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Results for “Non-equilibrium thermodynamics”

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 NTRS1990

Flux-split algorithms for flows with non-equilibrium chemistry and vibrational relaxation

The present consideration of numerical computation methods for gas flows with nonequilibrium chemistry thermodynamics gives attention to an equilibrium model, a general nonequilibrium model, and a simplified model based on vibrational relaxation. Flux-splitting procedures are developed for the fully-coupled inviscid equations encompassing fluid dynamics and both chemical and internal energy-relaxation processes. A fully coupled and implicit large-block structure is presented which embodies novel forms of flux-vector split and flux-difference split algorithms valid for nonequilibrium flow; illustrative high-temperature shock tube and nozzle flow examples are given.

Grossman, B.↗
DOE OSTI2026

Data-driven particle dynamics: Structure-preserving coarse-graining for emergent behavior in non-equilibrium systems

Multiscale systems are ubiquitous in science and technology, but are notoriously challenging to simulate as short spatiotemporal scales must be appropriately linked to emergent bulk physics. When expensive high-dimensional dynamical systems are coarse-grained into low-dimensional models, the entropic loss of information leads to emergent physics which are dissipative, history-dependent, and stochastic. To machine learn coarse-grained dynamics from time-series observations of particle trajectories, we propose a framework using the metriplectic bracket formalism that preserves these properties by construction; most notably, the framework guarantees discrete notions of the first and second laws of thermodynamics, conservation of momentum, and a discrete fluctuation-dissipation balance crucial for capturing non-equilibrium statistics. We introduce the mathematical framework abstractly before specializing to a particle discretization. As labels are generally unavailable for entropic state variables, we introduce a novel self-supervised learning strategy to identify emergent structural variables. We validate the method on benchmark systems and demonstrate its utility on two challenging examples: (1) coarse-graining star polymers at challenging levels of coarse-graining while preserving non-equilibrium statistics, and (2) learning models from high-speed video of colloidal suspensions that capture coupling between local rearrangement events and emergent stochastic dynamics. We provide open-source implementations in both PyTorch and LAMMPS, enabling large-scale inference and extensibility to diverse particle-based systems.

Computational Engineering, Finance, and Science (c↗
DOE OSTI2026

Violation of detailed balance in non-equilibrium magnons observed by inelastic neutron scattering

Traditional inelastic neutron scattering (INS) characterizes excitations—such as phonons and magnons—in condensed matter systems at thermodynamic equilibrium. However, the most intriguing and puzzling many-body effects in open quantum systems often emerge from dissipative dynamics that are inherently out of equilibrium. Here, we use a combination of laser pumping and INS to experimentally observe long-lived nonequilibrium magnons in a two-dimensional (2D) square-lattice Heisenberg antiferromagnet. These nonequilibrium magnons manifest themselves as a violation of detailed balance in the dynamic structure factor and reach steady states under periodic driving, analogous to nonequilibrium steady states in driven dissipative systems. Furthermore, we show that the violation of detailed balance reflects the quantum-mechanical nature of the underlying dynamical system, where out-of-time-ordered correlations of creation and annihilation operators do not satisfy commutation relations. The in operando INS technique developed here provides a new approach to studying nonequilibrium magnons in prototypical 2D quantum magnets and can be extended to other systems, including one-dimensional spin chains and topological many-body spin systems, where nonequilibrium effects are widespread and rich in discovery potential.

