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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

High performance heat exchangers for next generation hybrid cooler (CRADA Final Report)

The evaporative cooling process has been successfully deployed in multiple energy conversion processes such as power generation, process cooling, heating, ventilation & cooling (HVAC), and commercial and industrial refrigeration. The heat exchanger is a very common yet extremely critical component of such systems. The device is important since the performance of the overall cooling system heavily relies on the thermal-hydraulic efficiency of the heat exchanger. The possible wet operation as evaporative cooling heat exchanger complicates the issue. Indeed, based on the hybrid nature of operation (fully dry, partially wet, fully wet) the efficiency can vary significantly and can cause performance variation for the whole system. Understanding the importance of the issue, Oak Ridge National Laboratory (Contractor) and Baltimore Aircoil Company (Participant) propose an activity focused on the analysis of the existing heat exchanger technology used in air and evaporative cooling processes and design, development and demonstration of a novel heat exchanger design based on porous materials. The potential candidates include metallic wire meshes and metal foams carefully designed for the proposed application. Prior research has indicated that these materials have great potential for deployment in thermal systems, particularly heat sinks and heat exchangers. It is expected that the successful completion of the project will lead to novel heat exchanger technology for hybrid systems (capable of dry and wet operation) by exploring newly emerging materials and their potential for heat transfer application. The overall goal is to develop a next generation heat exchanger technology which can be deployed in evaporative cooling systems. The impact of the such development is significant since, it will not only make the overall system highly efficient but will also, reduce the total refrigerant charge in the heat exchanger, a critical aspect for the deployment of refrigerants with lower Global Warming Potential (GWP).

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

Reducing Sample Loss in Measurement of Heat of Vaporization of Ethanol/Gasoline Blends by Differential Scanning Calorimetry/Thermogravimetric Analysis

Higher gasoline Heat of Vaporization (HOV) can enable higher compression-ratio direct injection spark ignition engines by providing evaporative cooling that effectively increases fuel knock resistance. Methods to directly measure this fuel property in complex gasoline samples are not well developed. The objective of the present study was to further improve a Differential Scanning Calorimetry/Thermogravimetric Analyzer (DSC/TGA) method to measure the total and partial HOV of gasoline. Ten market gasoline samples were chosen to have a wide range of properties to assess the method's capability across the entire volatility range with an emphasis on understanding how well the method captures the initial 10 percent (%) of sample evaporation and how much sample is left unevaporated at the end of the experiment. Modifications to the sample preparation/introduction method as well as to the instrument itself were made to reduce initial sample losses which included measurements of the HOV at 10 degrees C and 5 degrees C (in a cold chamber) as well as under (uncontrolled) ambient conditions. Experimental results from the DSC/TGA were compared to calculated total HOV results based on Detailed Hydrocarbon Analysis (DHA). Results from the two methods agreed very well with the difference being 5% or less in almost every case. In addition, the repeatability of the method was investigated by analyzing samples in triplicate at the three temperatures investigated. One valuable conclusion from the study was that the lower temperatures of 10 degrees C and 5 degrees C enabled more reproducible measurements for both total and partial HOV. This improved precision may be caused by the fact that temperature control in the cold chamber was more reliable than the ambient laboratory temperature control. Additionally, cold chamber experiments, due to ergonomic limitations, did not allow for the use of a lid on the sample pan. The reproducibility of the evaporation rate was found to be highly dependent on the pan/lid fit which can vary significantly such that elimination of the lid improved measurement precision while operation at sub-ambient temperature slowed the evaporation rate. Results detailing sample preparation and instrument modifications as well as a detailed comparison of total and partial HOV results are presented.

ADVANCED PROPULSION SYSTEMS,BIOMASS FUELS↗
DOE OSTI2026

The Fate of Nucleated Black Holes in de Sitter Quantum Gravity

The Euclidean Nariai geometry has long been proposed as the instanton describing the nucleation of maximal-mass black holes in de Sitter space. We place this interpretation on firmer footing by showing that, once an observer is included, the gravitational path integral produces the imaginary phase required for a transition rate. As a warmup, we revisit the Hawking-Moss instanton and, as a byproduct, find that scalar fields can enhance black-hole nucleation, suggesting a quantum-gravity bound on scalar potentials with de Sitter solutions. We then study the subsequent semiclassical evolution of the nucleated black hole. We show that the previously claimed "anti-evaporation" channel is unphysical, arising from a quantum state with singular horizons. In a smooth state, the black hole instead undergoes standard thermal Hawking evaporation. We verify explicit agreement with the no-boundary state and argue that this evaporation is not subject to large quantum-gravity corrections. The nucleated black hole thus evaporates completely back to the maximally-entropic empty de Sitter vacuum, making the full process a Boltzmann fluctuation.

