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All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

High Strength and Deformation Mechanisms of A l0.3 CoCrFeNi High-Entropy Alloy Thin Films Fabricated by Magnetron Sputtering

Recently, high-entropy alloy thin films (HEATFs) with nanocrystalline structures and high hardness were developed by magnetron sputtering technique and have exciting potential to make small structure devices and precision instruments with sizes ranging from nanometers to micrometers. However, the strength and deformation mechanisms are still unclear. In this work, nanocrystalline Al0.3CoCrFeNi HEATFs with a thickness of ~4 μm were prepared. The microstructures of the thin films were comprehensively characterized, and the mechanical properties were systematically studied. It was found that the thin film was smooth, with a roughness of less than 5 nm. The chemical composition of the high entropy alloy thin film was homogeneous with a main single face-centered cubic (FCC) structure. Furthermore, it was observed that the hardness and the yield strength of the high-entropy alloy thin film was about three times that of the bulk samples, and the plastic deformation was inhomogeneous. Our results could provide an in-depth understanding of the mechanics and deformation mechanism for future design of nanocrystalline HEATFs with desired properties.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Entropy and Gravitation—From Black Hole Computers to Dark Energy and Dark Matter

We show that the concept of entropy and the dynamics of gravitation provide the linchpin in a unified scheme to understand the physics of black hole computers, spacetime foam, dark energy, dark matter and the phenomenon of turbulence. We use three different methods to estimate the foaminess of spacetime, which, in turn, provides a back-door way to derive the Bekenstein-Hawking formula for black hole entropy and the holographic principle. Generalizing the discussion for a static spacetime region to the cosmos, we find a component of dark energy (resembling an effective positive cosmological constant of the correct magnitude) in the current epoch of the universe. The conjunction of entropy and gravitation is shown to give rise to a phenomenological model of dark matter, revealing the natural emergence, in galactic and cluster dynamics, of a critical acceleration parameter related to the cosmological constant; the resulting mass profiles are consistent with observations. Unlike ordinary matter, the quanta of the dark sector are shown to obey infinite statistics. This property of dark matter may lead to some non-particle phenomenology and may explain why dark matter particles have not been detected in dark matter search experiments. We also show that there are deep similarities between the problem of “quantum gravity” (more specifically, the holographic spacetime foam) and turbulence.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Quantifying Information without Entropy: Identifying Intermittent Disturbances in Dynamical Systems

A system’s response to disturbances in an internal or external driving signal can be characterized as performing an implicit computation, where the dynamics of the system are a manifestation of its new state holding some memory about those disturbances. Identifying small disturbances in the response signal requires detailed information about the dynamics of the inputs, which can be challenging. This paper presents a new method called the Information Impulse Function (IIF) for detecting and time-localizing small disturbances in system response data. The novelty of IIF is its ability to measure relative information content without using Boltzmann’s equation by modeling signal transmission as a series of dissipative steps. Since a detailed expression of the informational structure in the signal is achieved with IIF, it is ideal for detecting disturbances in the response signal, i.e., the system dynamics. Those findings are based on numerical studies of the topological structure of the dynamics of a nonlinear system due to perturbated driving signals. The IIF is compared to both the Permutation entropy and Shannon entropy to demonstrate its entropy-like relationship with system state and its degree of sensitivity to perturbations in a driving signal.

42 ENGINEERING↗
DOE OSTI2019

Relative entropy minimization over Hilbert spaces via Robbins-Monro

One way of getting insight into non-Gaussian measures is to first obtain good Gaussian approximations. These best fit Gaussians can then provide a sense of the mean and variance of the distribution of interest. They can also be used to accelerate sampling algorithms. This begs the question of how one should measure optimality, and how to then obtain this optimal approximation. Here, we consider the problem of minimizing the distance between a family of Gaussians and the target measure with respect to relative entropy, or Kullback-Leibler divergence. As we are interested in applications in the infinite dimensional setting, it is desirable to have convergent algorithms that are well posed on abstract Hilbert spaces. We examine this minimization problem by seeking roots of the first variation of relative entropy, taken with respect to the mean of the Gaussian, leaving the covariance fixed. We prove the convergence of Robbins-Monro type root finding algorithms in this context, highlighting the assumptions necessary for convergence to relative entropy minimizers. Numerical examples are included to illustrate the algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

High-entropy alloy screening for halide perovskites

We demonstrate the new concept of using unit cell volume coefficient of variation to approximate the enthalpic penalty of high-entropy alloy (HEA) candidates, and use it along with configurational entropy to map promising HEA halide perovskites.

