quantum spin state will frequently have additional structure. Spins of magnitude S have N = 2⁢S + 1 levels. Alternatively, the spin state is fully characterized by a set of N 2 - 1 local physical observables, which we interpret as generalized spin components. For example, a spin with S = 1 has three dipole components and five quadrupole components. Further, these components evolve under a generalization of the classical Landau-Lifshitz dynamics, which can be extended with noise and damping terms. In this paper, we reformulate the dynamical equations of motion as a Langevin dynamics of SU(N) coherent states in the Schrödinger picture. This viewpoint is especially useful as the basis for an efficient numerical method to sample spin configurations in thermal equilibrium and to simulate the relaxation and driven motion of topological solitons. To illustrate the approach, we simulate a nonequilibrium relaxation process that creates CP 2 skyrmions, which are topological defects with both dipole and quadrupole character.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

IACMI Project 4.2: Thermoplastic Composite Development for Wind Turbine Blades

(Section 5.1) Composites made from Arkema’s Elium® thermoplastic resin and Johns Manville fiberglass were researched during this project for applications in wind blade manufacturing. A techno-economic model was developed to model this wind blade manufacturing process using these materials in place of traditional composites made with thermoset resin. This model was based on manufacturing a 61.5-meter wind blade, which showed a 4.7% reduction in wind blade cost as compared traditional thermoset materials. These cost savings were not from the thermoplastic material costing less than traditional thermoset materials, but rather from decreased capital costs, faster cycle times and reduced energy requirements and labor costs. (Section 5.2) An infusion and curing model was developed for thermoplastic composite wind blades using PAM-RTM. The primary goal was to demonstrate the infusion simulation for the Elium® resin system on a 13-meter wind blade. Additionally, the exotherm temperature was predicted and compared to measurements, which showed model results within 10% of actual measurements. (Section 5.3) Composite laminate panels and composite sandwich panels with a balsa core were produced; specimens were cut and characterized. Similar composite specimens were made with Elium® thermoplastic resin and Hexion thermoset epoxy (RIMR135/RIMH1366) to enable comparisons between these resin systems. The static test methods included: tensile, compression, in-plane shear, interlaminar shear, flexural, sandwich core shear flexure, and single cantilever beam tests for sandwich beams. Fatigue testing at room temperature was completed to composite laminate panels at a stress ratio of R=0.1 and R=10. In addition, fatigue testing to laminate panels was completed at -30°C, and at room temperature after conditioning specimens at 70°C and 90% relative humidity. Overall, mechanical test results from Elium® composites are similar to epoxy composites. (Section 5.4) Elium composite panels were produced with intentional defects such as voids and nonwetting of fibers to begin to understand performance sensitivity to defects. A thermal digital image correlation (TDIC) method provides high spatial resolution strain field at elevated temperatures and can be used to identify defective regions within composite panels. Flexural modulus differences of 21% were seen between defect and non-defect panels. Other Elium® composite panels were forced to be defective by boiling the resin after infusion, which created voids throughout the composite laminate. X-ray computed tomography scanning was used to view the internal structure of the defect panels. Defect panels had a significant reduction in fatigue life as compared to baseline panels produced without intentional defects. (Section 5.5) Lap shear specimens were fabricated to compare the lap shear strength of an off-the-shelf adhesive (Plexus MA590) and two new adhesives developed by Arkema (Bostik SAF30 90 and Bostik SAF30 120). ISO standard 4587:2003 was used to standardize the testing method and sample fabrication. Lap shear specimens were made at 1mm, 3mm, and 10mm thicknesses. The Bostik adhesive lap shear test results were similar to Plexus for all thicknesses. (Section 5.6) Fiber-reinforced polymer (FRP) composites are typically used in high-performance applications (e.g., aerospace), and their expansion into high-volume industries (e.g. consumer automotive and wind turbine blade manufacturer or similar) is hindered by their cost and a lack of efficient manufacturing techniques. Monitoring the curing process of these composites during manufacturing can improve the efficiency of the process, and therefore reduce the manufacturing cost. Cure monitoring techniques were developed that use probabilistic estimation methods and surface temperature measurements made using infrared cameras. These techniques enable real-time monitoring of the infusion process to locate manufacturing flaws, and they can, potentially, estimate residual stresses in the part. Their commercialization will help facilitate expansion of FRP composites in high-volume industries. (Section 5.7) A 13-meter composite wind blade was produced with Elium® resin and Johns Manville fiberglass; this blade was made with VARTM processing similar to how megawatt-scale wind blades are currently manufactured, but no post-mold heating was used for this thermoplastic composite blade. The wind blade underwent full-scale validation for static loading (4-different load orientations) and flapwise fatigue loading to simulate 20-years of operational loads. The thermoplastic composite wind blade withstood the loading without any noted issues and performed similar to results from a previous full-scale validation to an equivalent epoxy composite wind blade produced with the same blade molds. (Section 5.8) A study was conducted to determine the feasibility of recycling composite wind turbine blade components fabricated with glass fiber reinforced Elium® thermoplastic resin. Dissolution, which is a process unique to thermoplastic matrices, allows recovery of both the polymer matrix and full-length glass fibers, while maintaining their stiffness and strength throughout the recovery process. The economics of recycling is favorable if 50% of the glass fiber is recovered and resold for a process of $\$$ 0.28/kg, and 90% of the resin is recovered and resold at a price of $\$$ 2.50/kg.(Section 10) Recommendations are outlined for commercializing thermoplastic resin for composite wind blade production, in addition to recommended areas for future research.

