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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
DOE OSTI2024

Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity

We report universal statistical properties displayed by ensembles of pure states that naturally emerge in quantum many-body systems. Specifically, two classes of state ensembles are considered: those formed by (i) the temporal trajectory of a quantum state under unitary evolution or (ii) the quantum states of small subsystems obtained by partial, local projective measurements performed on their complements. These cases, respectively, exemplify the phenomena of “Hilbert-space ergodicity” and “deep thermalization.” In both cases, the resultant ensembles are defined by a simple principle: The distributions of pure states have maximum entropy, subject to constraints such as energy conservation, and effective constraints imposed by thermalization. We present and numerically verify quantifiable signatures of this principle by deriving explicit formulas for all statistical moments of the ensembles, proving the necessary and sufficient conditions for such universality under widely accepted assumptions, and describing their measurable consequences in experiments. We further discuss information-theoretic implications of the universality: Our ensembles have maximal information content while being maximally difficult to interrogate, establishing that generic quantum state ensembles that occur in nature hide (scramble) information as strongly as possible. Our results generalize the notions of Hilbert-space ergodicity to time-independent Hamiltonian dynamics and deep thermalization from infinite to finite effective temperature. Our work presents new perspectives to characterize and understand universal behaviors of quantum dynamics using statistical and information-theoretic tools.

Eigenstate thermalization↗
DOE OSTI2023

Maximum entropy distributions of dark matter in ΛCDM cosmology

Context. Small-scale challenges to ΛCDM cosmology require a deeper understanding of dark matter physics. Aims. This paper aims to develop the maximum entropy distributions for dark matter particle velocity (denoted by X ), speed (denoted by Z ), and energy (denoted by E ) that are especially relevant on small scales where system approaches full virialization. Methods. For systems involving long-range interactions, a spectrum of halos of different sizes is required to form to maximize system entropy. While the velocity in halos can be Gaussian, the velocity distribution throughout the entire system, involving all halos of different sizes, is non-Gaussian. With the virial theorem for mechanical equilibrium, we applied the maximum entropy principle to the statistical equilibrium of entire system, such that the maximum entropy distribution of velocity (the X distribution) could be analytically derived. The halo mass function was not required in this formulation, but it did indeed result from the maximum entropy. Results. The predicted X distribution involves a shape parameter α and a velocity scale, v 0 . The shape parameter α reflects the nature of force ( α → 0 for long-range force or α → ∞ for short-range force). Therefore, the distribution approaches Laplacian with α → 0 and Gaussian with α → ∞. For an intermediate value of α , the distribution naturally exhibits a Gaussian core for v ≪ v 0 and exponential wings for v ≫ v 0 , as confirmed by N -body simulations. From this distribution, the mean particle energy of all dark matter particles with a given speed, v , follows a parabolic scaling for low speeds (∝ v 2 for v ≪ v 0 in halo core region, i.e., “Newtonian”) and a linear scaling for high speeds (∝ v for v ≫ v 0 in halo outskirt, i.e., exhibiting “non-Newtonian” behavior due to long-range gravity). We compared our results against N -body simulations and found a good agreement.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Model-Free Approach for Profiling of Polydisperse Soft Matter Using Small Angle Scattering

A strategy for determining the size polydispersity of systems from their small angle coherent scattering is outlined. Here, using the method of moment expansion, we show that the various central moments representing the average particle size, variance of particle size, and skewness of size distribution function (SDF) for polydisperse systems can be extracted from spectral analysis without bias. When the degree of polydispersity is moderate, SDF can be further reconstructed based on the maximum entropy principle. Numerical benchmarking of a model study over a wide range of size nonuniformity demonstrates the validity of this analytical approach for quantifying the size distribution of general soft matter systems in a model-free manner. Furthermore, the efficacy of this method was validated by successfully applying it to the fitting of small-angle neutron scattering data obtained from L64 Pluronic micelles using various form factor models. The numerical and experimental verification underscores the reliability and versatility of this method in accurately characterizing the size distribution of complex soft matter systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Stochastic fluctuations in relativistic fluids: Causality, stability, and the information current

We develop a general formalism for introducing stochastic fluctuations around thermodynamic equilibrium which takes into account, for the first time, recent developments in the causality and stability properties of relativistic hydrodynamic theories. The method is valid for any covariantly stable theory of relativistic viscous fluid dynamics derived from a covariant maximum entropy principle. We illustrate the formalism with some applications, showing how it could be used to consistently introduce fluctuations in a model of relativistic heat diffusion and in conformally invariant Israel-Stewart theory in a general hydrodynamic frame. Furthermore, the latter example is used to study the hydrodynamic frame dependence of the symmetric two-point function of fluctuations of the energy-momentum tensor.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Quantum maximum entropy closure for small flavor coherence