Hua, Chengyun [Oak Ridge National Laboratory (ORNL↗
DOE OSTI2026

Thermodynamics and its prediction and CALPHAD modeling: Review, state of the art, and perspectives

Thermodynamics is a science concerning the state of a system, whether it is stable, metastable, or unstable, when interacting with its surroundings. The combined law of thermodynamics derived by Gibbs about 150 years ago laid the foundation of thermodynamics. In Gibbs combined law, the entropy production due to internal processes was not included, and the 2nd law was thus practically removed from the Gibbs combined law, so it is only applicable to systems under equilibrium, thus commonly termed as equilibrium or Gibbs thermodynamics. Gibbs further derived the classical statistical thermodynamics in terms of the probability of configurations in a system in the later 1800's and early 1900's. With the quantum mechanics (QM) developed in 1920's, the QM-based statistical thermodynamics was established and connected to classical statistical thermodynamics at the classical limit as shown by Landau in the 1940's. In 1960's the development of density functional theory (DFT) by Kohn and co-workers enabled the QM prediction of properties of the ground state of a system. On the other hand, the entropy production due to internal processes in non-equilibrium systems was studied separately by Onsager in 1930's and Prigogine and co-workers in the 1950's. In 1960's to 1970's the digitization of thermodynamics was developed by Kaufman in the framework of the CALculation of PHAse Diagrams (CALPHAD) modeling of individual phases with internal degrees of freedom. CALPHAD modeling of thermodynamics and atomic transport properties has enabled computational design of complex materials in the last 50 years. Our recently termed zentropy theory integrates DFT and statistical mechanics through the replacement of the internal energy of each individual configuration by its DFT-predicted free energy. The zentropy theory is capable of accurately predicting the free energy of individual phases, transition temperatures and properties of magnetic and ferroelectric materials with free energies of individual configurations solely from DFT-based calculations and without fitting parameters, and is being tested for other phenomena including superconductivity, quantum criticality, and black holes. Those predictions include the singularity at critical points with divergence of physical properties, negative thermal expansion, and the strongly correlated physics. Furthermore, those individual configurations may thus be considered as the genomic building blocks of individual phases in the spirit of the materials genome®. This has the potential to shift the paradigm of CALPHAD modeling from being heavily dependent on experimental inputs to becoming fully predictive with inputs solely from DFT-based calculations and machine learning models built on those calculations and existing experimental data through newly developed and future open-source tools. Furthermore, through the combined law of thermodynamics including the internal entropy production, it is shown that the kinetic coefficient matrix of independent internal processes is diagonal with respect to the conjugate potentials in the combined law, and the cross phenomena that the phenomenological Onsager flux and reciprocal relationships are due to the dependence of the conjugate potential of a molar quantity on nonconjugate molar quantities and other potentials, which can be predicted by the zentropy theory and CALPHAD modeling.

42 ENGINEERING↗
NASA NTRS1979

Non-equilibrium processes in interstellar molecules

The types of nonequilibrium emission and absorption by interstellar molecules are summarized. The observed brightness emission temperatures of compact OH and H2O sources are discussed using the concept of maser amplification. A single thermodynamic approach was used in which masers and anti-masers are considered as heat engines for the theoretical interpretation of the cosmic maser and anti-maser phenomena. The requirements for different models of pumping are formulated and a classification is suggested for the mechanisms of pumping, according to the source and discharge of energy.

Strelnitskiy, V. S.↗
DOE OSTI2024

Classical-quantum simulation of non-equilibrium Marshak waves

In the radiation hydrodynamic simulations used to design inertial confinement fusion (ICF) and pulsed power experiments, nonlinear radiation diffusion tends to dominate CPU time. This raises the interesting question of whether a quantum algorithm can be found for nonlinear radiation diffusion which provides a quantum speedup. Recently, such a quantum algorithm was introduced based on a quantum algorithm for solving systems of nonlinear partial differential equations (PDEs) which provides a quadratic quantum speedup. Here, we apply this quantum PDE (QPDE) algorithm to the problem of a non-equilibrium Marshak wave propagating through a cold, semi-infinite, optically thick target, where the radiation and matter fields are not assumed to be in local thermodynamic equilibrium. The dynamics is governed by a coupled pair of nonlinear PDEs which are solved using the QPDE algorithm, as well as two standard PDE solvers: (i) Python's py-pde solver; and (ii) the KULL ICF simulation code developed at Lawrence-Livermore National Laboratory. We compare the simulation results obtained using the QPDE algorithm and the standard PDE solvers and find excellent agreement.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Elucidating key reducing species beyond ions in hydrogen plasma smelting reduction of iron ore