17 WIND ENERGY↗
DOE OSTI2026

Structural and Mechanical Analysis of Individual Mineralized Collagen Fibrils Using In Situ Transmission Electron Microscopy

Bone serves as an example of nature’s architectured material with its characteristic blend of strength and toughness, all at a lightweight design. Given the hierarchical nature of these materials, it is essential to understand the governing mechanisms and organization of their constituents across length scales for bioinspired structural design. Despite recent advances in transmission electron microscopy (TEM) that have allowed us to witness the hierarchical arrangement of bone at micro-down to the nanoscale, we are still missing the details about the structural organization and mechanical properties of the main building blocks of bone─mineralized collagen fibrils (MCFs). Here, we present a method to extract individual MCFs from nature’s model material, mineralized turkey leg tendon, using a dropcasting procedure. By isolating the MCFs onto TEM supporting grids, we visualized the arrangement of organic and mineral phases within individual MCFs at the nanoscale. Using a four-dimensional scanning transmission electron microscopy (4D-STEM) approach, the orientation of individual mineral crystals within the MCFs was examined. Furthermore, we conducted in situ tensile experiments, revealing exceptional tensile strains of at least 8%, demonstrating the intricate relationship between structural organization and the mechanical behavior of MCFs. These insights into the ultrastructure of mineralized tissue building blocks, as well as the proposed sample-extraction method compatible with in situ mechanical testing, provide a strong basis for research into nature-inspired material design.

4D-STEM↗
DOE OSTI2022

Diversity of Antibiotic Resistance genes and Transfer Elements-Quantitative Monitoring (DARTE-QM): a method for detection of antimicrobial resistance in environmental samples

Effective monitoring of antibiotic resistance genes and their dissemination in environmental ecosystems has been hindered by the cost and efficiency of methods available for the task. We developed the Diversity of Antibiotic Resistance genes and Transfer Elements-Quantitative Monitoring (DARTE-QM), a method implementing TruSeq high-throughput sequencing to simultaneously sequence thousands of antibiotic resistant gene targets representing a full-spectrum of antibiotic resistance classes common to environmental systems. In this study, we demonstrated DARTE-QM by screening 662 antibiotic resistance genes within complex environmental samples originated from manure, soil, and livestock feces, in addition to a mock-community reference to assess sensitivity and specificity. DARTE-QM offers a new approach to studying antibiotic resistance in environmental microbiomes, showing advantages in efficiency and the ability to scale for many samples. This method provides a means of data acquisition that will alleviate some of the obstacles that many researchers in this area currently face.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

A D-term Modeling Code (DMC) for Simultaneous Calibration and Full-Stokes Imaging of Very Long Baseline Interferometric Data

