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DOE OSTI2021

A Study on Computational Cost Reduction of Simulations of Phase-Change Material (PCM) Embedded Heat Exchangers

Thermal storage can be implemented using Phase-Change Materials (PCM), which absorb significant latent heat with a relatively small temperature change. PCM phase-change processes are transient and are driven by thermal diffusion and natural convection – the latter, especially for melting process. Modeling and simulation of PCM heat exchangers (HX’s) is typically computationally intensive due to the relatively complex time-dependent physics. Most of the PCM modeling work in the literature uses high-order modeling tools such as Computational Fluid Dynamics (CFD) and Lattice-Boltzmann Method (LBM). For design purposes, the existing PCM modeling approaches are not practical, limiting researchers in their ability to investigate new ideas and different PCM’s with faster turnarounds. This paper presents a study investigating the reduction of computational cost of PCM embedded HX’s CFD models by evaluating the feasibility of spatial reduction without losing accuracy. The analysis consists of comparing full and partial domain under full melting conditions. The subject of this study is a single straight tube with circular transverse fins in the vertical orientation, using PCM’s with 35oC nominal melting temperature. Different tube and fin dimensions are investigated. Results indicate that the reduced domain reproduces - in half the run time - the same behavior as the full domain since the buoyancy effects are localized and patterned. The outputs from the partial domain simulation were used to build a non-general correlation for the PCM heat transfer characteristics and demonstrated how it can be implemented in a Finite Control Volume Reduced Order Model (ROM). The ROM can accurately reproduce the CFD simulations at 4 to 5 orders of magnitude faster.

25 ENERGY STORAGE↗

DOE OSTI2024

Heat Transfer Experiments of Ribbed, Serpentine Cooling Passages with Supercritical CO2

The results of heat transfer experiments with supercritical CO2 (sCO2) to capture the performance of ribbed, serpentine cooling passages for Reynolds numbers in the range of 100,000 - 400,000 are presented. The oxy-combustion turbine operating in an Allam-Fetvedt cycle has a turbine inlet temperature exceeding 1100°C, necessitating internally cooled turbine blades due to material creep strength limits. Reynolds numbers for sCO2, with its combination of high fluid density and low viscosity, can be up to an order of magnitude higher than comparable internal cooling conditions for an air-breathing engine where the majority of experimental data exists. To improve the prediction of cooling performance through turbulated passages, a test rig was designed and constructed with interchangeable insert capability for operation in sCO2 with heat transfer from a heater outlet flow stream to a lower temperature recuperator outlet flow stream. The inserts included serpentine passage geometry with five passes, one of the inserts including chevron ribs and the other a plain wall. The multi-pass serpentine geometry allowed for the evaluation of the effects 180 deg. tip turns have on the return passage flow characteristics, as they can depart significantly from fully-developed flow characteristics. The test procedure included the use of a modified Wilson plot method, with hot flow stream conditions kept effectively constant so that monitored changes in the overall thermal resistance could be attributed to manipulations in cooling flow stream conditions. Conditions during testing consisted of test section pressures of approximately 180 bar, cooling flow stream temperature of 175°C and hot flow stream temperature of 410°C. Test points at discrete cool flow Reynolds numbers up to 400,000 demonstrated an expected trend of decreased fluid thermal resistance with increasing Reynolds number, while at comparable Reynolds number there was an exhibited lower thermal resistance and higher passage pressure drop for the ribbed insert compared to the plain-walled insert. Processing of test data included establishment of Nusselt number enhancement ratios, so that for different internal cooling passage dimensions in the actual turbine blade at comparable Reynolds number the ratio could be applied to predict cooling performance.

