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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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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Maximum-entropy probability distributions under Lp-norm constraints

Continuous probability density functions and discrete probability mass functions are tabulated which maximize the differential entropy or absolute entropy, respectively, among all probability distributions with a given L sub p norm (i.e., a given pth absolute moment when p is a finite integer) and unconstrained or constrained value set. Expressions for the maximum entropy are evaluated as functions of the L sub p norm. The most interesting results are obtained and plotted for unconstrained (real valued) continuous random variables and for integer valued discrete random variables. The maximum entropy expressions are obtained in closed form for unconstrained continuous random variables, and in this case there is a simple straight line relationship between the maximum differential entropy and the logarithm of the L sub p norm. Corresponding expressions for arbitrary discrete and constrained continuous random variables are given parametrically; closed form expressions are available only for special cases. However, simpler alternative bounds on the maximum entropy of integer valued discrete random variables are obtained by applying the differential entropy results to continuous random variables which approximate the integer valued random variables in a natural manner. All the results are presented in an integrated framework that includes continuous and discrete random variables, constraints on the permissible value set, and all possible values of p. Understanding such as this is useful in evaluating the performance of data compression schemes.

Dolinar, S.↗
NASA NTRS2011

Entropy Generation Across Earth's Bow Shock

Earth's bow shock is a transition layer that causes an irreversible change in the state of plasma that is stationary in time. Theories predict entropy increases across the bow shock but entropy has never been directly measured. Cluster and Double Star plasma experiments measure 3D plasma distributions upstream and downstream of the bow shock that allow calculation of Boltzmann's entropy function H and his famous H-theorem, dH/dt ~ O. We present the first direct measurements of entropy density changes across Earth's bow shock. We will show that this entropy generation may be part of the processes that produce the non-thermal plasma distributions is consistent with a kinetic entropy flux model derived from the collisionless Boltzmann equation, giving strong support that solar wind's total entropy across the bow shock remains unchanged. As far as we know, our results are not explained by any existing shock models and should be of interests to theorists.

Parks, George K.↗
DOE OSTI2026

From high-entropy ceramics to compositionally complex ceramics and beyond

Over the past decade, the field of high-entropy ceramics (HECs) has expanded rapidly to encompass a broad range of oxides, borides, silicides, and other ceramic solid solutions. In 2020, we proposed extending HECs to compositionally complex ceramics (CCCs), where non-equimolar compositions and the presence of long- or short-range order, although reducing configurational entropy, create new opportunities to tailor and enhance properties, often surpassing those of higher-entropy counterparts. Along these lines, several fundamental scientific questions arise. Is the entropy in HECs truly high? Is maximizing entropy always desirable? In this perspective article, I revisit key concepts and terminologies and highlight emerging directions, including dual-phase CCCs, ultrahigh-entropy phases, and novel processing routes such as ultrafast reactive sintering. I propose that exploring compositional complexity across vast non-equimolar spaces, together with exploiting correlated disorder (coupled chemical and structural short-range order), represents a transformative strategy for designing ceramics with superior performance.