In this paper we present DMC, a model and associated tool for polarimetric imaging of very long baseline interferometry data sets that simultaneously reconstructs the full-Stokes emission structure along with the station-based gain and leakage calibration terms. DMC formulates the imaging problem in terms of posterior exploration, which is achieved using Hamiltonian Monte Carlo sampling. The resulting posterior distribution provides a natural quantification of uncertainty in both the image structure and the data calibration. We run DMC on both synthetic and real data sets, the results of which demonstrate its ability to accurately recover both the image structure and calibration quantities, as well as to assess their corresponding uncertainties. The framework underpinning DMC is flexible, and its specific implementation is under continued development.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Toward reducing uncertainty quantification costs in DEM models of particulate flow: Testing simple, sensitivity-based, forward uncertainty propagation techniques

The performance of two conceptually-simple uncertainty quantification techniques are tested against the rigorous nested-loop sampling technique of Roy and Oberkampf (Comput Methods Appl Mech Eng, 200: 2131–2144, 2011) (herein called full-sampling) using two very small-scale DEM-based models of particulate flow (one gas-solid flow and one granular flow). The first simplified forward uncertainty propagation technique, reduced-sampling, uses a sensitivity analysis to eliminate uncertain inputs that have little impact on the model output prior to nested-loop sampling. The second technique, boundary-sampling, uses a sensitivity analysis to inform the selection of two bounding cases for each key model output. In conclusion, the uncertainties in the model outputs obtained via the reduced- and boundary-sampling methods agree well with those from full-sampling for both the gas-solid and granular flow models while yielding computational savings of 65–75% (reduced sampling) and 94–97% (boundary sampling).

42 ENGINEERING↗
DOE OSTI2022

J-PLUS: Support vector machine applied to STAR-GALAXY-QSO classification

Context. In modern astronomy, machine learning has proved to be efficient and effective in mining big data from the newest telescopes. Aims. In this study, we construct a supervised machine-learning algorithm to classify the objects in the Javalambre Photometric Local Universe Survey first data release (J-PLUS DR1). Methods. The sample set is featured with 12-waveband photometry and labeled with spectrum-based catalogs, including Sloan Digital Sky Survey spectroscopic data, the Large Sky Area Multi-Object Fiber Spectroscopic Telescope, and VERONCAT – the Veron Catalog of Quasars & AGN. The performance of the classifier is presented with the applications of blind test validations based on RAdial Velocity Extension, the Kepler Input Catalog, the Two Micron All Sky Survey Redshift Survey, and the UV-bright Quasar Survey. A new algorithm was applied to constrain the potential extrapolation that could decrease the performance of the machine-learning classifier. Results. The accuracies of the classifier are 96.5% in the blind test and 97.0% in training cross-validation. The F1-scores for each class are presented to show the balance between the precision and the recall of the classifier. We also discuss different methods to constrain the potential extrapolation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

In-Plane Liftout and Push-to-Pull for In Situ Mechanical Testing of Irradiated Inconel X-750

A streamlined sample preparation method for nanomechanical testing is needed to improve the quality of specimens, reduce the cost, and increase the versatility of specimen fabrication. This work outlines an in-plane liftout focused ion beam (FIB) fabrication procedure to prepare electron-transparent specimens for in situ transmission electron microscopy (TEM) nanomechanical testing. Ion etching and electron backscatter diffraction (EBSD) techniques were used to lift out a [110] oriented grain from a neutron-irradiated bulk X-750 alloy. Careful control of voltages and currents ensured precision. Top surface thinning sweeps prevented resurfacing and redeposition while dog-bone geometries were shaped with a 1:4 gauge width-to-milling pattern diameter ratio. Nanotensile testing in the TEM with a picoindenter allowed for the estimation of an ultimate tensile strength of 2.41 GPa, and inspection revealed a high density of bubbles in the X-750 matrix. The proposed fabrication procedure is significant for preparing samples from radioactive materials, studying complex structures that are orientation-dependent, and analyzing desired planar areas.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Y-12 Groundwater Protection Program Groundwater and Surface Water Sampling and Analysis Plan (CY 2021)

