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At least 523 records · Page 29

Multipartite reflected entropy

We discuss two methods that, through a combination of cyclically gluing copies of a given n-party boundary state in AdS/CFT and a canonical purification, creates a bulk geometry that contains a boundary homologous minimal surface with area equal to 2 or 4 times the n-party entanglement wedge cross-section, depending on the parity of the party number and choice of method. The areas of the minimal surfaces are each dual to entanglement entropies that we define to be candidates for the n-party reflected entropy. In the context of AdS 3 /CFT 2 , we provide a boundary interpretation of our construction as a multiboundary wormhole, and conjecture that this interpretation generalizes to higher dimensions.

97 MATHEMATICS AND COMPUTING↗

The first heat: production of entanglement entropy in the early universe

Entanglement entropy (EE) of a spatial region quantifies correlations between the region and its surroundings. For a free scalar in the adiabatic vacuum in de Sitter space the EE is known to remain low, scaling as the surface area of the region. Here, we study the evolution of entanglement after the universe transitions from de Sitter to flat space. We concentrate on the case of a massless minimally coupled scalar. We find numerically that, after the de Sitter stage ends, the EE and the R´enyi entropy rapidly grow and saturate at values obeying the volume law. The final state of the subsystem (region) is a partially thermalized state reminiscent of a generalized Gibbs ensemble. We comment on application of our results to the question of when and how cosmological perturbations decohere.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Gravitational Cardy limit and AdS black hole entropy

We explore the gravitational implementation of the field theory Cardy-like limit recently used in the successful microstate countings of AdS black hole entropy in various dimensions. On the field theory side, the Cardy-like limit focuses on a particular scaling of conserved electric charges and angular momenta and we first translate this scaling to the gravitational side by a limiting procedure on the black hole parameters. We note that the scaling naturally accompanies a near-horizon region for which these black hole solutions are greatly simplified. Applying the Kerr/CFT correspondence to the near-horizon region, we precisely reproduce the Bekenstein-Hawking entropy of asymptotically AdS 4,5,6,7 BPS black holes. Our results explicitly provide a microscopic and universal low energy description for AdS black holes across various dimensions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Reflected entropy in random tensor networks. Part III. Triway cuts

For general random tensor network states at large bond dimension, we prove that the integer Rényi reflected entropies (away from phase transitions) are determined by minimal triway cuts through the network. This generalizes the minimal cut description of bipartite entanglement for these states. A natural extrapolation away from integer Rényi parameters, suggested by the triway cut problem, implies the holographic conjecture S R = 2EW, where S R is the reflected entropy and EW is the entanglement wedge cross-section. Minimal triway cuts can be formulated as integer programs which cannot be relaxed to find a dual maximal flow/bit-thread description. This sheds light on the gap between the existence of tripartite entanglement in holographic states and the bipartite entanglement structure motivated by bit-threads. In particular, we prove that the Markov gap that measures tripartite entanglement is lower bounded by the integrality gap of the integer program that computes the triway cut.

AdS-CFT correspondence↗

Cluster Variation Method Analysis of Correlations and Entropy in BCC Solid Solutions

Solid solutions occur when multiple chemical species share sites of a common crystal lattice. Although the single site occupation is random, chemical interaction preferences bias the occupation probabilities of neighboring sites, and this bias reduced the entropy of mixing below its ideal value. Sufficiently strong bias leads to symmetry-breaking phase transitions. Here, we apply the cluster variation method to explore solid solutions on body centered cubic lattices in the context of two specific compounds that exhibit opposite ordering trends. Employing density functional theory to model the energetics, we show that CuZn exhibits an order-disorder transition to the CsCl prototype structure, while AlLi instead takes the NaTl prototype structure, and we evaluate their temperature-dependent order parameters, correlations and entropies.