36 MATERIALS SCIENCE↗
DOE OSTI2024

High-entropy Li-rich layered oxide cathode for Li-ion batteries

High-entropy oxides (HEOs) are emerging as promising cathode materials for Li-ion batteries (LIBs) due to their stable solid-state phase and compositional flexibility. Herein, we investigate the structural and electrochemical properties of a novel non-equimolar high-entropy cathode material, termed high-entropy Li-rich layered oxide (HE-LLO, Li 1.15 Na 0.05 Ni 0.19 Mn 0.56 Fe 0.02 Mg 0.02 Al 0.02 O 1.97 F 0.03 ), in comparison to a pristine Li-rich layered oxide (PR-LLO, Li1.2Ni0.2Mn0.6O2). The incorporation of multiple cations (Na + , Al 3+ , Mg 2+ , Fe 3+ ) and anion (F - ) into HE-LLO introduces compositional diversity, enhancing structural stability through the entropy stabilization effect. Theoretical calculations confirm a significantly higher configurational entropy in HE-LLO compared to PRLLO, supporting its high-entropy nature. Electrochemical evaluations demonstrate that HE-LLO exhibits considerable capacity retention, preserving 76.8 % of its discharge capacity at 0.5C after 200 cycles, compared to only 36.2 % for PR-LLO. Even under high-temperature conditions, HE-LLO outperformed PR-LLO, maintaining 76.1 % of its discharge capacity after 100 cycles at 5C, while PR-LLO retained only 12.4 %. These enhancements are attributed to the improved phase reversibility and higher Li + ion diffusion coefficients of HE-LLO, validated by ex-situ characterizations using a synchrotron X-ray technique, along with density functional theory (DFT) calculations. In conclusion, these findings highlight the promise of non-equimolar HEOs as a novel design strategy for highperformance cathode materials.

25 ENERGY STORAGE↗
DOE OSTI2025

Generalized approach for rapid entropy calculation of liquids and solids

We build a comprehensive methodology for the fast computation of entropy across both solid and liquid phases. The proposed method utilizes a single trajectory of molecular dynamics (MD) to facilitate the calculation of entropy, which is composed of three components. The electronic entropy is determined through the temporal average acquired from density functional theory MD simulations. The vibrational entropy, typically the predominant contributor to the total entropy, even within the liquid state, is evaluated by computing the phonon density of states via the velocity autocorrelation function. The most arduous component to quantify, the configurational entropy, is assessed by probability analysis of the local structural arrangement and atomic distribution. We illustrate, through a variety of examples, that this method is both a versatile and valid technique for characterizing the thermodynamic states of both solids and liquids. Furthermore, this method is employed to expedite the calculation of melting temperatures, demonstrating its practical utility in computational thermodynamics.

36 MATERIALS SCIENCE↗
NASA NTRS2001

Entropy generation method to quantify thermal comfort

The present paper presents a thermodynamic approach to assess the quality of human-thermal environment interaction and quantify thermal comfort. The approach involves development of entropy generation term by applying second law of thermodynamics to the combined human-environment system. The entropy generation term combines both human thermal physiological responses and thermal environmental variables to provide an objective measure of thermal comfort. The original concepts and definitions form the basis for establishing the mathematical relationship between thermal comfort and entropy generation term. As a result of logic and deterministic approach, an Objective Thermal Comfort Index (OTCI) is defined and established as a function of entropy generation. In order to verify the entropy-based thermal comfort model, human thermal physiological responses due to changes in ambient conditions are simulated using a well established and validated human thermal model developed at the Institute of Environmental Research of Kansas State University (KSU). The finite element based KSU human thermal computer model is being utilized as a "Computational Environmental Chamber" to conduct series of simulations to examine the human thermal responses to different environmental conditions. The output from the simulation, which include human thermal responses and input data consisting of environmental conditions are fed into the thermal comfort model. Continuous monitoring of thermal comfort in comfortable and extreme environmental conditions is demonstrated. The Objective Thermal Comfort values obtained from the entropy-based model are validated against regression based Predicted Mean Vote (PMV) values. Using the corresponding air temperatures and vapor pressures that were used in the computer simulation in the regression equation generates the PMV values. The preliminary results indicate that the OTCI and PMV values correlate well under ideal conditions. However, an experimental study is needed in the future to fully establish the validity of the OTCI formula and the model. One of the practical applications of this index is that could it be integrated in thermal control systems to develop human-centered environmental control systems for potential use in aircraft, mass transit vehicles, intelligent building systems, and space vehicles.