Marshall, Michael↗

DOE OSTI2020

Dependence of Enstrophy Transport and Mixed Mass on Dimensionality and Initial Conditions in the Richtmyer–Meshkov Instability Induced Flows

Here we present a comparative study of the enstrophy budget and mixed mass between two- and three-dimensional flows induced by Richtmyer–Meshkov instability (RMI). Specifically, the individual contributions to the enstrophy budget due to the production from baroclinicity and from vortex stretching (which vanishes in two-dimensional (2D) flow) are delineated. This is enabled by a set of two- and three-dimensional computations at Atwood 0.5 having both narrow- and broad-band perturbations. A further three-dimensional (3D) computation is conducted at Atwood 0.9 using an identical narrowband perturbation to the Atwood 0.5 case to examine the sensitivity to density ratio. The mixed mass is also considered with the goal to obtain insight on how faithfully a simplified calculation performed in two dimensions can capture the mixed mass for an inertial confinement fusion (ICF) or other practical application. It is shown that the late time power law decay of variable density enstrophy is substantially different in two and three dimensions for the narrowband initial perturbation. The baroclinic production term is negligible in three dimensions (aside from the initial shock interaction), as vortex stretching is larger by two orders of magnitude. The lack of vortex stretching considerably reduces the decay rate in both narrowband and broadband perturbations in two dimensions. In terms of mixed mass, the lack of vortex stretching reduces the mixed mass in two dimensions compared to three in all cases. In the broadband cases, the spectral bandwidth in the 2D case is wider; hence, there is a longer time period of sustained linear growth which reduces the normalized mixed mass further.

42 ENGINEERING↗

DOE OSTI2024

Ultrahigh-resolution mass spectrometry data associated with the manuscript “A functional microbiome catalog crowdsourced from North American rivers"

This data package is associated with the publication “A functional microbiome catalog crowdsourced from North American rivers” submitted to Nature (Borton et al., 2024); (https://www.biorxiv.org/content/10.1101/2023.07.22.550117v1). Predicting elemental cycles and maintaining water quality under increasing anthropogenic influence requires understanding the spatial drivers of river microbiomes. However, the unifying microbial determinants governing river biogeochemistry are hindered by a lack of genome-resolved functional insights and sampling across multiple rivers. Here we employed a community science effort to accelerate the sampling of river microbiomes to create the Genome Resolved Open Watersheds database (GROWdb). GROWdb is a publicly available resource that paves the way for watershed predictive modeling and microbiome-based management practices. This resource profiled the identity, distribution, function, and expression of thousands of microbial genomes across rivers covering 90% of United States watersheds. We identified the most cosmopolitan microbiome members, while also revealing local drivers of strain endemism across ecological dimensions. We provide the first evidence that microbial functional trait expression followed the tenets of the River Continuum Concept, suggesting the structure and function of river microbiomes is predictable. The Fourier-transform ion cyclotron resonance mass spectrometry (FTICR-MS) data were one of many different data types used in establishing the ecological dimensions along which different microbes were detected .This data package only contains the processed FTICR-MS data associated with this manuscript; all other data is accessible via Zenodo (https://zenodo.org/records/8173287), GitHub (https://github.com/jmikayla1991/Genome-Resolved-Open-Watersheds-database-GROWdb), KBase (https://doi.org/10.25982/109073.30/1895615), and NCBI via Bioproject PRJNA946291.This dataset consists of (1) a file-level metadata (flmd) file; (2) a data dictionary (dd) file; (3) a readme; (4) three Fourier-transform ion cyclotron resonance mass spectrometry (FTICR-MS) processed data files (a ‘data’ file containing peak-by-sample observations, a ‘mol’ file containing peak metadata, and a transformation profile containing transformation-by-sample observations). All files are .csv or .pdf.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Universality of Rényi Entropy in Conformal Field Theory

We use the thermal effective theory to prove that, for the vacuum state in any conformal field theory in 𝑑 dimensions, the 𝑛th Rényi entropy 𝑆$^{(𝑛)}_{𝐴}$ behaves as 𝑆$^{(𝑛)}_{𝐴}$ = [𝑓⁡/(2⁢𝜋⁢𝑛) 𝑑−1 ]⁢[Area⁡(∂𝐴)/(𝑑−2)⁢𝜀 𝑑−2 ]⁢(1+𝑂⁡(𝑛)) in the 𝑛 → 0 limit when the boundary of the entanglement domain 𝐴 is spherical with the UV cutoff 𝜀. The theory dependence is encapsulated in the cosmological constant 𝑓 in the thermal effective action. Using this result, we estimate the density of states for large eigenvalues of the modular Hamiltonian for the domain 𝐴. In two dimensions, we can use the hot spot idea, which describes the effective action in the high-temperature limit when the temperature is position-dependent, to derive more powerful formulas valid for arbitrary positive 𝑛. We discuss the difference between two and higher dimensions and clarify the applicability of the hot spot idea. We also use the thermal effective theory to derive an analog of the Cardy formula for boundary operators in higher dimensions.