14 SOLAR ENERGY↗
DOE OSTI2021

Universal entropy and hawking radiation of near-extremal AdS4 black holes

We compute the Bekenstein-Hawking entropy of near-extremal asymptotically AdS 4 electrically charged rotating black holes using three different methods: (i) from the gravity solution, (ii) from the near-horizon Kerr/CFT correspondence and (iii) from the boundary conformal field theory. The results from these three different approaches match exactly, giving us a unique and universal expression for the entropy and the microstate counting of near-extremal AdS black holes via the AdS/CFT correspondence. In the second method, we extend the Kerr/CFT correspondence to the near-extremal case to compute the left and right central charges. We also use hidden conformal symmetry of the near-horizon geometry to compute the Frolov-Thorne temperatures. From the results of the near-extremal AdS 4 black hole entropy, we provide a microscopic foundation for Hawking radiation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Logarithmic corrections to the entropy of rotating black holes and black strings in AdS 5

We investigate logarithmic corrections to the entropy of supersymmetric, rotating, asymptotically AdS 5 black holes and black strings. Within the framework of the AdS/CFT correspondence, the entropy of these black objects is determined, on the field theory side, by the superconformal index and the refined topologically twisted index of $\mathcal{N}$ = 4 supersymmetric Yang-Mills theory, respectively. We read off the logarithmic correction from those field-theoretic partition functions. On the gravity side, we take the near-horizon limit and apply the Kerr/CFT correspondence whose associated charged Cardy formula describes the degeneracy of states at subleading order and determines the logarithmic correction to the entropy. We find perfect agreement between these two approaches. Our results provide a window into precision microstate counting and demonstrate the efficacy of low-energy, symmetry-based approaches such as the Kerr/CFT correspondence for asymptotically AdS black objects under certain conditions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Thermal Bekenstein-Hawking entropy from the worldsheet

We define and compute the leading sphere diagram contribution to the entropy of the BTZ black hole supported by Kalb-Ramond flux in bosonic string theory. In a winding condensate description, integrating exactly over the constant mode for the radial direction of AdS 3 reduces the problem to one of the correlation functions of winding operators in the free theory. The volume of the residual PSL(2,ℂ) gauge group of the sphere is canceled by the action of conformal transformations on the winding interaction insertions. We formulate a precise version of the replica trick in terms of (infinitesimally) non-integer winding condensates to produce the entropy of the BTZ black hole. The resulting entropy can be calculated from the one-point function of a non-local operator on the worldsheet.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

The Page curve for reflected entropy

We study the reflected entropy $S_{R}$ in the West Coast Model, a toy model of black hole evaporation consisting of JT gravity coupled to end-of-the-world branes. We demonstrate the validity of the holographic duality relating it to the entanglement wedge cross section away from phase transitions. Further, we analyze the important non-perturbative effects that smooth out the discontinuity in the phase transition. By performing the gravitational path integral, we obtain the reflected entanglement spectrum analytically. The spectrum takes a simple form consisting of superselection sectors, which we interpret as a direct sum of geometries, a disconnected one and a connected one involving a closed universe. We find that area fluctuations of $\textit{O}$$\sqrt{G_N}$ spread out the $S_{R}$ phase transition in the canonical ensemble, analogous to the entanglement entropy phase transition. We also consider a Renyi generalization of the reflected entropy and show that the location of the phase transition varies as a function of the Renyi parameter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Local quenches, bulk entanglement entropy and a unitary Page curve

Quantum corrections to the entanglement entropy of matter fields interacting with dynamical gravity have proven to be very important in the study of the black hole information problem. We consider a one-particle excited state of a massive scalar field infalling in a pure AdS 3 geometry and compute these corrections for bulk subregions anchored on the AdS boundary. In the dual CFT 2 , the state is given by the insertion of a local primary operator and its evolution thereafter. We calculate the area and bulk entanglement entropy corrections at order $$ \mathcal{O}\left({N}^0\right), $$ O N 0 , both in AdS and its CFT dual. The two calculations match, thus providing a non-trivial check of the FLM formula in a dynamical setting. Further, we observe that the bulk entanglement entropy follows a Page curve. We explain the precise sense in which our setup can be interpreted as a simple model of black hole evaporation and comment on the implications for the information problem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Higher-derivative corrections to entropy and the weak gravity conjecture in Anti-de Sitter space