This plan provides a description of the groundwater and surface water quality monitoring activities planned for calendar year (CY) 2021 at the U.S. Department of Energy Y-12 National Security Complex (Y-12) that will be managed by the Y-12 Groundwater Protection Program (GWPP). Groundwater and surface water monitoring is performed by the GWPP. Groundwater and surface water monitoring will be performed in three hydrogeologic regimes at Y-12: the Bear Creek Hydrogeologic Regime (Bear Creek Regime), the Upper East Fork Poplar Creek Hydrogeologic Regime (East Fork Regime), and the Chestnut Ridge Hydrogeologic Regime (Chestnut Ridge Regime). The Bear Creek and East Fork regimes are located in Bear Creek Valley and the Chestnut Ridge Regime is located south of Y-12. Additional surface water monitoring will be performed north of Pine Ridge along the boundary of the Oak Ridge Reservation. The following sections of this report provide details regarding the CY 2021 groundwater and surface water monitoring activities. Section 2 describes the monitoring locations in each regime and the processes used to select the sampling locations. A description of the field measurements and laboratory analytes is provided in Section 3. Sample collection methods and procedures are described in Section 4, and Section 5 lists the documents cited for more detailed operational and technical information. The narrative sections of the report reference several appendices. Figures (maps and diagrams) and tables (excluding a data summary table presented in Section 4) are in Appendix A and Appendix B, respectively. Groundwater Monitoring Schedules (when issued throughout CY 2021) will be inserted in Appendix C, and addenda to this plan (if issued) will be inserted in Appendix D. Laboratory requirements (bottle lists, holding times, etc.) are provided in Appendix E, and an approved Waste Management Plan is provided in Appendix F. Modifications to the CY 2021 monitoring program may be necessary during implementation. Changes in programmatic requirements may alter the analytes specified for selected monitoring wells or may add or remove wells from the planned monitoring network. Each modification to the monitoring program will be approved by the Y-12 GWPP manager and documented as an addendum to this sampling and analysis plan.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Alkaline-SDS cell lysis of microbes with acetone protein precipitation for proteomic sample preparation in 96-well plate format

Plate-based proteomic sample preparation offers a solution to the large sample throughput demands in the biotechnology field where hundreds or thousands of engineered microbes are constructed for testing is routine. Meanwhile, sample preparation methods that work efficiently on broader microbial groups are desirable for new applications of proteomics in other fields, such as microbial communities. Here, we detail a step-by-step protocol that consists of cell lysis in an alkaline chemical buffer (NaOH/SDS) followed by protein precipitation with high-ionic strength acetone in 96-well format. The protocol works for a broad range of microbes ( e . g ., Gram-negative bacteria, Gram-positive bacteria, non-filamentous fungi) and the resulting proteins are ready for tryptic digestion for bottom-up quantitative proteomic analysis without the need for desalting column cleanup. The yield of protein using this protocol increases linearly with respect to the amount of starting biomass from 0.5–2.0 OD*mL of cells. By using a bench-top automated liquid dispenser, a cost-effective and environmentally-friendly option to eliminating pipette tips and reducing reagent waste, the protocol takes approximately 30 minutes to extract protein from 96 samples. Tests on mock mixtures showed expected results that the biomass composition structure is in close agreement with the experimental design. Lastly, we applied the protocol for the composition analysis of a synthetic community of environmental isolates grown on two different media. This protocol has been developed to facilitate rapid, low-variance sample preparation of hundreds of samples and allow flexibility for future protocol development.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Tests of a High Temperature Sample Conditioner for the Waste Treatment Plant LV-S2, LV S3, HV S3A and HV-S3B Exhaust Systems

Tests were performed to evaluate a sample conditioning unit for stack monitoring at Hanford Tank Waste Treatment and Immobilization Plant (WTP) exhaust stacks with elevated air temperatures. The LV-S2, LV-S3, HV-S3A and HV-S3B exhaust stacks are expected to have elevated air temperature and dew point. At these emission points, exhaust temperatures are too high to deliver the air sample directly to the required stack monitoring equipment. As a result, a sample conditioning system is considered to cool and dry the air prior to its delivery to the stack monitoring system. The method proposed for the sample conditioning is a dilution system that will introduce cooler, dry air to the air sample stream. This method of sample conditioning is meant to reduce the sample temperature while avoiding condensation of moisture in the sample stream. An additional constraint is that the ANSI/HPS N13.1-1999 standard states that at least 50% of the 10 µm aerodynamic diameter (AD) particles present in the stack free stream must be delivered to the sample collector. In other words, depositional loss of particles should be limited to 50% in the sampling, transport, and conditioning systems. Based on estimates of particle penetration through the LV-S3 sampling system, the diluter should perform with about 80% penetration or better to ensure that the total sampling system passes the 50% or greater penetration criterion.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