Conformal field theory↗

DOE OSTI2021

Fractal dimension of optical cirrus in Stripe82

ABSTRACT The geometric characteristics of dust clouds provide important information on the physical processes that structure such clouds. One of such characteristics is the 2D fractal dimension D of a cloud projected on to the sky plane. In previous studies, which were mostly based on infrared (IR) data, the fractal dimension of individual clouds was found to be in a range from 1.1 to 1.7 with a preferred value of 1.2–1.4. In this work, we use data from Stripe82 of the Sloan Digital Sky Survey to measure the fractal dimension of the cirrus clouds. This is done here for the first time for optical data with significantly better resolution as compared to IR data. To determine the fractal dimension, the perimeter-area method is employed. We also consider IR (IRAS and Herschel) counterparts of the corresponding optical fields to compare the results between the optical and IR. We find that the averaged fractal dimension across all clouds in the optical is $\langle D \rangle =1.69^{+0.05}_{-0.05}$ which is significantly larger than the fractal dimension of its IR counterparts $\langle D\rangle =1.38^{+0.07}_{-0.06}$. We examine several reasons for this discrepancy (choice of masking and minimal contour level, image and angular resolution, etc.) and find that for approximately half of our fields the different angular resolution (point spread function) of the optical and IR data can explain the difference between the corresponding fractal dimensions. For the other half of the fields, the fractal dimensions of the IR and visual data remain inconsistent, which can be associated with physical properties of the clouds, but further physical simulations are required to prove it.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Radiation-induced Alteration of Meta-chert

Concrete aggregate identified as “meta-chert” was irradiated with gamma-rays and neutrons. To identify the volume expansion of the aggregate under neutron irradiation, herein the following analyses were performed for pristine and irradiated α-quartz and meta-chert: X-ray diffraction (XRD)/Rietveld analysis, dimension change, water pycnometry, He-pycnometry, light optical microscopy (LOM), and scanning electron microscopy (SEM). From the difference of volume expansion observed from dimension change and water / helium pycnometry, the crack opening inside the aggregate subjected to irradiation was elucidated, and this was confirmed by LOM and SEM analysis. The crack contribution to the expansion of the aggregate was significant for neutron fluence > 6.99 × 1019 n/cm 2 , for E ≥ 0.01 MeV. Based on the XRD analysis, changes in lattice parameters were identified and the cell volume expansion was compared with the data by helium pycnometry. Based on the density change calculation and phase calculation data, the density of X-ray amorphous phase was consistent with that of expanded crystal α-quartz.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Weak phylogenetic and habitat effects on root trait variation of 218 Neotropical tree species

Tropical forests harbor a large diversity of closely related tree species that can thrive across habitats. This biodiversity has been found to correspond to large functional diversity in aboveground traits, and likely also relates to belowground trait variation. Globally, root trait (co-)variation is driven by different belowground resource strategies of species, environmental variation, and phylogeny; however, these patterns mostly reflect observations from temperate biomes and remain unconfirmed in tropical trees. We examine phylogenetic and environmental effects on root trait (co-)variation of trees across habitats in an Amazonian rainforest. Roots of 218 tree species from ten dominant families were sampled across three major habitats near Manaus, Brazil. We quantified five morphological and architectural root traits to (i) investigate how they reflected different resource strategies across species, (ii) compare them between families and superorders to test phylogenetic effects, and (iii) compare them between habitats to determine environmental effects on root trait expressions and variability. Root traits discriminated species along a tradeoff between root diameter and root branching and, secondly, due to variation in root tissue density. Our results further show weak phylogenetic effects on tropical tree root variation, for example, families from the same superorder showed large divergence in their root traits, while those from different superorders often overlapped in their root morphology and architecture. Root traits differed significantly between habitats but habitat type had only little effect on overall root trait variation. Our work suggests that the dimensions and drivers that underlie (co-)variation in tropical root traits may differ from global patterns defined by mostly temperate datasets. Due to (a)biotic environmental differences, different root trait dimensions may underlie the belowground functional diversity in (Neo)tropical forests, and we found little evidence for the strong phylogenetic conservatism observed in root traits in temperate biomes. We highlight important avenues for future research on tropical roots in order to determine the degree of, and shifts in functional diversity belowground as communities and environments change in tropical forests.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