Models, Biological↗
NASA NTRS2020

Entropy Stable h/p-Nonconforming Discretization with the Summation-by-Parts Property for the Compressible Euler and Navier–Stokes Equations

In this paper, we extend the entropy conservative/stable algorithms presented by Del Rey Fernandez and coauthors for the compressible Euler and Navier-Stokes equations on nonconforming p-refined/coarsened curvilinear grids to h/p refinement/coarsening. The main difficulty in developing nonconforming algorithms is the construction of appropriate coupling procedures across nonconforming interfaces. Here, we utilize a computationally simple and efficient approach based upon using decoupled interpolation operators. The resulting scheme is entropy conservative/stable and elementwise conservative. Numerical simulations of the isentropic vortex and viscous shock propagation con firm the entropy conservation/stability and accuracy properties of the method (achieving ~ p + 1 convergence), which are comparable to those of the original conforming scheme. Simulations of the Taylor{Green vortex at R(e) = 1,600 and turbulent flow past a sphere at R(e(infinity)) = 2,000 show the robustness and stability properties of the overall spatial discretization for unstructured grids. Finally, to demonstrate the entropy conservation property of a fully-discrete explicit entropy stable algorithm with h=p refinement/coarsening, we present the time evolution of the entropy function obtained by simulating the propagation of the isentropic vortex using a relaxation Runge-Kutta scheme.

Nonconforming interfaces↗
DOE OSTI2025

Generalized entropy of gravitational fluctuations

The corrections to holographic entanglement entropy from bulk quantum fields in a classical gravitational background are now well understood. They lead, in particular, to unitary Page curves for evaporating black holes. However, the correct treatment of quantum fluctuations of the metric, including graviton excitations, is a longstanding problem. We provide a gauge-invariant prescription for the generalized entropy of gravitons in anti-de Sitter space in terms of areas and bulk entanglement entropy, generalizing the quantum extremal surface prescription to accommodate fluctuations in the semiclassical spacetime geometry. This task requires a careful treatment of the area operator on the graviton Hilbert space and the definition of a “quantum extremal gauge” in which the extremal surface is unperturbed. It also requires us to determine the correct vacuum modular Hamiltonian for the graviton field, which we fix by requiring that it doesn’t contain a boundary term in extremal gauge. We check our prescription with an explicit computation of the vacuum-subtracted generalized entropy of states containing a graviton in an AdS-Rindler background. Our results exactly match vacuum-subtracted von Neumann entropies for stress-tensor excited states in holographic conformal field theory with d > 2 dimensions. We also use covariant phase space techniques to give a partial proof of our prescription when the entanglement wedge for the background spacetime has a bifurcate Killing horizon. Along the way, we identify a class of perturbative graviton states that have parametrically larger generalized entropy, in the small G N expansion, than any low-energy excitations of an ordinary quantum field.

1/N expansion↗
DOE OSTI2025

Entropy-Driven Structural Evolution in Ceramic Oxides

High-entropy ceramics, with five or more elements randomly occupying the same cation crystallographic sites, offer vast compositional diversity and unique properties for material design and applications. However, for many dissimilar elements, entropic stabilization cannot overcome the enthalpic barrier to cation substitution. As a result, most high-entropy ceramics incorporate only a few similar elements, limiting the in-depth exploration of the effect of entropy on ceramic properties. Here, we first use density functional theory to model fluorite crystal structures composed of 1-10 elements and then experimentally present practical fluorite oxide nanostructures containing 1, 3, 8, and 15 metals, as well as a record-breaking 25-element high-entropy ceramic incorporating a diverse palette of rare-earth, transition, alkaline, p-block, and noble metals. As entropy increases, structural and configurational disorder in the solid solution rises, altering structural features such as lattice distortion, crystallinity, homogeneity, defect density, and thermal stability. This research provides new insights and understanding of the role of entropy in stabilizing compositionally complex ceramics.

Liu, Shuo↗
NASA NTRS1986

Entropy conservative finite element schemes

The question of entropy stability for discrete approximations to hyperbolic systems of conservation laws is studied. The amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison. To this end, two main ingredients are used: entropy variables and the construction of certain entropy conservative schemes in terms of piecewise-linear finite element approximations. It is then shown that conservative schemes are entropy stable, if and (for three-point schemes) only if, they contain more numerical viscosity than the abovementioned entropy conservation ones.