36 MATERIALS SCIENCE↗

Effect of Strain Rate on the Tensile Behavior of CoCrFeNi and CoCrFeMnNi High-Entropy Alloys

High-entropy alloys (HEAs), a novel class of metal alloys, have been receiving increasing attention from the scientific community. HEAs have the potential to be used in critical load-bearing applications in replacement of conventional alloys such as stainless steel and nickel-base superalloys. Tensile experiments at quasi-static to dynamic strain rates (10{sup −4}-10{sup 3} s{sup −1}) were performed on two single-phase face-centered cubic HEAs, CoCrFeNi and CoCrFeMnNi. Electron backscatter diffraction was used to study the microstructure of the samples before the experiments, and transmission electron microscopy was performed postmortem. The dominant deformation mechanisms were dislocation slip at quasi-static strain rates with the addition of deformation nano-twins at dynamic strain rates. Ultimate dynamic tensile strength and ductility improved with the increase in strain rate, which can be attributed to the activation of deformation nano-twins in HEAs. CoCrFeNi and CoCrFeMnNi both have low stacking fault energies, which could promote twinning at high strain rates to accommodate plastic deformation. The strain rate sensitivity of the flow stress increased with increasing strain rate, beginning with negligible strain rate sensitivity in the quasi-static range to high strain rate sensitivity in the dynamic range. CoCrFeMnNi showed greater strain rate sensitivity of flow stress. CoCrFeNi, with less configurational entropy, had higher mechanical properties and strain-hardening rates compared to CoCrFeMnNi, which was attributed to the weakening effect of the addition of Mn on the solid solution hardening.

36 MATERIALS SCIENCE↗

First-principles study, fabrication and characterization of (Zr 0.25 Nb 0.25 Ti 0.25 V 0.25 )C high-entropy ceramics

The formation possibility of a new (Zr 0.25 Nb 0.25 Ti 0.25 V 0.25 )C high-entropy ceramics (ZHC-1) was first analyzed by the first-principles calculations and thermodynamical analysis and then it was successfully fabricated by hot pressing sintering technique. The first-principles calculation results showed that the mixing enthalpy of ZHC-1 was 5.526 kJ/mol and the mixing entropy of ZHC-1 was in the range of 0.693R–1.040R. The thermodynamical analysis results showed that ZHC-1 was thermodynamically stable above 959 K owing to its negative mixing Gibbs free energy. The experimental results showed that the as-prepared ZHC-1 (95.1% relative density) possessed a single rock-salt crystal structure, some interesting nano-plate-like structures, and high compositional uniformity from nanoscale to microscale. By taking advantage of these unique features, compared with the initial metal carbides (ZrC, NbC, TiC and VC), it showed a relatively low thermal conductivity of 15.3 ± 0.3 W/(m·K) at room temperature, which was due to the presence of solid solution effects, nanoplates and porosity. Meanwhile, it exhibited the relatively high nanohardness of 30.3 ± 0.7 GPa and elastic modulus of 460.4 ± 19.2 GPa and the higher fracture toughness of 4.7 ± 0.5 MPam 1/2 , which were attributed to the solid solution strengthening mechanism and nanoplate pullout and microcrack deflection toughening mechanism.

36 MATERIALS SCIENCE↗

High entropy alloys: A focused review of mechanical properties and deformation mechanisms