Parallelized domain decomposition for multi-dimensional Lagrangian random walk mass-transfer particle tracking schemes

Lagrangian particle tracking schemes allow a wide range of flow and transport processes to be simulated accurately, but a major challenge is numerically implementing the inter-particle interactions in an efficient manner. This article develops a multi-dimensional, parallelized domain decomposition (DDC) strategy for mass-transfer particle tracking (MTPT) methods in which particles exchange mass dynamically. We show that this can be efficiently parallelized by employing large numbers of CPU cores to accelerate run times. In order to validate the approach and our theoretical predictions we focus our efforts on a well-known benchmark problem with pure diffusion, where analytical solutions in any number of dimensions are well established. In this work, we investigate different procedures for “tiling” the domain in two and three dimensions (2-D and 3-D), as this type of formal DDC construction is currently limited to 1-D. An optimal tiling is prescribed based on physical problem parameters and the number of available CPU cores, as each tiling provides distinct results in both accuracy and run time. We further extend the most efficient technique to 3-D for comparison, leading to an analytical discussion of the effect of dimensionality on strategies for implementing DDC schemes. Increasing computational resources (cores) within the DDC method produces a trade-off between inter-node communication and on-node work. For an optimally subdivided diffusion problem, the 2-D parallelized algorithm achieves nearly perfect linear speedup in comparison with the serial run-up to around 2700 cores, reducing a 5 h simulation to 8 s, while the 3-D algorithm maintains appreciable speedup up to 1700 cores.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Origin of the background absorption in carbon nanotubes: Phonon-assisted excitonic continuum

Excitonic effects in 1D semiconductors can be qualitatively different from those in higher dimensions. In particular, the Sommerfeld factor, the ratio of the above-band-edge excitonic continuum absorption to free electron-hole pair generation, has been shown to be less than 1 (suppressed) in 1D systems while it is larger than 1 (enhanced) in 2D and 3D systems. Strong continuum suppression indeed exists in semiconducting single-wall carbon nanotubes, a prototypical 1D semiconductor. However, absorption spectra for carbon nanotubes are typically fit with a combination of Lorentzians and a polynomial background baseline with little physical meaning. We performed absorption measurements in aligned single-chirality (6,5) carbon nanotube films. The obtained spectra were fit with our theoretical model obtained by solving the Boltzmann scattering equation involving fifty-nine different types of transitions among three different types of quasiparticles. Specifically, we took into account microscopic interactions between photons, phonons, and excitons, including their dispersions, which unambiguously demonstrated that the background absorption is due to phonon-assisted transitions from the semiconductor vacuum to finite-momentum continuum states of excitons. The excellent agreement we obtained between experiment and theory suggests that our numerical technique can be seamlessly extended to compute strongly out-of-equilibrium many-body dynamics and time-resolved spectra in low-dimensional materials.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Analytical closure to the spatially-filtered Euler equations for shock-dominated flows

To ensure numerical stability in the vicinity of shocks, a variety of methods have been used, including shock-capturing schemes such as weighted essentially non-oscillatory schemes, as well as the addition of artificial diffusivities to the governing equations. Centered finite difference schemes are often avoided near discontinuities due to the tendency for significant oscillations. However, such schemes have desirable conservation properties compared to many shock-capturing schemes. The objective of this work is to derive all necessary viscous/diffusion terms from first principles and then demonstrate the performance of these analytical terms within a centered differencing framework. The physical Euler equations are spatially-filtered with a Gaussian-like filter. Sub-filter scale (SFS) terms arise in the momentum and energy equations. Analytical closure is provided for each of them by leveraging the jump conditions for a shock. No SFS terms are present in the continuity or species equations. Here, this approach is tested for several problems involving shocks in one and two dimensions. Implemented within a centered difference code, the SFS terms perform well for a range of flow conditions without introducing excessive diffusion.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Hidden zeros for particle/string amplitudes and the unity of colored scalars, pions and gluons