We compute the four-derivative corrections to the geometry, extremality bound, and thermodynamic quantities of AdS-Reissner-Nordström black holes for general dimensions and horizon geometries. We confirm the universal relationship between the extremality shift at fixed charge and the shift of the microcanonical entropy, and discuss the consequences of this relation for the Weak Gravity Conjecture in AdS. The thermodynamic corrections are calculated using two different methods: first by explicitly solving the higher-derivative equations of motion and second, by evaluating the higher-derivative Euclidean on-shell action on the leading-order solution. In both cases we find agreement, up to the addition of a Casimir energy in odd dimensions. We derive the bounds on the four-derivative Wilson coefficients implied by the conjectured positivity of the leading corrections to the microcanonical entropy of thermodynamically stable black holes. These include the requirement that the coefficient of Riemann-squared is positive, meaning that the positivity of the entropy shift is related to the condition that c – a is positive in the dual CFT. We discuss implications for the deviation of η/s from its universal value and a potential lower bound.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Effective action for relativistic hydrodynamics: fluctuations, dissipation, and entropy inflow

We present a detailed and self-contained analysis of the universal SchwingerKeldysh effective field theory which describes macroscopic thermal fluctuations of a relativistic field theory, elaborating on our earlier construction. We write an effective action for appropriate hydrodynamic Goldstone modes and fluctuation fields, and discuss the symmetries to be imposed. The constraints imposed by fluctuation-dissipation theorem are manifest in our formalism. Consequently, the action reproduces hydrodynamic constitutive relations consistent with the local second law at all orders in the derivative expansion, and captures the essential elements of the eightfold classification of hydrodynamic transport of. We demonstrate how to recover the hydrodynamic entropy and give predictions for the non-Gaussian hydrodynamic fluctuations. The basic ingredients of our construction involve (i) doubling of degrees of freedom a la Schwinger-Keldysh, (ii) an emergent gauge U(1) T symmetry associated with entropy which is encapsulated in a Noether current a la Wald, and (iii) a BRST/topological supersymmetry imposing the fluctuation-dissipation theorem a la Parisi-Sourlas. The overarching mathematical framework for our construction is provided by the balanced equivariant cohomology of thermal translations, which captures the basic constraints arising from the Schwinger-Keldysh doubling, and the thermal Kubo-Martin-Schwinger relations. All these features are conveniently implemented in a covariant superspace formalism. An added benefit is that the second law can be understood as being due to entropy inflow from the Grassmann-odd directions of superspace.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

The Markov gap for geometric reflected entropy

The reflected entropy S R (A : B) of a density matrix ρ AB is a bipartite correlation measure lower-bounded by the quantum mutual information I(A : B). In holographic states satisfying the quantum extremal surface formula, where the reflected entropy is related to the area of the entanglement wedge cross-section, there is often an order-N 2 gap between S R and I. We provide an information-theoretic interpretation of this gap by observing that S R - I is related to the fidelity of a particular Markov recovery problem that is impossible in any state whose entanglement wedge cross-section has a nonempty boundary; for this reason, we call the quantity S R - I the Markov gap. We then prove that for time-symmetric states in pure AdS 3 gravity, the Markov gap is universally lower bounded by log(2)ℓ AdS /2G N times the number of endpoints of the cross-section. We provide evidence that this lower bound continues to hold in the presence of bulk matter, and comment on how it might generalize above three bulk dimensions. Finally, we explore the Markov recovery problem controlling S R - I using fixed area states. This analysis involves deriving a formula for the quantum fidelity — in fact, for all the sandwiched Rényi relative entropies — between fixed area states with one versus two fixed areas, which may be of independent interest. We discuss, throughout the paper, connections to the general theory of multipartite entanglement in holography.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Absolute entropy and the observer’s no-boundary state

We investigate the no-boundary proposal for closed universes with an observer. We argue that the observer’s no-boundary state is the identity operator on the physical Hilbert space, i.e., the maximum entropy state and show this explicitly in Jackiw-Teitelboim gravity. Geometrically, the no-boundary state is a bra-ket wormhole. Expectation values in the no-boundary state provide a trace for the observer’s algebra, which allows one to define von Neumann entropy for observers in different universes as the relative entropy with respect to the no-boundary state. This result is consistent with all previously discussed cases of traces for invariantly defined regions.