FOS: Physical sciences↗
DOE OSTI2021

Empirical prediction of saline water atomization pressure loss and spray phase change using local flow pressure analysis

A pressure analysis technique was developed to obtain spray spatial evaporation profile in a thermal desalination process. The technique can replace temperature-based evaporation measurement methods that are challenged by liquid-phase interference. It also provides an alternative to optical methods with high cost and complexity. Fundamental analysis was developed to determine local humidity ratios from changes in local static and dynamic pressures. The analysis was applied to data obtained from an external mixing air-assist atomizer. An empirical model was developed for the pressure loss in atomization process and was used in the analysis of humidity ratio. The results were used to develop empirical correlations for local humidity ratio in spray mediums using inlet conditions. Utilizing inlet conditions to predict evaporation profiles is an important contribution as it eliminates the need to take local spray measurements. Obtaining local data is often difficult and expensive; Our method and correlation circumvent the need for that. Finally, the correlations presented in this paper apply to saline water sprays with total dissolved salt of 0-10 wt%. The salinity-specific correlations are accurate to within ±10% of experimental data. The individual models were aggregated into a unified correlation for salinities within 0-10 wt%. The unified correlation is accurate to within ±18% of experimental data.

42 ENGINEERING↗
DOE OSTI2025

Evapotranspiration Partitioning Using Flux Tower Data in a Semi-Arid Ecosystem

Information about evapotranspiration (ET) and its components, that is, evaporation and transpiration, is crucial for a wide range of water and ecosystem management applications. However, partitioning ET into its two components is often challenging because of their spatiotemporal variabilities and lack of process understanding. This study developed a machine learning (ML) framework to shed light on ET processes and assess the relative importance of different drivers by incorporating hydrometeorology and biomass productivity variables. The Shapley Additive Explanations (SHAP) approach was applied to enhance explainability and rank the importance of ET drivers and their components. A total of 62 variables covering hydrometeorological and biomass productivity dimensions were considered from the Reynolds Creek Critical Zone Observatory (CZO) station in Idaho. The variable importance assessment identified the leading drivers individually for evaporation, transpiration and ET (soil water content for evaporation, vapour pressure deficit for transpiration and soil water content for ET). The results further highlighted the value of combining hydrometeorological and biomass productivity variables to achieve better predictability of ET processes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Relationships between Cloud Droplet Spectral Relative Dispersion and Entrainment Rate and Their Impacting Factors

Cloud microphysical properties are significantly affected by entrainment and mixing processes. However, it is unclear how the entrainment rate affects the relative dispersion of cloud droplet size distribution. Previously, the relationship between relative dispersion and entrainment rate was found to be positive or negative. To reconcile the contrasting relationships, the Explicit Mixing Parcel Model is used to determine the underlying mechanisms. When evaporation is dominated by small droplets, and the entrained environmental air is further saturated during mixing, the relationship is negative. However, when the evaporation of big droplets is dominant, the relationship is positive. Whether or not the cloud condensation nuclei are considered in the entrained environmental air is a key factor as condensation on the entrained condensation nuclei is the main source of small droplets. However, if cloud condensation nuclei are not entrained, the relationship is positive. If cloud condensation nuclei are entrained, the relationship is dependent on many other factors. High vertical velocity, relative humidity of environmental air, liquid water content, and low droplet number concentration are more likely to cause the negative relationship since new saturation is easier to achieve by evaporation of small droplets. Further, the signs of the relationship are not strongly affected by the turbulence dissipation rate, but the higher dissipation rate causes the positive relationship more significant for a larger entrainment rate. A conceptual model is proposed to reconcile the contrasting relationships. This work enhances the understanding of relative dispersion and lays a foundation for the quantification of entrainment-mixing mechanisms.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Evapotranspiration Partitioning of Eucalyptus benthamii and Pinus taeda During Early Stand Development

