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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2019

Entropy Stable Method for the Euler Equations Revisited: Central Differencing via Entropy Splitting and SBP

The two decades old high order central differencing via entropy splitting and summation-by-parts (SBP) difference boundary closure of Ols- son & Oliger (1994), Gerritsen & Olsson (1996), and Yee et al. (2000) is revisited. The entropy splitting is a form of skew-symmetric splitting of the nonlinear Euler flux derivatives. Central differencing applied to the entropy splitting form of the Euler flux derivatives together with SBP difference operators will, hereafter, be referred to as entropy split schemes. This study is prompted by the recent growing interest in numerical methods for which a discrete entropy conservation law holds, a discrete global entropy conservation can be proved and/or the numerical method possesses a stable entropy in the framework of SBP difference operators and L2-energy norm estimate. The objective of this paper is to recast the entropy split scheme as the re- cent definition of an entropy stable method for central differencing with SBP operators for both periodic and non-periodic boundary conditions for non- linear Euler equations. Standard high order spatial central differencing as well as high order central spatial DRP (dispersion relation preserving) spatial differencing is part of the entropy stable methodology framework. Long time integration of 2D and 3D test cases is included to show the comparison of this efficient entropy stable method with the Tadmor-type of entropy conservative methods. Studies also include the comparison among the three skew-symmetric splittings on their nonlinear stability and accuracy performance without added numerical dissipations for smooth flows. These are, namely, entropy splitting, Ducros et al. splitting and the Kennedy & Grub- ber splitting.

Sjogreen, Bjorn↗
NASA NTRS2019

Entropy Stable Method for the Euler Equations Revisited: Central Differencing via Entropy Splitting and SBP

The two decades old high order central differencing via entropy splitting and summation-by-parts (SBP) difference boundary closure of Olsson & Oliger, Gerritsen & Olsson, and Yee et al. (15, 7, 37) is revisited. The objective of this paper is to prove for the first time that the entropy split scheme is an entropy stable method for central differencing with SBP operators for both periodic and non-periodic boundary conditions for nonlinear Euler equations. Standard high order spatial central differencing as well as high order central spatial DRP (dispersion relation preserving) spatial differencing is part of the entropy stable methodology framework. The proof is to replace the spatial derivatives by summation-by-parts (SBP) difference operators in the entropy split form of the equations using the physical entropy of the Euler equations. The numerical boundary closure follows directly from the SBP operator. No additional numerical boundary procedure is required. In contrast, Tadmor-type entropy conserving schemes (31) using mathematical entropies and more recently in (35], do not naturally come with a numerical boundary closure and a generalized SBP operator has to be developed (18). Long time integration of 2D and 3D test cases is included to show the comparison of this efficient entropy stable method with the Tadmor-type of entropy conservative methods. Studies also include the comparison among the three skew-symmetric splittings on their nonlinear stability and accuracy performance without added numerical dissipations for smooth flows. These are, namely, entropy splitting, Ducros et al. splitting and the Kennedy & Grubber splitting.

Sjogreen, Bjorn↗
NASA NTRS1993

Entropy and climate. I - ERBE observations of the entropy production of the earth

An approximate method for estimating the global distributions of the entropy fluxes flowing through the upper boundary of the climate system is introduced, and an estimate of the entropy exchange between the earth and space and the entropy production of the planet is provided. Entropy fluxes calculated from the Earth Radiation Budget Experiment measurements show how the long-wave entropy flux densities dominate the total entropy fluxes at all latitudes compared with the entropy flux densities associated with reflected sunlight, although the short-wave flux densities are important in the context of clear sky-cloudy sky net entropy flux differences. It is suggested that the entropy production of the planet is both constant for the 36 months of data considered and very near its maximum possible value. The mean value of this production is 0.68 x 10 exp 15 W/K, and the amplitude of the annual cycle is approximately 1 to 2 percent of this value.