Cosmological models↗
DOE OSTI2025

On the completeness of contraction map proof method for holographic entropy inequalities

The contraction map proof method is the commonly used method to prove holographic entropy inequalities. Existence of a contraction map corresponding to a holographic entropy inequality is a sufficient condition for its validity. But is it also necessary? In this note, we answer that question in affirmative for all linear holographic entropy inequalities with rational coefficients. We show that the pre-image of a non-contraction map is not a hypercube, but a proper cubical subgraph, and show that this manifests as alterations to the geodesic structure in the bulk, which leads to the violation of inequalities by holographic geometries obeying the RT formula.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Variational approach to relative entropies with an application to QFT

Abstract We define a new divergence of von Neumann algebras using a variational expression similar in nature to Kosaki’s formula for Umegaki’s relative entropy. Our divergence satisfies several of the usual desirable properties, upper bounds the sandwiched Renyi entropy and reduces to the fidelity in a limit. As an illustration, we use the formula in quantum field theory to compute our divergence between the vacuum in a bipartite system and an “orbifolded”—in the sense of a conditional expectation—system in terms of the Jones index. We take the opportunity to point out an entropic certainty relation associated with an inclusion of von Neumann factors related to the relative entropy. This certainty relation has an equivalent formulation in terms of error correcting codes.

Hollands, Stefan↗
DOE OSTI2019

Effect of Cobalt Content on Thermal, Mechanical, and Microstructural Properties of Al{sub 0.4}FeCrNiCo{sub x} (x = 0, 0.25, 0.5, 1.0 mol) High-Entropy Alloys

Al{sub 0.4}FeCrNiCo{sub x} (x = 0, 0.25, 0.5, 1.0 mol) high-entropy alloys are developed by arc melting route to investigate the effect of cobalt content on thermal, mechanical, and microstructural properties. The phase, microstructure, and chemical composition are analyzed using x-ray diffraction, transmission electron microscope, and scanning electron microscope with attached energy-dispersive x-ray spectrometer. The obtained results have shown that the Al{sub 0.4}FeCrNiCo{sub x} (x = 0-0.5 mol) high-entropy alloys form a simple FCC + BCC-type solid solution and Al{sub 0.4}FeCrNiCo{sub x=1} HEA forms a single-phase FCC structure. The compressive yield strength, microhardness, and thermal conductivity are observed to decrease from 965.22 to 233.37 MPa, 253.6 to 155.6 HV, and from 4.87 to 2.674 W/mK, respectively, whereas the electrical resistivity is observed to increase from 150.30 to 273.74 µΩ-cm with the addition of cobalt from x = 0-1 mol. Differential scanning calorimetry analysis has indicated that the Al{sub 0.4}FeCrNiCo{sub x} (x = 0, 0.25, 0.5, 1.0 mol) high-entropy alloys are thermally stable up to 1000 °C.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Off-policy deep reinforcement learning with automatic entropy adjustment for adaptive online grid emergency control

Electric overloading conditions and contingencies put modern power systems at risk of voltage collapse and blackouts. Load shedding is crucial to maintain voltage stability for grid emergency control. However, the rule- or model-based schemes rely on accurate dynamic system models and face considerable challenges in adapting to various operating conditions and uncertain event occurrences. Here, to address these issues, this paper proposes a novel deep reinforcement learning (DRL)-based voltage stability control algorithm with automatic entropy adjustment (AEA) for grid emergency control. Various dynamic network components for complex system operations are modeled to construct the DRL environment. An off-policy soft actor-critic architecture is developed to maximize the expected reward and policy entropy simultaneously. The AEA mechanism is proposed to facilitate the policy maximum entropy procedure, and the proposed method can automatically provide effective discrete and continuous actions against various fault scenarios. Our approach accomplishes high sampling efficiency, scalability, and auto-adaptivity of the control policies under high uncertainties. Comparative studies with the existing DRL-based control methods in IEEE benchmarks indicate salient performance improvement of the proposed method for dynamic system emergency control.

24 POWER TRANSMISSION AND DISTRIBUTION↗