Hydrogen plasma smelting reduction (HPSR) of iron ore has attracted significant attention over the past decade due to its high-temperature operation, rapid plasma mediated reduction kinetics, and simpler density-based separation of molten iron product, compared to H2-based solid-state reduction. All of these attributes enable processing of low-grade ores for downstream use in electric-arc furnaces, as virgin iron with low gangue content is required for high quality steel and improved furnace operation. While positive ions exist within the plasma arc, this work demonstrates that near the anodic ore surface, hydrogen radicals and vibrationally excited hydrogen species dominate and their densities correlate well with observed reduction rates. Species concentrations in the transferred plasma arc and at the plasma-ore interface are evaluated using coupled thermal plasma and near-wall non-equilibrium plasma models. The thermal plasma model is validated against experimental voltage data and spectroscopic measurements of plasma temperature and density for varying current inputs. Modeling of the near surface thermochemical non-equilibrium and micrometer scale anode sheath layer reveals, in addition to the expected H + , significant concentrations of ArH + and H$^+_3$ ions, typically not observed in thermal plasmas under thermodynamic equilibrium. Our results show that the inverted sheath structure at the anodic ore surface strongly suppresses reactive positive ion fluxes, while non-equilibrium electron-impact processes generate abundant hydrogen radicals and vibrationally excited species. These findings highlight the critical role of non-equilibrium effects in hydrogen arc-driven iron ore reduction and advance understanding beyond prevailing hypotheses centered on hydrogen ion-driven mechanisms.

08 HYDROGEN↗
NASA NTRS1992

Innovative techniques for the production of energetic radicals for lunar processing including cold plasma processing of local planetary ores

Hydrogen reduction of ilmenite has been studied by a number of investigators as a potential means for recovery of oxygen from lunar soil. Interest in this process has always rested with the simplicity of the flow diagram and the utilization of established technology. Effective utilization of hydrogen in the reduction process at temperatures of 1200 C and below has always been disappointing and, as such, has led other investigators to focus attention on other systems. Effective utilization of hydrogen in the reduction of ilmenite can be significantly enhanced in the presence of a non-equilibrium hydrogen plasma. Ilmenite at solid specimen temperatures of 600 C to 970 C were reacted in a hydrogen plasma. Those experiments revealed that hydrogen utilization can be significantly enhanced. At a specimen temperature of 850 C the fraction of H2 reacted was 24 percent compared to the 7 percent theoretical limit calculated with thermodynamic theory for the same temperature. An added advantage for a hydrogen plasma involves further reduction of TiO2. Reduction of the iron oxide in ilmenite yields TiO2 and metallic iron as by products. Titanium forms a number of oxides including TiO, Ti2O3, Ti3O5 and the Magneli oxides (Ti4O7 to Ti50O99). In conventional processing of ilmenite with hydrogen it is possible to reduce TiO2 to Ti7O13 within approximately an hour, but with poor utilization of hydrogen on the order of one mole of H2 per thousand. In the cold or non-equilibrium plasma TiO2 can be rapidly reduced to Ti2O3 with hydrogen utilization exceeding 10 percent. Based on design considerations of the plasma reactor greater utilization of the hydrogen in the reduction of TiO2 is possible.

Bullard, D.↗
NASA NTRS1991

Metastable phase formation in undercooled liquid lead alloys

During non-equilibrium processes metastable phases are formed instead of stable phases due to the operation of various kinetic or structural constraints. By removing the most effective nucleation sites for the stable phase using emulsified droplet samples, stable phase formation can be prohibited in a broad range of undercooling and the phase space available in the metastable regime can be mapped out. With this method the thermodynamic properties of the undercooled liquid and the metastable phase boundaries corresponding to reversible metastable (solid + liquid) phase equilibria are examined from experimental data. The analysis reveals important implications for the nucleation kinetics and the choice of the kinetically most favored solidification path.