Quantum angular moment transport schemes are an important avenue toward describing neutrino flavor mixing phenomena in dense astrophysical environments such as supernovae and merging neutron stars. Successful implementation will require new closure relations that go beyond those used in classical transport. In this paper, we derive the first analytic expression for a quantum M1 closure, valid in the limit of small flavor coherence, based on the maximum entropy principle. We verify that the resulting closure relation has the appropriate limits and characteristic speeds in the diffusive and free-streaming regimes. We then use this new closure in a moment linear stability analysis to search for fast flavor instabilities in a binary neutron star merger simulation and find better results as compared with previously designed, ad hoc , semiclassical closures.

astrophysical & cosmological simulations↗
DOE OSTI2021

Understanding protein-complex assembly through grand canonical maximum entropy modeling

Inside a cell, heterotypic proteins assemble in inhomogeneous, crowded systems where the abundance of these proteins vary with cell types. While some protein complexes form putative structures that can be visualized with imaging, there are far more protein complexes that are yet to be solved because of their dynamic associations with one another. Nevertheless, it is possible to infer these protein complexes through a physical model. However, it is often not clear to physicists what kind of data from biology is necessary for such a modeling endeavor. Here, we aim to model these clusters of coarse-grained protein assemblies from multiple subunits through the constraints of interactions among the subunits and the chemical potential of each subunit. We obtained the constraints on the interactions among subunits from the known protein structures. We inferred the chemical potential that dictates the particle number distribution of each protein subunit from the knowledge of protein abundance from experimental data. Guided by the maximum entropy principle, we formulated an inverse statistical mechanical method to infer the distribution of particle numbers from the data of protein abundance as chemical potentials for a grand canonical multicomponent mixture. Using grand canonical Monte Carlo simulations, we captured a distribution of high-order clusters in a protein complex of succinate dehydrogenase with four known subunits. The complexity of hierarchical clusters varies with the relative protein abundance of each subunit in distinctive cell types such as lung, heart, and brain. When the crowding content increases, we observed that crowding stabilizes emergent clusters that do not exist in dilute conditions. We, therefore, proposed a testable hypothesis that the hierarchical complexity of protein clusters on a molecular scale is a plausible biomarker of predicting the phenotypes of a cell.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Boundary-induced classical generalized Gibbs ensemble with angular momentum

We investigate how confinement geometry leads to the emergence of a Generalized Gibbs Ensemble (GGE) in classical systems. Unlike the standard Gibbs ensemble, the GGE includes additional conserved quantities, such as angular momentum, that arise from boundary-induced symmetries. Using analytical arguments based on the maximum entropy principle, we show that circular boundaries preserve angular momentum and drive the system toward a chiral, non-ergodic GGE that violates time-reversal symmetry. This ensemble differs fundamentally from the Gibbs case, producing near-boundary condensation and revealing how geometry alone can alter thermal equilibration. To quantify these effects, we introduce an order parameter measuring deviations from Gibbs behavior and demonstrate that conventional Monte Carlo methods must incorporate angular momentum conservation under such conditions. Our study highlights how geometric constraints shape non-equilibrium statistical ensembles and lead to subtle departures from the Bohr-van Leeuwen theorem. These predictions are validated through detailed simulations of confined classical hard-disk gases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Efficient First-Order Algorithms for Large-Scale, Non-Smooth Maximum Entropy Models with Application to Wildfire Science

Maximum entropy (MaxEnt) models are a class of statistical models that use the maximum entropy principle to estimate probability distributions from data. Due to the size of modern data sets, MaxEnt models need efficient optimization algorithms to scale well for big data applications. State-of-the-art algorithms for MaxEnt models, however, were not originally designed to handle big data sets; these algorithms either rely on technical devices that may yield unreliable numerical results, scale poorly, or require smoothness assumptions that many practical MaxEnt models lack. In this paper, we present novel optimization algorithms that overcome the shortcomings of state-of-the-art algorithms for training large-scale, non-smooth MaxEnt models. Our proposed first-order algorithms leverage the Kullback–Leibler divergence to train large-scale and non-smooth MaxEnt models efficiently. For MaxEnt models with discrete probability distribution of n elements built from samples, each containing m features, the stepsize parameter estimation and iterations in our algorithms scale on the order of O(mn) operations and can be trivially parallelized. Moreover, the strong ℓ1 convexity of the Kullback–Leibler divergence allows for larger stepsize parameters, thereby speeding up the convergence rate of our algorithms. To illustrate the efficiency of our novel algorithms, we consider the problem of estimating probabilities of fire occurrences as a function of ecological features in the Western US MTBS-Interagency wildfire data set. Our numerical results show that our algorithms outperform the state of the art by one order of magnitude and yield results that agree with physical models of wildfire occurrence and previous statistical analyses of wildfire drivers.