Stephens, G. L.↗
DOE OSTI2025

The Path towards Plasma Facing Components: A Review of State-of-the-art in W-Based Refractory High-Entropy Alloys

Developing advanced materials for plasma-facing components (PFCs) in fusion reactors is a crucial aspect for achieving sustained energy production. Tungsten (W) - based refractory high-entropy alloys (RHEAs) have emerged as promising candidates due to their superior radiation tolerance and high-temperature strength. This review paper will focus on recent advancements in W-based RHEA research, particularly emphasizing the key role of modelling using machine learning (ML) in the stage of discovery by predicting properties for each composition and expediting the identification of optimal RHEA compositions with desired properties. Additionally, the application of additive manufacturing (AM) techniques for fabricating W-based RHEAs is explored, highlighting their advantages for rapid prototyping and multi-compositional sample production in a high throughput manner. The review critically evaluates the current understanding of mechanical properties relevant to PFC applications, including high-temperature strength and ductility. Furthermore, the radiation tolerance of W-based RHEAs under irradiated conditions is discussed. Finally, the validity of current AM-manufactured W-based RHEAs as PFC materials is assessed, and key challenges and opportunities for future research are identified. This review aims to provide a comprehensive overview of W-based RHEAs for fusion applications and their potential to guide the development and validation of advanced refractory high entropy alloys.

Hatler, Caleb [University of Wisconsin-Madison]↗
DOE OSTI2024

Era of entropy: Synthesis, structure, properties, and applications of high-entropy materials

The field of high-entropy materials (HEMs) has emerged as a dynamic area of scientific exploration, driven by the exceptional properties arising from their compositional complexity. Encompassing both high-entropy alloys (HEAs) and high-entropy ceramics (HECs), these materials have garnered significant attention across diverse research domains. From investigations into phase evolution and mechanical characteristics to studies of ionic, electronic, and magnetic behaviors, HEMs demonstrate remarkable potential for a wide array of applications. These range from catalysis and tribology to energy storage and superconductivity. Fundamental research has shed light on crucial phenomena such as configurational entropy, lattice distortion, and sluggish diffusion. These discoveries are paving the way for materials design strategies that enable new functional tunability and resistance to application-specific harsh environments. This burgeoning field promises to revolutionize material design and performance across numerous technological sectors. Here, this special collection between Applied Physics Letters and the Journal of Applied Physics provides a timely overview of the latest research in this area. It highlights the growing interest in understanding the impact of high compositional complexity on conventional structure–process–property–performance relationships in HEMs.

36 MATERIALS SCIENCE↗
DOE OSTI2026

High entropy oxides prediction and discovery by the Mixed Enthalpy-Entropy Descriptor

The vast, high-dimensional composition space of high-entropy oxides (HEOs) offers exceptional opportunities for functional materials discovery, yet it also poses a fundamental challenge: the rational and efficient prediction of stable, synthesizable compositions and the corresponding structure–property relationships. Despite growing interest, the field still lacks broadly applicable, physically grounded descriptors capable of navigating various large chemical spaces. Here, we introduce a Mixed Enthalpy–Entropy Descriptor (MEED) that enables rapid, first-principles–based prediction of HEOs synthesizability across diverse chemistries. Using MEED, we perform high-throughput screening of two distinct HEO families: rocksalt oxides and perovskite oxides. The predicted top candidates in each family were experimentally validated. MEED reveals unifying thermodynamic and structural principles governing stability across both chemical compositions and polymorphs, providing mechanistic insight into the formation of high-entropy phases. This work significantly broadens the accessible chemical design space for HEOs and establishes a data-efficient framework for accelerating the discovery of next-generation functional materials.