Recent years have seen the emergence of a new understanding of scattering amplitudes in the simplest theory of colored scalar particles — the Tr(Φ 3 ) theory — based on combinatorial and geometric ideas in the kinematic space of scattering data. In this paper we report a surprise: far from the toy model it appears to be, the “stringy” Tr(Φ 3 ) amplitudes secretly contains the scattering amplitudes for pions, as well as non-supersymmetric gluons, in any number of dimensions. The amplitudes for the different theories are given by one and the same function, related by a simple shift of the kinematics. This discovery was spurred by another fundamental observation: the tree-level Tr(Φ 3 ) field theory amplitudes have a hidden pattern of zeros when a special set of non-planar Mandelstam invariants is set to zero. These zeros are not manifest in Feynman diagrams but are made obvious by the connection of these amplitudes to the new understanding of associahedra arising from “causal diamonds” in kinematic space. Furthermore, near these zeros, the amplitudes simplify, by factoring into a non-trivial product of smaller amplitudes. Remarkably the amplitudes for pions and gluons are observed to also vanish in the same kinematical locus. These properties for Tr(Φ 3 ) amplitudes hold and further generalize to the “stringy” Tr(Φ 3 ) amplitudes. The “kinematic causal diamond” picture suggests a unique shift of the kinematic data that preserves the zeros, and this shift is precisely the one that unifies colored scalars, pions, and gluons into a single object. We will focus in this paper on explaining the hidden zeros and factorization properties and the connection between all the colored theories, working for simplicity at tree level. Subsequent works will describe this new formulation for the Non-linear Sigma Model and non-supersymmetric Yang-Mills theory, at all loop orders.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Integrating tactical planning, operational planning and scheduling using data-driven feasibility analysis

Supply chain operations and scheduling are well-studied problems in the literature. Although these problems are related, they are often solved sequentially. This uncoordinated approach usually leads to sub-optimal solutions. Here this paper proposes a methodology for integrating scheduling operations into the supply chain network, motivated by the available enterprise data, and feasibility analysis. Existing literature on integrated models for addressing the supply chain is reviewed and classified. Then the mathematical model formulation for each level is discussed, after which the proposed data-driven integrated framework is described. The methodology is tested on two different case studies of varying dimensions. For each case study, the solution solves a multi-objective problem with the overall aim of an optimal solution that is robust towards achieving optimal cost while keeping customer satisfaction in mind.

42 ENGINEERING↗

DOE OSTI2026

Enabling microbial electrolysis cell scale-up via electrochemistry-, hydrodynamic-, and microbial ecology-informed framework

Microbial electrolysis cells (MECs) can produce green hydrogen while removing organic contaminants from liquid waste streams by leveraging the metabolic activity of electroactive microorganisms. Despite their potential in a sustainable, circular economy, large-scale MECs that can treat relevant volumes of wastewater have failed to deliver performance proportional to their lab-scale counterparts. The reason behind this lower performance at scale remains unclear. Here, in this study, we developed a combined electrochemistry-, hydrodynamic-, and microbial ecology-informed framework to analyze and optimize MEC performance during scale-up, enabling accurate quantification of major limitations and the identification of strategies to overcome them, ultimately facilitating equivalent performance at scale. Applying this framework to the scale-up of a zero-gap MEC from 9 cm 2 electrode area to 100 cm 2 electrode area, resulted in similar maximum current densities in a 100 cm 2 MEC (21.7 ± 1.1 A/m 2 ) compared to a 9 cm 2 system (25.1 ± 2.7 A/m 2 ), as well as equivalent hydrogen production rates of 69.3 L/L-d (100 cm 2 ) and 67.7 ± 2.4 L/L-d (9 cm 2 ). COMSOL flow dynamics simulations were used to scale up the reactor configuration without negatively affecting electrolyte velocity and distribution in the cell, minimizing the increase in internal resistances during scale-up (11.7 ± 0.5 mΩm 2 at 9 cm 2 ; 19.7 ± 1.3 mΩm 2 at 100 cm 2 ). Microbial community structures were assessed at both scales using high-throughput sequencing, highlighting the differences of populations across electrode dimensions and operational parameters. The framework presented here accelerates the development of effective strategies toward the scale-up of MECs by furthering the understanding of how electrochemical, hydrodynamic, and microbial ecology parameters change as the reactor dimension is increased. Ultimately, this approach contributes to advancing electrochemical biotechnology toward practical deployment in energy-efficient wastewater treatment systems.