Fecht, Hans J.↗
NASA NTRS1993

Thermophysical properties of simple liquid metals: A brief review of theory

In this paper, we review the current theory of the thermophysical properties of simple liquid metals. The emphasis is on thermodynamic properties, but we also briefly discuss the nonequilibrium properties of liquid metals. We begin by defining a 'simple liquid metal' as one in which the valence electrons interact only weakly with the ionic cores, so that the interaction can be treated by perturbation theory. We then write down the equilibrium Hamiltonian of a liquid metal as a sum of five terms: the bare ion-ion interaction, the electron-electron interaction, the bare electron-ion interaction, and the kinetic energies of electrons and ions. Since the electron-ion interaction can be treated by perturbation, the electronic part contributes in two ways to the Helmholtz free energy: it gives a density-dependent term which is independent of the arrangement of ions, and it acts to screen the ion-ion interaction, giving rise to effective ion-ion pair potentials which are density-dependent, in general. After sketching the form of a typical pair potential, we briefly enumerate some methods for calculating the ionic distribution function and hence the Helmholtz free energy of the liquid: monte Carlo simulations, molecular dynamics simulations, and thermodynamic perturbation theory. The final result is a general expression for the Helmholtz free energy of the liquid metal. It can be used to calculate a wide range of thermodynamic properties of simple metal liquids, which we enumerate. They include not only a range of thermodynamic coefficients of both metals and alloys, but also many aspects of the phase diagram, including freezing curves of pure elements and phase diagrams of liquid alloys (including liquidus and solidus curves). We briefly mention some key discoveries resulting from previous applications of this method, and point out that the same methods work for other materials not normally considered to be liquid metals (such as colloidal suspensions, in which the suspended microspheres behave like ions screened by the salt solution in which they are suspended). We conclude with a brief discussion of some non-equilibrium (i.e., transport) properties which can be treated by an extension of these methods. These include electrical resistivity, thermal conductivity, viscosity, atomic self-diffusion coefficients, concentration diffusion coefficients in alloys, surface tension and thermal emissivity. Finally, we briefly mention two methods by which the theory might be extended to non-simple liquid metals: these are empirical techniques (i.e., empirical two- and three-body potentials), and numerical many-body approaches. Both may be potentially applicable to extremely complex systems, such as nonstoichiometric liquid semiconductor alloys.

Stroud, David↗
DOE OSTI2025

Potentials of mean force fail to describe chemical bond-breaking in solution

Many liquid phase studies assume that the potential energy surfaces of reacting molecules are the same as in the gas phase, neglecting complex solvent dynamics that can completely alter the nature of chemical reactivity. Even studies that include solvent effects typically only consider them in an average, equilibrium way as part of a potential of mean force (PMF). In this work, we use mixed quantum/classical simulations to compare how equilibrium and non-equilibrium solvent motions affect the photodissociation of a simple diatomic molecule, NaK + , in liquid tetrahydrofuran. A PMF analysis shows that as the excited-state molecule dissociates with the solvent at equilibrium, the bonding electron remains associated with K + at short bond distances but eventually localizes on Na + at the end of dissociation. When we examine non-equilibrium dynamical photodissociation trajectories, however, we find that they fall into three distinct categories: about a quarter of them have the bonding electron mainly associated with Na + , another quarter stay mainly associated with K + , and about half have the bonding electron shared roughly equally between the two ions. The results show that equilibrium PMFs cannot accurately describe the dynamics of bond-breaking chemical reactions in solution because there is insufficient time for the solvent to reach equilibrium on the time scale over which bond dissociation occurs. Furthermore, our analysis shows that the solvent coupling between the electronic energy surfaces is similar at and away from equilibrium, suggesting that other factors, such as solute velocity-driven solvent memory effects, play a more important role in explaining the failure of the equilibrium PMF to predict the non-equilibrium dynamics.