Yu, Liping [University of Central Florida]↗
DOE OSTI2026

A Comparative Study of Thermal Oxidization Resistance of a High-Entropy Metal Boride and a High-Entropy Metal Carbide

We present a systematic study of thermal oxidation resistance of transition metal borides and carbides up to 1300 °C in a dry air environment. A High-Entropy Metal Boride (HEMB), of composition (Hf 0.2 , Mo 0.2 , Nb 0.2 , Ta 0.2 , Zr 0.2 )B 2 , and a similar High-Entropy Metal Carbide (HEMC) (Hf, Mo, Nb, Ta, Zr)C 5 were synthesized from precursor mixtures, under 30 MPa of pressure at a temperature of 1800 °C using a Spark Plasma Sintering Device. The synthesized phases were confirmed via X-ray Diffraction analysis, which showed a pure hexagonal AlB 2 -type structure for HEMB and a face-centered cubic (FCC) structure for HEMC, with lattice parameters, a = 3.10 Å and c = 3.37 Å for HEMB and a = 4.524 Å for HEMC. Oxidation resistance was evaluated using a simultaneous thermogravimetric analysis and differential scanning calorimetry (TGA/DSC) stage in which HEMB and HEMC were heated up to 1300 °C at a rate of 2 °C/min in a dry air environment. Scanning electron microscopy (SEM) was used to analyze the resulting oxidized material. Our study demonstrates that HEMB shows better thermal oxidation resistance as compared to a similar metal composition HEMC at high temperatures.

36 MATERIALS SCIENCE↗
NASA NTRS2019

Approximate Entropy and Sample Entropy: A Comprehensive Tutorial

Approximate Entropy and Sample Entropy are two algorithms for determining the regularity of series of data based on the existence of patterns. Despite their similarities, the theoretical ideas behind those techniques are different but usually ignored. This paper aims to be a complete guideline of the theory and application of the algorithms, intended to explain their characteristics in detail to researchers from different fields. While initially developed for physiological applications, both algorithms have been used in other fields such as medicine, telecommunications, economics or Earth sciences. In this paper, we explain the theoretical aspects involving Information Theory and Chaos Theory, provide simple source codes for their computation, and illustrate the techniques with a step by step example of how to use the algorithms properly. This paper is not intended to be an exhaustive review of all previous applications of the algorithms but rather a comprehensive tutorial where no previous knowledge isrequired to understand the methodology.

Delgado-Bonal, Alfonso↗
NASA NTRSDate not supplied

A New Approach for a Wider Class of Entropy Split Methods for Compressible Gas Dynamics and MHD

The high order entropy split methods of Sjögreen & Yee [1, 2] by entropy splitting of the compressible Euler (inviscid) flux derivatives for a thermally-perfect gas are based on Harten’s entropy function [3, 4, 5]. Their derivation takes advantage of the homogeneity property of Euler flux, symmetrizable Euler flux derivatives and energy-norm stability in conjunction with high order classical spatial central, DRP (dispersion relation-preserving) [6, 7, 8] or Padé (compact) spatial discretizations [9] with summation-by-parts (SBP) operators [10]. Our entropy split methods have been proven entropy conserving and stable [1, 11, 12]. Our proofs do not rely on a two-point numerical flux, but rather only a linear difference operator is required to derive these methods. To extend the entropy split method for the MHD, we used the Godunov symmetrizable non-conservative MHD form [12, 13, 14]. These high order entropy split methods not only preserve certain physical properties of the chosen governing equations but are also known to either improve numerical stability, and/or minimize aliasing errors in long time integration of turbulent flow computations without the aid of added numerical dissipation. In our previous published work, extensive error norm comparison with grid refinement was performed to show the high accuracy performance of these methods. These studies also showed how well the entropy split methods conserve the entropy, momentum and mass, and preserve the kinetic energy for long time integration of the various flows [1, 2, 12, 13, 14]. The objective of the present work is to use a new approach to obtain a wider class of entropy split methods consisting of a two-point numerical flux portion and a non-conservative portion in such a way that the homogeneity property of the compressible Euler flux is not required. For high order classical spatial central, DRP (dispersion relation-preserving) or Padé (compact) spatial discretizations, this new approach can be proven to be entropy conservative with conservative spatial dsicretizations while at the same time allowing a wider class of symmetrizable inviscid flux derivatives. We also use this generalization to derive an entropy split scheme that is entropy conserving for the equations of MHD without the homogeneity property using the Godunov symmetrizable ideal MHD formulation [15].