Increasing demand for bioenergy from intensively managed woody crops raises concerns of increased evapotranspiration and potential decreases in water yield. Pinus taeda (loblolly pine) is currently the most cultivated species in the southeastern USA, the country’s wood basket. However, Eucalyptus species could achieve greater productivity but with unknown ramifications for water budgets. To address the knowledge gap, we determined annual water budgets of loblolly pine and Eucalyptus benthamii (eucalypt) from growing years 3 through 5 in a replicated (n = 3) two-factor design comparing species and groundwater depth. Paired plots were established across a depth-to-groundwater gradient from shallow (~ 2 m) to deep (~ 8 m). Hydrologic budgets were constructed by measuring precipitation, interception, soil evaporation, and transpiration. Eucalypt evapotranspiration and above-ground biomass production for growing years 3 through 5 were on average 25 and 14% greater than pine, respectively; however, evapotranspiration did not differ across groundwater depths. At the end of growing year 5, eucalypt had higher transpiration and evapotranspiration per unit area than pine. Soil evaporation was substantial in young plantations (nearly 500 mm) in growing year 3 but declined as the canopy closed. Partitioning of evapotranspiration components in developing bioenergy plantations was dynamic due to canopy development driven decreases in soil evaporation and increases in transpiration and interception; total evapotranspiration was less variable from year to year. Water use efficiency (WUE, kg biomass/m 3 H 2 O) per unit evapotranspiration was similar between species, but WUE per unit transpiration was higher in pine. As a result, considering total evapotranspiration in young plantations can affect WUE interpretations.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Modelling the interlayer bond strength of 3D printed concrete with surface moisture

Highlights: • An analytical model for interlayer adhesion of 3DPC is proposed based on the amount of surface moisture on the interlayer. • For this mix, the model accurately (RMSE=2.5%) predicts the reduction in interlayer adhesion from 30% to 50%. • Internal curing with superabsorbent polymers increases the interlayer adhesion by 10% and flexural strength by 19%. • SAPs also improve the initial thixotropy by 49% and buildability by 25% compared to the reference. Providing additional water to the hydrating cementitious particles is essential to achieve the optimal mechanical performance of the low w/b concrete mixes preferred for 3D printing. This study incorporates superabsorbent polymers (SAP) and additional water in 3D printed concrete (3DPC) to promote the hydration process through delayed internal water release. The study shows that a retentive SAP modifies the rheological development by absorbing the pore fluid for a short period after printing. The absorption-induced stiffening increases the thixotropy and buildability by 49% and 25%, respectively. A retentive SAP increases the flexural strength and interlayer adhesion by 19% and 10%, respectively. This is due to the internal water release that promotes hydration. Evaporation of the interlayer moisture during the pass time has the opposite effect— evaporation reduces the interlayer adhesion. Based on this assumption, an analytical model is proposed. The model accounts for the pass time, bleeding, and the environmental evaporation rate to estimate the surface moisture and predict the lack of interlayer adhesion. In this study, the model accurately (RMSE = 2.5%) predicted an interlayer adhesion reduction from 30% to 50%. The interlayer adhesion results of other studies could also be predicted.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Thin hybrid capillary two-phase cooling system

A novel hybrid two-phase cooling system was developed that integrated a mechanically pumped two-phase loop with a capillary-driven two-phase cooling device. The latter cooling mechanism was based on evaporation/boiling from wick structures made by sintering copper particles on the interior surfaces of a copper cold plate. The cold plate provided cooling to two surfaces and each of them included four heaters in series. The novelty of the developed technology was preventing flooding of the evaporator wicks by isolating the evaporation surface from the pumped liquid flow that fed them. This arrangement allowed for a high liquid feed flow rate much greater than would be allowed by a capillary pumped system while maintaining a low thermal resistance at the evaporation surface. Using this approach, the cooling system removed over 850 W with a low pumping power below 1.0 W while using R245fa as the working fluid. The equivalent heat fluxes exceeded 970 W/cm 2 over areas less than 0.12 cm 2 . The measured thermal resistance was as low as 0.09 K-cm 2 /W. The presented thermal management solution enables an increase in the power of high heat flux electronic devices beyond the state-of-the-art.