Physics↗
DOE OSTI2024

Maximum Entropy Theory of Multiscale Coarse-Graining via Matching Thermodynamic Forces: Application to a Molecular Crystal (TATB)

The MSCG/FM (multiscale coarse-graining via force-matching) approach is an efficient supervised machine learning method to develop microscopically informed coarse-grained (CG) models. Here we present a theory based on the principle of maximum entropy (PME) enveloping the existing MSCG/FM approaches. This theory views the MSCG/FM method as a special case of matching the thermodynamic forces from the extended ensemble described by the set of thermodynamic (relevant) system coordinates. This set may include CG coordinates, the stress tensor, applied external fields, and so forth, and may be characterized by nonequilibrium conditions. Following the presentation of the theory, we discuss the consistent matching of both bonded and nonbonded interactions. The proposed PME formulation is used as a starting point to extend the MSCG/FM method to the constant strain ensemble, which together with the explicit matching of the bonded forces is better suited for coarse-graining anisotropic media at a submolecular resolution. The theory is demonstrated by performing the fine coarse-graining of crystalline 1,3,5-triamino-2,4,6-trinitrobenzene (TATB), a well-known insensitive molecular energetic material, which exhibits highly anisotropic mechanical properties.

1,3,5-triamino-2,4,6-trinitrobenzene↗
DOE OSTI2024

Proximal Galerkin: A Structure-Preserving Finite Element Method for Pointwise Bound Constraints

The proximal Galerkin finite element method is a high-order, low iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of pointwise bound constraints in infinite-dimensional function spaces. This paper introduces the proximal Galerkin method and applies it to solve free boundary problems, enforce discrete maximum principles, and develop a scalable, mesh-independent algorithm for optimal design with pointwise bound constraints. This paper also introduces the latent variable proximal point (LVPP) algorithm, from which the proximal Galerkin method derives. When analyzing the classical obstacle problem, we discover that the underlying variational inequality can be replaced by a sequence of second-order partial differential equations (PDEs) that are readily discretized and solved with, e.g., the proximal Galerkin method. Throughout this work, we arrive at several contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and certain infinite-dimensional Lie groups; and (3) a gradient-based, bound-preserving algorithm for two-field, density-based topology optimization. The complete proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. Open-source implementations of our methods accompany this work to facilitate reproduction and broader adoption.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Energy efficiency in industrial drying: A hybrid ultrasonic system with a novel dynamic optimization framework

Drying processes are among the most energy-consuming operations in industrial and manufacturing settings, demanding strategic selection, design, and control for enhanced efficiency. Advancing drying technologies is critical for improving sustainability, lowering energy use, reducing carbon emissions, and minimizing waste. This study explores two innovative strategies aimed at transforming drying processes into sustainable, low-carbon systems by reducing energy consumption, minimizing waste, and maintaining a strong emphasis on preserving product quality. The first strategy showcases a sub-pilot scale hybrid ultrasonic-convective dryer for agrifood products. This technology, powered by electricity (process electrification), integrates non-thermal ultrasonic dehydration with convective heating and is presented as a sustainable and energy-efficient solution that enhances eco-friendly practices. The second strategy involves introducing and implementing a novel, multiobjective, mixed integer dynamic optimization technique to determine the optimal time-dependent process parameter values for the drying operation. This optimization technique yields operating conditions that are piecewise constant in time aiming to maximize the energy efficiency of the hybrid ultrasonic-convective dryer while ensuring strict adherence to product quality constraints. By adopting the hybrid ultrasonic-convective dryer, a notable 35% improvement in energy efficiency was achieved compared to conventional hot-air drying systems for drying apple slices. The proposed optimization framework further enhanced energy efficiency by nearly 14% over the most efficient process on the identical testbed, under static operating conditions. The reported enhancements have been experimentally validated. Regarding drying time (thereby improving production yield), the developed hybrid ultrasonic-convective dryer demonstrates as much as a 41% reduction in total processing time, which is further optimized by an additional 10% using our proposed optimization framework. The research outcomes have profound implications for the design and operation of drying systems, encompassing crucial aspects such as process electrification, cost-effectiveness, energy savings, time efficiency, product yield, product quality, and process automation.