Studying the Collective Functional Response of a Receptor in Alchemical Ligand Binding Free Energy Simulations with Accelerated Solvation Layer Dynamics

Ligand binding free energy simulations (LB-FES) that involve sampling of protein functional conformations have been longstanding challenges in research on molecular recognition. Particularly, modeling of the conformational transition pathway and design of the heuristic biasing mechanism are severe bottlenecks for the existing enhanced configurational sampling (ECS) methods. Inspired by the key role of hydration in regulating conformational dynamics of macromolecules, this report proposes a novel ECS approach that facilitates binding-associated structural dynamics by accelerated hydration transitions in combination with the lambda-exchange of free energy perturbation (FEP). Further, two challenging protein-ligand binding processes involving large configurational transitions of the receptor are studied, with hydration transitions at binding sites accelerated by Hamiltonian-simulated annealing of the hydration layer. Without the need for pathway analysis or ad hoc barrier flattening potential, LB-FES were performed with FEP/lambda-exchange molecular dynamics simulation at a minor overhead for annealing of the hydration layer. The LB-FES studies showed that the accelerated rehydration significantly enhances the collective conformational transitions of the receptor, and convergence of binding affinity calculations is obtained at a sweet-spot simulation time scale. Alchemical LB-FES with the proposed ECS strategy is free from the effort of trial and error for the setup and realizes efficient on-the-fly sampling for the collective functional response of the receptor and bound water and therefore presents a practical approach to high-throughput screening in drug discovery.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Accelerating Ultrafast Spectroscopy with Compressive Sensing

We report ultrafast spectroscopy is an important tool for studying photoinduced dynamical processes in atoms, molecules, and nanostructures. Typically, the time to perform these experiments ranges from several minutes to hours depending on the choice of spectroscopic method. It is desirable to reduce this time overhead not only to shorten time and laboratory resources, but also to make it possible to examine fragile specimens that quickly degrade during long experiments. In this article, we motivate using compressive sensing to significantly shorten data acquisition time by reducing the total number of measurements in ultrafast spectroscopy. We apply this technique to experimental data from ultrafast transient absorption spectroscopy and ultrafast terahertz spectroscopy and show that good estimates can be obtained with as low as 15% of the total measurements, implying a sixfold reduction in the data acquisition time.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Variational Path Sampling of Rare Dynamical Events

This article reviews the concepts and methods of variational path sampling. These methods allow computational studies of rare events in systems driven arbitrarily far from equilibrium. Based upon a statistical mechanics of trajectory space and leveraging the theory of large deviations, they provide a perspective from which dynamical phenomena can be studied with the same types of ensemble reweighting ideas that have been used for static equilibrium properties. Applications to chemical, material, and biophysical systems are highlighted.

Singh, Aditya N↗
DOE OSTI2022

Trajectory Ensemble Methods Provide Single-Molecule Statistics for Quantum Dynamical Systems

The emergence of experiments capable of probing quantum dynamics at the single-molecule level requires the development of new theoretical tools capable of simulating and analyzing these dynamics beyond an ensemble-averaged description. In this article, we present an efficient method for sampling and simulating the dynamics of the individual quantum systems that make up an ensemble and apply it to study the nonequilibrium dynamics of the ubiquitous spin-boson model. We generate an ensemble of single-system trajectories, and we analyze this trajectory ensemble using tools from classical statistical mechanics. Our results demonstrate that the dynamics of quantum coherence is highly heterogeneous at the single-system level due to variations in the initial bath configuration, which significantly affects the transient exchange of coherence between the system and its bath. Here, we observe that single systems tend to retain coherence over time scales longer than that of the ensemble. We also compute a novel thermodynamic entanglement entropy that quantifies a thermodynamic driving force favoring system–bath entanglement.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