42 ENGINEERING↗
DOE OSTI2020

Combining Mass Spectrometry of Picoliter Samples with a Multicompartment Electrodynamic Trap for Probing the Chemistry of Droplet Arrays

Single droplet levitation provides contactless access to the microphysical and chemical properties of micrometer-sized samples. Most applications of droplet levitation to chemical and biological systems use nondestructive optical techniques to probe droplet properties. To provide improved chemical specificity, we coupled a multicompartment quadrupole electrodynamic trap (QET) with single droplet mass spectrometry. Our QET continuously traps a monodisperse droplet population (tens to hundreds of droplets) and allows for the simultaneous sizing of a single droplet using its Mie scattering pattern. Single droplets are subsequently ejected into the ionization region of an ambient pressure inlet mass spectrometer. We optimized two complementary soft ionization techniques for picoliter aqueous droplets: (1) paper spray (PS) ionization and (2) thermal desorption glow discharge (TDGD) ionization. Both techniques detect oxygenated organic acids in single droplets, with signal-to-noise ratios >100 and detection limits on the order of 10 pg. Sensitivity and reproducibility across single droplets are driven by the droplet deposition location and spray stability in PS-MS and the ionization region humidity and analyte evaporation rate in TDGD-MS. Importantly, the analyte evaporation rate can control the TDGD-MS quantitative capability because high evaporation rates result in significant ion suppression. Additionally, this effect is mitigated by optimizing the vaporization temperature, droplet size range, and analyte volatility. We demonstrate quantitative and reproducible measurements with a droplet internal standard (<10% RSD) and compare the sensitivity of PS-MS and TDGD-MS. Finally, we demonstrate the application of QET-MS to the study of heterogeneous chemical kinetics with the reaction of gas phase O 3 and aqueous maleic acid droplets.

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

Experiments on the Capillary Condensation/Evaporation Hysteresis of Pure Fluids and Binary Mixtures in Cylindrical Nanopores

Here, a new experimental method, i.e., isochoric cooling/heating cycle measurement using differential scanning calorimeter (DSC), is applied to investigate the hysteretic phenomenon of pure components and mixtures confined in two different types of cylindrical nanopores (SBA-15 and KIT-6). The capillary condensation/evaporation hysteresis end point (T he ) for a specific system is determined by performing a series of measurements with different densities by increasing initial temperature and pressure. We confirm that for a pure component, T he is lower when confined in smaller nanopores, whereas T he for CH 4 /CO 2 and CH 4 /C 2 H 6 mixtures at the specific composition investigated are higher than that of pure CO 2 and C 2 H 6 , respectively, when confined in the same nanopores. To the best of our knowledge, this is the first time that T he of fluid mixture is experimentally studied, which further demonstrates that binary mixtures behave similarly to pure fluids when confined in nanoporous media. At low temperatures where hysteresis is observed, the shape as well as the duration of the exothermic peak (due to capillary condensation) and endothermic peak (due to capillary evaporation) indicate that capillary condensation, rather than capillary evaporation, takes place at/near a thermodynamic equilibrium. Within the accuracy of the measurements, we find that the total heat of capillary condensation is identical to that of capillary evaporation for all systems examined, regardless of the presence of hysteresis. By comparing the heat per unit volume among different systems, we also find that the heat per unit volume of the phase transition of confined pure fluid is lower than that of bulk, which further demonstrates that the molar density of confined pure liquid is less than that of bulk pure liquid at saturation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Zero Liquid Discharge and Water Reuse in Recirculating Cooling Towers at Power Facilities: Review and Case Study Analysis

Zero liquid discharge (ZLD) systems installed at power facilities with the primary purpose of meeting water discharge regulations have the added benefit of providing high quality effluent that can be reused in the facility. This paper provides a review of water use in power sector recirculating cooling towers and a baseline assessment of on-site water reuse at natural gas combined cycle (NGCC) power facilities. Two NGCC facilities with reverse-osmosis (RO) or brine-concentrator processes followed by evaporation ponds were selected as case studies; data from these facilities were used to quantify the water, energy, and cost implications of implementing conventional and emerging ZLD technologies. At one case study facility, model results show that implementation of ZLD would reduce water withdrawals by 18%, which is less than savings associated with implementation of dry cooling but comparable to current efforts to reduce water withdrawals by increasing cycles of concentration. Implementation of ZLD using high-recovery RO resulted in a doubling of the levelized cost of water (LCOW). LCOW increased more when a brine concentrator was used. For both case studies, the ZLD system using high-recovery RO required less than 0.1% of a facilitiy's annual electricity generation and the ZLD system using a brine concentrator process required less than 0.8%. Additionally, increasing the evaporation pond area to minimize required ZLD system recovery rates and reduce system electricity costs does not reduce the LCOW. Instead, the LCOW increases because less water is recovered and more water is lost to evaporation. Furthermore, if water availability decreases or water competition/cost increases, facilities may be incentivized to maximize water recovery from ZLD systems.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2022