Tadmor, E.↗
NASA NTRS1995

High Order Entropy-Constrained Residual VQ for Lossless Compression of Images

High order entropy coding is a powerful technique for exploiting high order statistical dependencies. However, the exponentially high complexity associated with such a method often discourages its use. In this paper, an entropy-constrained residual vector quantization method is proposed for lossless compression of images. The method consists of first quantizing the input image using a high order entropy-constrained residual vector quantizer and then coding the residual image using a first order entropy coder. The distortion measure used in the entropy-constrained optimization is essentially the first order entropy of the residual image. Experimental results show very competitive performance.

Kossentini, Faouzi↗
NASA NTRS2002

Groups and the Entropy Floor: XMM-Newton Observations of Two Groups

Using XMM-Newton spatially resolved X-ray imaging spectroscopy we obtain the temperature, density, entropy, gas mass, and total mass profiles for two groups of galaxies out to approximately 0.3 R(sub vir)(R(sub vir), the virial radius). Our density profiles agree well with those derived previously, and the temperature data are broadly consistent with previous results but are considerably more precise. Both of these groups are at the mass scale of 2x10(exp 13) M(solar mass), but have rather different properties. Both have considerably lower gas mass fractions at r < 0.3 R(sub vir), than the rich clusters. NGC2563, one of the least luminous groups for its X-ray temperature, has a very low gas mass fraction of approximately 0.004 inside 0.1 R(sub vir), which increases with radius. NGC4325, one of the most luminous groups at the same average temperature, has a higher gas mass fraction of 0.02. The entropy profiles and the absolute values of the entropy as a function of virial radius also differ, with NGC4325 having a value of approximately 100 keV cm(exp -2) and NGC2563 a value of approximately 300 keV cm(exp -2) at r approximately 0.1 R(sub vir). For both groups the profiles rise monotonically with radius and there is no sign of an entropy 'floor'. These results are inconsistent with pre-heating scenarios that have been developed to explain a possible entropy floor in groups, but are broadly consistent with models of structure formation that include the effects of heating and/or the cooling of the gas. The total entropy in these systems provides a strong constraint on all models of galaxy and group formation, and on the poorly defined feedback process that controls the transformation of gas into stars and thus the formation of structure in the universe.

Mushotzky, R. F.↗
DOE OSTI2025

A General Strategy for Bandgap Engineering Via Anion‐Lattice Doping in High‐Entropy Oxides

Bandgap engineering is a critical tool for tailoring the electronic properties of functional materials, traditionally achieved by modifying the cation sublattice. Here, a generalizable strategy is introduced that leverages facile anion-lattice doping in high entropy materials to modulate the bandgap in high-entropy metal oxides (HEMOs). By incorporating nitrogen into a single-phase high-entropy metal oxide/nitride (HEMO:HEMN) solid solution, a substantial bandgap reduction is achieved from 3.55 eV (HEMO) to ≈2.46 eV (HEMO:HEMN), significantly enhancing electronic conductivity. Unlike conventional bandgap tuning approaches that rely on cation substitution or heterojunction formation, this method exploits anion-mediated entropy stabilization, enabling uniform bandgap narrowing across the entire solid solution. This anion-lattice engineering strategy is broadly applicable to high-entropy systems, providing a new pathway for designing energy materials with tailored electronic properties. The resulting HEMO:HEMN solid solution exhibits a tenfold increase in capacitance and capacity compared to HEMO in supercapacitor and lithium-ion battery tests, demonstrating the transformative potential of anion-driven bandgap modulation for next-generation energy storage and conversion technologies.

energy storage↗
DOE OSTI2025

Structure-preserving neural networks for the regularized entropy-based closure of a linear, kinetic, radiative transport equation

The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural network-based approximation to the entropy-based closure method to accurately compute the solution of the multi-dimensional moment system with a low memory footprint and competitive computational time. We extend methods developed for the standard entropy-based closure to the regularized entropy-based closures. The main idea is to interpret structure-preserving neural network approximations of the regularized entropy-based closure as a two-stage approximation to the original entropy-based closure. We conduct a numerical analysis of this approximation and investigate optimal parameter choices. Our numerical experiments demonstrate that the method has a much lower memory footprint than traditional methods with competitive computation times and simulation accuracy. The code and all trained networks are provided on GitHub.