High Order Physical Preserving Methods↗
NASA NTRS2020

Global and Regional Entropy Production by Radiation Estimated from Satellite Observations

Vertical profiles of shortwave and longwave irradiances computed with satellite-derived cloud properties and temperature and humidity profiles from reanalysis are used to estimate entropy production. Entropy production by shortwave radiation is computed by the absorbed irradiance within layers in the atmosphere and by the surface divided by their temperatures. Similarly, entropy production by longwave radiation is computed by emitted irradiance to space from layers in the atmosphere and surface divided by their temperatures. Global annual mean entropy production by shortwave absorption and longwave emission to space are, respectively, 0.852 and 0.928 W/sq.mK. With a steady-state assumption, entropy production by irreversible processes within the Earth system is estimated to be 0.076 W/sq.mK and by nonradiative irreversible processes to be 0.049 W/sq.mK. Both global annual mean entropy productions by shortwave absorption and longwave emission to space increase with increasing shortwave absorption (i.e., with decreasing the planetary albedo). The increase of entropy production by shortwave absorption is, however, larger than the increase of entropy production by longwave emission to space. The result implies that global annual mean entropy production by irreversible processes decreases with increasing shortwave absorption. Input and output temperatures derived by dividing the absorbed shortwave irradiance and emitted longwave irradiance to space by respective entropy production are, respectively, 282 and 259 K, which give the Carnot efficiency of the Earth system of 8.5%.

Seiji Kato↗
NASA NTRS2003

An Equation for Moist Entropy in a Precipitating and Icy Atmosphere

Moist entropy is nearly conserved in adiabatic motion. It is redistributed rather than created by moist convection. Thus moist entropy and its equation, as a healthy direction, can be used to construct analytical and numerical models for the interaction between tropical convective clouds and large-scale circulations. Hence, an accurate equation of moist entropy is needed for the analysis and modeling of atmospheric convective clouds. On the basis of the consistency between the energy and the entropy equations, a complete equation of moist entropy is derived from the energy equation. The equation expresses explicitly the internal and external sources of moist entropy, including those in relation to the microphysics of clouds and precipitation. In addition, an accurate formula for the surface flux of moist entropy from the underlying surface into the air above is derived. Because moist entropy deals "easily" with the transition among three water phases, it will be used as a prognostic variable in the next generation of cloud-resolving models (e. g. a global cloud-resolving model) for low computational noise. Its equation that is derived in this paper is accurate and complete, providing a theoretical basis for using moist entropy as a prognostic variable in the long-term modeling of clouds and large-scale circulations.

Tao, Wei-Kuo↗
DOE OSTI2025

Entropy of the Quantum–Classical Interface: A Potential Metric for Security

Hybrid quantum–classical systems are emerging as key platforms in quantum computing, sensing, and communication technologies, but the quantum–classical interface (QCI)—the boundary enabling these systems—introduces unique and largely unexplored security vulnerabilities. This position paper proposes using entropy-based metrics to monitor and enhance security, specifically at the QCI. We present a theoretical security outline that leverages well-established information-theoretic entropy measures, such as Shannon entropy, von Neumann entropy, and quantum relative entropy, to detect anomalous behaviors and potential breaches at the QCI. By linking entropy fluctuations to scenarios of practical relevance—including quantum key distribution, quantum sensing, and hybrid control systems—we promote the potential value and applicability of entropy-based security monitoring. While explicitly acknowledging practical limitations and theoretical assumptions, we argue that entropy-based metrics provide a complementary approach to existing security methods, inviting further empirical studies and theoretical refinements that can strengthen future quantum technologies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Programming entropy production hotspots via interaction patterning