Modeling Solution Drying by Moving a Liquid-Vapor Interface: Method and Applications

A method of simulating the drying process of a soft matter solution with an implicit solvent model by moving the liquid-vapor interface is applied to various solution films and droplets. For a solution of a polymer and nanoparticles, we observe “polymer-on-top” stratification, similar to that found previously with an explicit solvent model. Furthermore, “polymer-on-top” is found even when the nanoparticle size is smaller than the radius of gyration of the polymer chains. For a suspension droplet of a bidisperse mixture of nanoparticles, we show that core-shell clusters of nanoparticles can be obtained via the “small-on-outside” stratification mechanism at fast evaporation rates. “Large-on-outside” stratification and uniform particle distribution are also observed when the evaporation rate is reduced. Polymeric particles with various morphologies, including Janus spheres, core-shell particles, and patchy particles, are produced from drying droplets of polymer solutions by combining fast evaporation with a controlled interaction between the polymers and the liquid-vapor interface. Our results validate the applicability of the moving interface method to a wide range of drying systems. The limitations of the method are pointed out and cautions are provided to potential practitioners on cases where the method might fail.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Environmental and economic analyses of chemical recycling via dissolution of waste polyethylene terephthalate

Globally, more than 1000 organizations and 175 nations are facing the plastic waste problem and have realized the need to transition from “linear-to-circular” economy of plastics. While the current mechanical recycling technologies for plastics are struggling to increase the U.S. plastic recycling rates beyond 9%, chemical recycling technologies become important complementary technologies to the predominant mechanical recycling that are needed to realize the circular economy in plastics supply chains. Dissolution is one such chemical recycling technology that can recycle waste plastic back into high-quality virgin grade plastic. However, the environmental and economic impacts of chemical recycling of waste polyethylene terephthalate (PET) via dissolution technology using a green solvent are unknown. Our study evaluated environmental metrics such as greenhouse gas (GHG) emissions and cumulative energy demand, and economic metrics such as net present value (NPV), minimum selling price, payback period, return on investment, and discounted internal rate of return for three dissolution processes with polymer recovery via anti-solvent, evaporation, and cooling precipitation techniques. The dissolution process with evaporation technique was the most economically favorable, whereas that with cooling technique was the most environmentally favorable. The anti-solvent approach had low economic performance and the highest environmental impacts. The NPV for all of these technologies ranged from $2.67 MM to $10.93 MM for a capacity of 8,400 MT/year and was found to be the highest for dissolution with evaporation approach and the least for anti-solvent approach. The cradle-to-gate GHG emissions and energy demand for PET dissolution processes ranged from 1.33-3.77 kg CO2-eq/kg of chemically recycled (CR) PET and18.9-56.1 MJ/kg of CR-PET, respectively. These economic and environmental metrics will be helpful in evaluating the sustainability of circular PET supply chains in the U.S.

09 BIOMASS FUELS↗
DOE OSTI2024

Iodine Modulates the MACl‐Assisted Growth of FAPbI 3 for High Efficiency Perovskite Solar Cells

The preferential growth of α-phase formamidinium perovskite (α-FAPbI 3 ) at low temperatures can be achieved with the incorporation of chloride-based additives, with methylammonium chloride (MACl) being the most common example. However, compared to other less-volatile chloride additives, MACl only remains in the growing perovskite film for a short time before evaporating during annealing, primarily influencing the early stages of film formation. In addition, evaporation of MACl as methylamine (MA 0 ) and HCl can introduce a side reaction between MA 0 and formamidinium (FA), undermining the compositional purity and phase stability of α-FAPbI 3 . In this study, it is demonstrated that addition of iodine (I 2 ) into the FAPbI 3 precursor solution containing MACl suppresses the MA-FA side reaction during annealing. Additionally, MACl evaporation is delayed owing to strong interaction with triiodide. The added I 2 facilitates spontaneous growth of α-FAPbI 3 prior to annealing, with an improved bottom morphology due to the formation of fewer byproducts. Perovskite solar cells derived from an I 2 -incorporated solution deliver a champion power conversion efficiency of 25.2% that is attributed to suppressed non-radiative recombination.