The high-entropy alloy (HEA) concept was based on the idea that high mixing entropy can promote formation of stable single-phase microstructures. During the past 15 years, various alloy systems have been explored to identify HEA systems with improved property combinations, leading to an extraordinary growth of this field. In the large pool of alloys with varying characteristics, the first single-phase HEA with good tensile properties, the equiatomic CrMnFeCoNi alloy has become the benchmark material, and it forms the basis of much of our current fundamental understanding of HEA mechanical behavior. As the field is evolving to the more broadly defined complex concentrated alloys (CCAs) and the available data in the literature increase exponentially, a fundamental question remains unchanged: how special are these new materials? In the first part of this review, select mechanical properties of HEAs and CCAs are compared with those of conventional engineering alloys. This task is difficult because of the limited tensile data available for HEAs and CCAs. Additionally, the wider suite of mechanical properties needed to assess structural materials is woefully lacking. Nonetheless, our evaluations have not revealed many HEAs or CCAs with properties far exceeding those of conventional engineering alloys, although specific alloys can show notable enhancements in specific properties. Consequently, it is reasonable to first approach the understanding of HEAs and CCAs through the assessment of how the well-established deformation mechanisms in conventional alloys operate or are modified in the presence of the high local complexity of the HEAs and CCAs. The second part of the paper provides a detailed review of the deformation mechanisms of HEAs with the FCC and BCC structures. For the former, we chose the CrMnFeCoNi (Cantor) alloy because it is the alloy on which the most rigorous and thorough investigations have been performed and, for the latter, we chose the TiZrHfNbTa (Senkov) alloy because this is one of the few refractory HEAs that exhibits any tensile ductility at room temperature. As expected, our review shows that the fundamental deformation mechanisms in these systems, and their dependence on basic physical properties, are broadly similar to those of conventional FCC and BCC metals. The third part of this review examines the theoretical and modeling efforts to date that seek to provide either qualitative or quantitative understanding of the mechanical performance of FCC and BCC HEAs. Since experiments reveal no fundamentally new mechanisms of deformation, this section starts with an overview of modeling perspectives and fundamental considerations. Next, the review turns to the evolution of modeling and predictions as compared to recent experiments, highlighting both successes and limitations. Finally, in spite of some significant successes, important directions for further theory development are discussed. Overall, while the individual deformation mechanisms or properties of the HEAs and CCAs are not, by and large, “special” relative to conventional alloys, the present HEA rush remains valuable because the compositional freedom that comes from the multi-element space will allow exploration of whether multiple mechanisms can operate sequentially or simultaneously, which may yet lead to the creation of new alloys with a spectrum of mechanical properties that are significantly superior to those of current engineering alloys.

36 MATERIALS SCIENCE↗

Vacancy-mediated complex phase selection in high entropy alloys

Phase selection in Ti-Zr-Hf-Al high-entropy alloys was investigated by in-situ high-energy x-ray diffraction, single-crystal x-ray diffraction, and KKR-CPA electronic-structure methods that address disorder and vacancies, predicting formation enthalpy and chemical short-range order (SRO). Samples with varying Al content were synthesized, characterized, and computationally assessed to ascertain the composition-dependent phase selection, as increased Al content often acts as a stabilizer of a body-centered-cubic structure. Equiatomic TiZrHfAl was especially interesting due to its observed bcc superstructure – a variant of γ-brass with 4 vacancies per cell (not 2 as in γ-brass). We highlight how vacancy ordering mediates selection of this variant of γ-brass, which is driven by vacancy-atom SRO that dramatically suppress all atomic SRO. As vacancies are inherent in processing refractory systems, we expect that similar discoveries await in other high entropy alloys or in revisiting older experimental data.

36 MATERIALS SCIENCE↗

Entanglement entropy and non-local duality: Quantum channels and quantum algebras

Here, we investigate the transformation of entanglement entropy under dualities, using the Kramers–Wannier duality present in the transverse field Ising model as our example. Entanglement entropy between local spin degrees of freedom is not generically preserved by the duality; instead, entangled states may be mapped to states with no local entanglement. To understand the fate of this entanglement, we consider two quantitative descriptions of degrees of freedom and their transformation under duality. The first involves Kraus operators implementing the partial trace as a quantum channel, while the second utilizes the algebraic approach to quantum mechanics, where degrees of freedom are encoded in subalgebras. Using both approaches, we show that entanglement of local degrees of freedom is not lost; instead it is transferred to non-local degrees of freedom by the duality transformation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Fracture resistance of high entropy alloys: A review