Dynamic optimization↗
DOE OSTI2025

Bayesian Entropy Neural Networks for physics-aware prediction

This article addresses the need for deep learning models to integrate well-defined constraints into their outputs, driven by their application in surrogate models, learning with limited data and partial information, and scenarios requiring flexible model behavior to incorporate non-data sample information. We introduce Bayesian Entropy Neural Networks (BENN), a framework grounded in Maximum Entropy (MaxEnt) principles, designed to impose constraints on Bayesian Neural Network (BNN) predictions. BENN is capable of constraining not only the predicted values but also their derivatives and variances, ensuring a more robust and reliable model output. To achieve simultaneous uncertainty quantification and constraint satisfaction, we employ the method of multipliers approach. This allows for the concurrent estimation of neural network parameters and the Lagrangian multipliers associated with the constraints. Our experiments, spanning diverse applications such as beam deflection modeling and microstructure generation, demonstrate the effectiveness of BENN. The results highlight significant improvements over traditional BNNs and showcase competitive performance relative to contemporary constrained deep learning methods.

14 SOLAR ENERGY↗
DOE OSTI2021

Resolving Dynamics in the Ensemble: Finding Paths through Intermediate States and Disordered Protein Structures

Proteins have been found to inhabit a diverse set of three-dimensional structures. The dynamics that govern protein interconversion between structures happen over a wide range of time scales-picoseconds to seconds. Our understanding of protein functions and dynamics is largely reliant upon our ability to elucidate physically populated structures. From an experimental structural characterization perspective, we are often limited to measuring the ensemble-averaged structure both in the steady-state and time-resolved regimes. Generating kinetic models and understanding protein structure–function relationships require atomistic knowledge of the populated states in the ensemble. Here, we present ensemble refinement methodologies that integrate time-resolved experimental signals with molecular dynamics models. We first discuss integration of experimental structural restraints to molecular models in disordered protein systems that adhere to the principle of maximum entropy for creating a complete set of ensemble structures. We then propose strategies to find kinetic pathways between the refined structures, using time-resolved inputs to guide molecular dynamics trajectories and the use of inference to generate tailored stimuli to prepare a desired ensemble of protein states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Physics-based stabilized finite element approximations of the Poisson–Nernst–Planck equations

We present and analyze two stabilized finite element methods for solving numerically the Poisson–Nernst–Planck equations. The stabilization we consider is carried out by using a shock detector and a discrete graph Laplacian operator for the ion equations, whereas the discrete equation for the electric potential need not be stabilized. Discrete solutions stemmed from the first algorithm preserve both maximum and minimum discrete principles. For the second algorithm, its discrete solutions are conceived so that they hold discrete principles and obey an entropy law provided that an acuteness condition is imposed for meshes. Remarkably the latter is found to be unconditionally stable. We validate our methodology through transient numerical experiments that show convergence toward steady-state solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Probabilistic and maximum entropy modeling of chemical reaction systems: Characteristics and comparisons to mass action kinetic models

We demonstrate and characterize a first-principles approach to modeling the mass action dynamics of metabolism. Starting from a basic definition of entropy expressed as a multinomial probability density using Boltzmann probabilities with standard chemical potentials, we derive and compare the free energy dissipation and the entropy production rates. We express the relation between entropy production and the chemical master equation for modeling metabolism, which unifies chemical kinetics and chemical thermodynamics. Because prediction uncertainty with respect to parameter variability is frequently a concern with mass action models utilizing rate constants, we compare and contrast the maximum entropy model, which has its own set of rate parameters, to a population of standard mass action models in which the rate constants are randomly chosen. We show that a maximum entropy model is characterized by a high probability of free energy dissipation rate and likewise entropy production rate, relative to other models. We then characterize the variability of the maximum entropy model predictions with respect to uncertainties in parameters (standard free energies of formation) and with respect to ionic strengths typically found in a cell.

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

Effect of atomic size mismatch and chemical complexity on the local lattice distortion of BCC solid solution alloys

Here, the effects of atomic size mismatch and chemical complexity on the local lattice distortion of solid-solution alloys VNbTa, TiVNbMo, TiVNbMoTa and TiVNbMoTaWRe with body-centered cubic (BCC) structure are quantitatively studied with time-of-flight neutron total scattering, extended X-ray absorption fine structure (EXAFS) measurements and first principles calculations. Neutron atomic pair distribution function (PDF) measurements found that the local lattice distortion in the ternary solid-solution alloy VNbTa is 1.1 %, obviously larger than that of the most complicated solid-solution alloy (0.27% for TiVNbMoTaWRe). Our results suggested that atomic size mismatch in high entropy alloys is more critical to the local lattice distortion than chemical complexity. Both EXAFS analysis and theoretical calculations indicate that there is a maximum of ~4 % difference between the bonding length of different atomic pairs in VNbTa.

36 MATERIALS SCIENCE↗