Dissipation in soft matter and living systems is highly heterogeneous, giving rise to complex local entropy production patterns. Recent work has identified the connection between local entropy production and locally extractable amount of work. This suggests that locally produced entropy can be recovered to power nanorobots and biological machines, prompting the need for efficient strategies to modulate and fine-tune local entropy production. In this work, we propose to program entropy production hotspots by leveraging local interaction patterns and test this approach in simulations of a fluid driven through a nanopore or past an obstacle. Here, the results show that patterning the surface of the pore with a repulsive patch gives rise to an entropy production hotspot around the patch, while an attractive patch leads to an entropy production cold spot. Varying the strength of the interaction and width of the patch enables modulating the hotness and extent of the hot spot. In flows past interaction patterned-obstacles, we show that the combined effects of steric hindrance and attraction allows to program a specific entropy production map, thereby opening the door to the precise powering of nanomachines.

Desgranges, Caroline [University of Massachusetts,↗
DOE OSTI2026

Exploring the holographic entropy cone via reinforcement learning

We develop a reinforcement learning algorithm to study the holographic entropy cone. Given a target entropy vector, our algorithm searches for a graph realization whose min-cut entropies match the target vector. If the target vector does not admit such a graph realization, it must lie outside the cone, in which case the algorithm finds a graph whose corresponding entropy vector most nearly approximates the target and allows us to probe the location of the facets. For the N = 3 cone, we confirm that our algorithm successfully rediscovers monogamy of mutual information beginning with a target vector outside the holographic entropy cone. We then apply the algorithm to the N = 6 cone, analyzing the 6 mystery extreme rays of the subadditivity cone from [1] that satisfy all known holographic entropy inequalities yet lacked graph realizations. We found realizations for 3 of them, proving they are genuine extreme rays of the holographic entropy cone, while providing evidence that the remaining 3 are not realizable, implying unknown holographic inequalities exist for N = 6.

AdS-CFT correspondence↗
DOE OSTI2024

Should We Conserve Entropy or Energy when Computing CAPE with Mixed-Phase Precipitation Physics?

Abstract The rapidly increasing resolution of global atmospheric reanalysis and climate model datasets necessitates finding methods for computing convective available potential energy (CAPE) both efficiently and accurately. To this end, this article compares two common methods for computing CAPE which conserve either energy or entropy. Inaccuracies in these computations arise from both physical and numerical errors. For instance, computing CAPE with entropy conserved results in physical errors from nonequilibrium phase transitions but minimizes numerical errors because solutions are analytic at each height. In contrast, computing CAPE with energy conserved avoids these physical errors, but accumulates numerical errors that are grid-resolution-dependent because the numerical integration of a differential equation is required. Analysis of CAPE computed with large databases of soundings from the tropical Amazon and midlatitude storm environments shows that physical errors from the entropy method are typically 1%–3% as large as CAPE, which is comparable to the numerical errors from conserving energy with grid spacing of 25 and 250 m using explicit first-order and second-order integration schemes, respectively. Errors in entropy-based CAPE calculations are also insensitive to vertical grid spacing, in contrast to energy-based calculations whose error strongly scales with the grid spacing. It is shown that entropy-based methods are advantageous when intercomparing datasets with differing vertical resolution because they produce accurate and reasonably fast results that are insensitive to grid resolution, whereas a second-order energy-based method is advantageous when analyzing data with a consistent vertical resolution because of its superior computational efficiency. Significance Statement Convective available potential energy (CAPE) is a measure of instability in the atmosphere that helps forecasters and researchers understand when and where thunderstorms will form. The purpose of this article is to identify the most efficient and accurate methods for computing CAPE. Two methods are considered here, one that relates to the entropy (a measure of thermodynamic disorder) of an air parcel and one that relates to the energy of an air parcel. Results indicate that the entropy method is most accurate and insensitive to the resolution of the data used for the calculation (which can vary considerably), whereas the energy method uses the least computation time.

Peters, John M.↗