Fascinated by the exceptional mechanical properties of high entropy alloys (HEAs), unremitting endeavors are placed on accelerating their engineering applications in multiple critical fields. As all other structural materials, attaining sufficient fracture resistance is a vital requirement for HEAs, particularly for safety critical applications. Along this line, the fracture resistance of a number of HEAs and medium-entropy alloys (MEAs) had been studied in the past decade. While some exhibit unprecedented fracture toughness akin to the toughest materials ever known, others are just alike brittle materials. Herein, we summarize one decade of investigations of the fracture resistance of HEAs and MEAs, including the characterization of fracture toughness, disclosure of fractographic characteristics, and understanding of fracture micro-mechanisms. The role of alloy composition, temperature, phase constituent, and characterization techniques in altering the fracture toughness are discussed; characteristics of the cleavage and shear fractures are detailed; toughening and weakening mechanisms, from the atomic to the defect level, are reviewed. In conclusion, some key questions are raised, and the directions for future research are suggested.

36 MATERIALS SCIENCE↗

High entropy alloys with hexagonal close-packed structure derived from thin film combinatorial approach

A thin film combinatorial synthesis approach was utilized to develop a compositional and structural library for the OsRuWCo alloy system. The survey of this alloy space produced 24 unique compositions and their corresponding crystal structures, which represent a phase map where amorphous and single-phase hexagonal close-packed alloys were identified. Based on the identification of a promising candidate film region, a new high entropy alloy based on OsRuWCo, but with non-equiatomic composition, was synthesized in bulk form. The alloy exhibited a single-phase hexagonal close-packed structure in the as-cast state. Three derivatives from this system were also developed by considering the heat of mixing, atomic size, and binary solubility. These new alloys are based on OsRuWCoIr and OsRuWCoFe, both of which exhibit single-phase hexagonal close-packed as-cast structures, as determined by X-ray diffraction and electron microscopy. Additionally, this large compositional space was utilized to evaluate conventional parameters that describe high entropy alloys (ΔS mix , ΔH mix , Ω, δ, and VEC), and these were found to elucidate the criteria for solid solution formation in this system. Additionally, trends illustrating the evolution from amorphous to crystalline phases are demonstrated and discussed. It is concluded that in this particular case, the dominant factors promoting crystallinity are thermodynamic or electronic, rather than geometric.

36 MATERIALS SCIENCE↗

Coverage, repulsion, and reactivity of hydrogen on High-Entropy alloys

Modeling hydrogen evolution reaction (HER) activity probability on IrPdPtRhRu(1 1 1) high-entropy alloys. Determining hydrogen coverages based on ligand effects and generalized hydrogen–hydrogen repulsion. The rate of H 2 formation is highly impacted by the level of hydrogen coverage on the catalyst surface. In search of optimal catalytic properties high-entropy alloys (HEA) are promising candidates that utilize the compositional space of multiple elements. Based on simulations of HEA model (1 1 1) surfaces with a range of hydrogen coverages, distributions of binding energies are used to construct a framework that approximates the probability that adsorbed hydrogen may lead to the formation of H 2 as a function of applied potential. By optimizing the alloy compositions for the highest activity probability at given potentials the best and most efficient catalyst candidates for HER can be identified. Treating hydrogen–hydrogen repulsion effects and binding energy separately, we find that the repulsion is larger for HEAs than for pure metals. Differing isotherm slopes in the mean adsorption and desorption energies demonstrate a possible hysteresis for hydrogen adsorption on HEAs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Entropy-based closure for probabilistic learning on manifolds

In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization from a non-Gaussian random vector. The manifold structure is learned using diffusion manifolds and the statistical sample generation is accomplished using a projected Itˆo stochastic differential equation. This probabilistic learning approach has been extended to polynomial chaos representation of databases on manifolds and to probabilistic nonconvex constrained optimization with a fixed budget of function evaluations. The methodology introduces an isotropic-diffusion kernel with hyperparameter ". Currently, " is more or less arbitrarily chosen. In this paper, we propose a selection criterion for identifying an optimal value of ", based on a maximum entropy argument. The result is a comprehensive, closed, probabilistic model for characterizing data sets with hidden constraints. This entropy argument ensures that out of all possible models, this is the one that is the most uncertain beyond any specified constraints, which is selected. Applications are presented for several databases.