entropy closure↗
DOE OSTI2026

Neural entropy-stable conservative flux form neural networks for learning hyperbolic conservation laws

We propose a neural entropy-stable conservative flux form neural network (NESCFN) for learning hyperbolic conservation laws and their associated entropy functions directly from solution trajectories, without requiring any predefined numerical discretization. While recent neural network architectures have successfully integrated classical numerical principles into learned models, most rely on prior knowledge of the governing equations or assume a fixed discretization. Our approach removes this dependency by embedding entropy-stable design principles into the learning process itself, enabling the discovery of physically consistent dynamics in a fully data-driven setting. By jointly learning both the flux function and a corresponding entropy, NESCFN promotes conservation and entropy dissipation, which is critical for long-term stability and fidelity in the system of hyperbolic conservation laws. Furthermore, numerical results demonstrate that the method achieves stability and conservation over extended time horizons and accurately captures shock propagation speeds, even without oracle access to future-time solution profiles in the training data.

Conservative flux form↗
DOE OSTI2024

A general flame aerosol route to high-entropy nanoceramics

High-entropy ceramics are an emerging class of materials with fascinating characteristics. However, elemental immiscibility and crystal complexity limit the development of a general synthesis strategy, and common methods yield bulk materials. Here, we introduce a transformative non-equilibrium flame aerosol technique for synthesizing high-entropy nanoceramics. This scalable, one-step process enables the production of high-entropy oxide nanoceramics with an unprecedented diversity of crystal structures, including fluorite-phase materials that integrate up to 22 distinct cation elements. The method’s capacity for entropic stabilization and grain refinement significantly improves the thermal stability of these nanostructures. In a representative application, a Pt-(MgCoNiCuZn)O high-entropy single-atom catalyst showed superior activity and long-term stability, maintaining constant CO 2 conversion over 670 h and dramatically outperforming conventional catalysts. Finally, the general approach opens a vast composition and structure space for the creation of high-entropy oxide nanomaterials for application across diverse fields, including catalysis, energy storage, sensing, and thermal management.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Computational Analysis of the Energetic Stability of High-Entropy Structures of a Prototypical Lanthanide-Based Metal–Organic Framework

High-entropy materials are characterized by their complex compositions, typically comprising five or more elements in near-equiatomic proportions. Applying this concept to metal ions in metal−organic frameworks (MOFs) has paved the way for exploring a new class of high-entropy MOFs. While the compositional strategy of high-entropy materials leverages configurational entropy to aid thermodynamic stability, it also poses significant analytical challenges due to the vast compositional landscape and diverse phases that these materials can adopt. We present a computational study of several complexities associated with selecting potential high-entropy versions of a prototype lanthanidebased MOF. We compute the energetics of metal mixing of these heterometallic MOFs using density functional theory (DFT) and machine learning interatomic potential (MLIP) methods. The use of MLIP methods allows a systematic exploration of the convex hull of thermodynamically stable MOF structures containing up to 5 distinct metals.

Chemical structure↗
DOE OSTI2024

QCD evolution of entanglement entropy

Entanglement entropy has emerged as a novel tool for probing nonperturbative quantum chromodynamics (QCD) phenomena, such as color confinement in protons. While recent studies have demonstrated its significant capability in describing hadron production in deep inelastic scatterings, the QCD evolution of entanglement entropy remains unexplored. Here, in this work, we investigate the differential rapidity-dependent entanglement entropy within the proton and its connection to final-state hadrons, aiming to elucidate its QCD evolution. Our analysis reveals a strong agreement between the rapidity dependence of von Neumann entropy, obtained from QCD evolution equations, and the corresponding experimental data on hadron entropy. These findings provide compelling evidence for the emergence of a maximally entangled state, offering new insights into the nonperturbative structure of protons.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