14 SOLAR ENERGY↗
DOE OSTI2021

A dynamical mechanism for the Page curve from quantum chaos

If the evaporation of a black hole formed from a pure state is unitary, the entanglement entropy of the Hawking radiation should follow the Page curve, increasing from zero until near the halfway point of the evaporation, and then decreasing back to zero. The general argument for the Page curve is based on the assumption that the quantum state of the black hole plus radiation during the evaporation process is typical. In this paper, we show that the Page curve can result from a simple dynamical input in the evolution of the black hole, based on a recently proposed signature of quantum chaos, without resorting to typicality. Our argument is based on what we refer to as the “operator gas” approach, which allows one to understand the evolution of the microstate of the black hole from generic features of the Heisenberg evolution of operators. One key feature which leads to the Page curve is the possibility of dynamical processes where operators in the “gas” can “jump” outside the black hole, which we refer to as void formation processes. Such processes are initially exponentially suppressed, but dominate after a certain time scale, which can be used as a dynamical definition of the Page time. In the Hayden-Preskill protocol for young and old black holes, we show that void formation is also responsible for the transfer of information from the black hole to the radiation. We conjecture that void formation may provide a microscopic explanation for the recent semi-classical prescription of including islands in the calculation of the entanglement entropy of the radiation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

On quantum information before the Page time

While recent progress in the black hole information problem has shown that the entropy of Hawking radiation follows a unitary Page curve, the quantum state of Hawking radiation prior the Page time is still treated as purely thermal, containing no information about the microstructure of the black hole. We demonstrate that there is significant quantum information regarding the quantum state of the black hole in the Hawking radiation prior to the Page time. By computing of the quantum fidelity in a 2D boundary conformal field theory (BCFT) model of black hole evaporation, we demonstrate that an observer outside of an evaporating black hole may distinguish different black holes via measurements of the Hawking radiation at any time during the evaporation process, albeit with an exponentially large number of measurements. Furthermore, our results are universal, applicable to general BCFTs including those with large central charge and rational BCFTs. The techniques we develop for computing the fidelity are more generally applicable to excited states in CFT. As such, we are able to characterize more general aspects of thermalization in 2D conformal field theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Entanglement wedge reconstruction and the information paradox

When absorbing boundary conditions are used to evaporate a black hole in AdS/CFT, we show that there is a phase transition in the location of the quantum Ryu-Takayanagi surface, at precisely the Page time. The new RT surface lies slightly inside the event horizon, at an infalling time approximately the scrambling time β/2 π logS BH into the past. We can immediately derive the Page curve, using the Ryu-Takayanagi formula, and the Hayden-Preskill decoding criterion, using entanglement wedge reconstruction. Because part of the interior is now encoded in the early Hawking radiation, the decreasing entanglement entropy of the black hole is exactly consistent with the semiclassical bulk entanglement of the late-time Hawking modes, despite the absence of a firewall.By studying the entanglement wedge of highly mixed states, we can understand the state dependence of the interior reconstructions. A crucial role is played by the existence of tiny, non-perturbative errors in entanglement wedge reconstruction. Directly after the Page time, interior operators can only be reconstructed from the Hawking radiation if the initial state of the black hole is known. As the black hole continues to evaporate, reconstructions become possible that simultaneously work for a large class of initial states. Using similar techniques, we generalise Hayden-Preskill to show how the amount of Hawking radiation required to reconstruct a large diary, thrown into the black hole, depends on both the energy and the entropy of the diary. Finally we argue that, before the evaporation begins, a single, state-independent interior reconstruction exists for any code space of microstates with entropy strictly less than the Bekenstein-Hawking entropy, and show that this is sufficient state dependence to avoid the AMPSS typical-state firewall paradox.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