97 MATHEMATICS AND COMPUTING↗

High-entropy materials: fundamentals and applications

Metallic high-entropy materials (HEMs), also known as high-entropy alloys (HEAs), are an exotic class of materials that possess desirable properties, such as exceptional strength and ductility, high wear resistance, and corrosion resistance. Due to these positive attributes, HEAs have been proposed for use in the automotive and aerospace industries, nuclear reactor technology, and the biomedical field. In terms of composition, HEAs contain five or more elements in amounts ranging from 5 to 35 atomic percent (at.%) each, resulting in a vast compositional space that is still mainly unexplored to this day. More recently, the field of HEMs has broadened to include materials such as polymers and ceramics.

36 MATERIALS SCIENCE↗

A snapshot of high-entropy alloy processing techniques and their effects on resulting mechanical properties

High-entropy alloys (HEAs) exhibit exceptional strength, corrosion resistance, and thermal stability, making them promising candidates for nuclear, aerospace, and other extreme applications. While most prior work has focused on compositional design, manufacturing techniques themselves can alter microstructure and mechanical properties as dramatically as alloy chemistry. This review compiles and compares the effects of processing routes—including arc melting, induction melting, mechanical alloying with spark plasma sintering, and additive manufacturing—on the structure and properties of HEAs. Quantitative comparisons highlight, for example, that SPS-processed alloys can achieve ∼20–45 % higher yield and tensile strength than arc-melted counterparts, while Bridgman solidification produces nearly single-crystal structures with elongation to failure exceeding 80 %. Additive manufacturing routes such as selective laser melting offer fine microstructures but also introduce anisotropy and porosity, leading to yield strengths spanning 100–600 MPa for the same composition. By synthesizing such results, this review provides actionable insight into how processing routes interact with HEA core effects (high entropy, lattice distortion, sluggish diffusion, and cocktail effect) to determine performance, thereby offering a practical guide for optimizing manufacturing strategies.

36 MATERIALS SCIENCE↗

Process window estimation in manufacturing through Entropy-Sigma active learning

In manufacturing, there exist boundary identification problems for defining parameter spaces that meet desired thresholds on outcomes. This paper presents an Entropy-Sigma acquisition function for active learning of the process window/map in manufacturing using a Gaussian Process surrogate. Here, the method is applied to identify the stability boundary for the stability process map in machining using time-domain simulations with a periodic sampling stability metric. Results show that the proposed Entropy-Sigma method significantly outperforms Latin hypercube sampling or grid-based methods. The described method can be applied to identify the process window/map for any manufacturing application using a quantitative process outcome metric.

42 ENGINEERING↗

Entropy modeling on serrated flows in carburized steels

Samples comprised of carburized steel alloys, 4615, 4720, and 10B22, were tension tested at room temperature and at a strain rate of 2 × 10 -4 s -1 . The serrated-flow behavior was modeled and analyzed, using the refined composite multiscale entropy (RCMSE) method. High energy X-ray diffraction revealed the body-centered-cubic (BCC) structure of the three alloys in the as-received condition. Moreover, Vickers-hardness experiments were performed, which showed an increase in the hardness of the alloy that corresponded to increasing impurity concentrations. Here the diffusion coefficient of carbon in the three alloys were estimated, respectively, to be 2.5 × 10 -11 m 2 /s, 5.1 × 10 -11 m 2 /s, and 2.8 × 10 -11 m 2 /s for alloys, 10B22, 4615, and 4720, respectively, which agree with the values found in the literature for α-iron. Moreover, the sample entropy, on average, increased with respect to the heating time, and, consequently, the amount of carbon that had diffused into the alloy. Finally, the above results show that the complexity of the serration behavior in the alloys studied increases with respect to the amount of carbon that has diffused into the material.

36 MATERIALS SCIENCE↗