Flow path↗

DOE OSTI2026

Competition between charge-density-wave and superconducting orders on eight-leg square Hubbard cylinders

The issue of whether d-wave superconductivity (SC) occurs in the square-lattice Hubbard model with U of order of the bandwidth has been one of the most debated issues to emerge from the study of high temperature SC. Here, we report variational results on eight-leg cylinders with next-nearest-neighbor hopping in the range $-0.5t\le t^{\prime} \le 0.25t$ with U = 8t and 12t and doped hole concentrations δ = 1/12 and 1/8. For $t^{\prime} \le 0$, the ground-state appears to be a charge-density wave (CDW) of one sort or another with SC correlations that are extremely short-ranged. In contrast, in some cases, the local magnetic order has a correlation length greater than half the cylinder width - suggestive that magnetic order might also arise in the 2D limit. For $t^{\prime} \le 0$, our results depend more strongly on boundary conditions (periodic vs antiperiodic), making it still harder to correctly guess whether SC or CDW correlations dominate in the 2D limit. These results were obtained employing matrix-product states with bond dimensions large enough that energy differences as small as 10 −3 t per site can be resolved.

materials science↗

DOE OSTI2020

Low-rank Sachdev-Ye-Kitaev models

Motivated by recent proposals of experimental realization of fast scramblers, we study a family of solvable variants of the ($\textit{q}$ = 4) Sachdev-Ye-Kitaev model in which the rank and eigenvalue distribution of the coupling matrix $J_{ ij,kl}$ are tuneable. When the rank is proportional to the number of fermions, the low temperature behavior is sensitive to the eigenvalue distribution. We obtain a complete classification of the possible non-Fermi liquid quantum phases. These include two previously studied phases whose fermion scaling dimension depends continuously on the rank; we show that they are maximally chaotic, but necessitate an extensively degenerate or negative semidefinite coupling matrix. In this work, more generic distributions give rise to “almost Fermi liquids” with a scaling dimension Δ = 1/2, but which differ from a genuine Fermi liquid in quasiparticle decay rate, quantum Lyapunov exponent, and/or specific heat.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Electrical Manipulation of Quantum Coherence in a Two-Level Molecular System

We report the manipulation of ultrafast quantum coherence of a two-level single hydrogen molecular system by employing static electric field from the sample bias in a femtosecond terahertz scanning tunneling microscope. A H 2 molecule adsorbed on the polar Cu 2⁢ N surface develops an electric dipole and exhibits a giant Stark effect. An avoided crossing of the quantum state energy levels is derived from the resonant frequency of the single H 2 two levels in a double-well potential. The dephasing time of the initial wave packet can also be changed by applying the electric field. The electrical manipulation for different tunneling gaps in three dimensions allows quantification of the surface electrostatic fields at the atomic scale. Further, our work demonstrated the potential application of molecules as controllable two-level molecular systems.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Relative State Counting for Semiclassical Black Holes

It has been shown that entropy differences between certain states of perturbative quantum gravity can be computed without specifying an ultraviolet completion. This is analogous to the situation in classical statistical mechanics, where entropy differences are defined but absolute entropy is not. Unlike in classical statistical mechanics, however, the entropy differences computed in perturbative quantum gravity do not have a clear physical interpretation. Here we construct a family of perturbative black hole states for which the entropy difference can be interpreted as a relative counting of states. Conceptually, this Letter begins with the algebra of mass fluctuations around a fixed black hole background, and points out that while this is a type I algebra, it is not a factor and therefore has no canonical definition of entropy. As in previous work, coupling the mass fluctuations to quantum matter embeds the mass algebra within a type II factor, in which entropy differences (but not absolute entropies) are well defined. It is then shown that for microcanonical wave functions of mass fluctuation, the type II entropy difference equals the logarithm of the dimension of the extra Hilbert space that is needed to map one microcanonical window to another using gauge-invariant unitaries. The Letter closes with comments on type II entropy difference in a more general class of states, where the von Neumann entropy difference does not have a physical interpretation, but “one-shot” entropy differences do. Published by the American Physical Society 2024

Akers, Chris (ORCID:0000000227929827)↗