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

Incorporating the molecular-scale into a hydrodynamic description of confined aqueous systems

Hydrodynamics provides a continuum-level description of fluid motion, but its applicability at the nanoscale becomes uncertain due to the emerging importance of molecular-level effects such as spatial heterogeneity. Hydrodynamic boundary conditions that incorporate molecular details allow us to partition the system into a near-wall region and a bulk fluid region. We identify a hydrodynamic wall located inside the fluid that determines where slip begins. By extending the hydrodynamic wall with the slip length, the position of the extrapolated wall is established. This offers a unified description of both slip and stagnant flow behaviors, with wall hydrophobicity characterized by the relative location of the extrapolated wall with respect to the physical wall. Employing this concept in analyses of equilibrium molecular dynamics (MD) and non-equilibrium MD simulations of Couette and Poiseuille flows, our results demonstrate consistency between equilibrium and non-equilibrium approaches across different flow types and confinement levels. This demonstrates the robust nature of linear response theory. We then explore the effects of fluid-wall and bulk fluid interactions on the hydrodynamic properties. These findings enhance the effectiveness of molecular-based simulations for investigating complex confined systems in nanofluidics, biology, and colloidal science, offering a complementary molecular-scale perspective to traditional continuum approaches.

flow simulations↗
DOE OSTI2026

A modified scheil approach for nucleation-dependent solidification pathways

As-solidified microstructures of near-eutectic alloys often contain multiple primary phases that are not expected from equilibrium phase diagrams. Such microstructures are caused by cooling-rate-dependent solidification pathways, a factor not captured by the Scheil–Gulliver model or variations thereof. Here, we present a model and algorithm that incorporate the critical nucleation undercooling for each solid phase into the Scheil–Gulliver model. We hypothesize that the non-equilibrium microstructure formation is primarily governed by a nucleation-competition mechanism. This mechanism accounts for both stable/metastable phase selection and primary-phase formation within eutectic regions driven by asymmetric nucleation barriers. The model is validated against a hypereutectic Al-Fe alloy, where it successfully reproduces the observed microstructural constituents, revealing the key dependencies of solidification microstructure on nucleation kinetics. Applicability to multicomponent systems is demonstrated through a hypereutectic Al–Fe–Si ternary alloy, where the model successfully predicts divorced eutectic microstructures and the associated oscillatory solidification pathways along univariant lines. As a result, the proposed framework establishes a nucleation-dependent computational approach for interpreting and predicting solidification microstructures.

Alloy design↗
DOE OSTI2024

Flame kinetics at scramjet-engine-relevant conditions: Role of prompt dissociation of weakly-bound radicals

Combustion in high-speed ram-based propulsion engines occurs under distinct thermodynamic conditions of high reactant temperatures (greater than 1000 K) and relatively low pressures (<5 atm). There is a lack of fundamental flame measurements at such conditions that result in adiabatic flame temperatures (T ad ) exceeding 2500 K. In this work, we have measured laminar flame speeds of oxygen-enriched CH 4 /oxidizer mixtures at sub-atmospheric conditions to probe kinetics at high T ad using the isobaric spherically expanding flame approach. Simulations with recent kinetic models revealed increasing differences between data and model predictions with increasing T ad , reaching up to 25 %. Kinetic analyses reveal that at the thermodynamic conditions in these O 2 -enriched flames, i.e., lower pressures and higher T ad , the effects of HCO prompt dissociation are accentuated. In addition to HCO, the prompt dissociations of CH 2 OH and C 2 H 5 are also considered. Here, the prompt dissociations of all three radicals were evaluated and their effects considered in flame speed simulations. Reaction path analysis for the present flames revealed that approximately half of the reaction flux for HCO formation undergoes prompt dissociation to H + CO. Furthermore, these analyses also revealed that the pathways and sensitive reactions are similar between oxygen-enriched fuel/oxidizer mixtures and preheated fuel/air mixtures, if both have similar T ad . Thus, flames of oxygen-enriched mixtures could be a surrogate to probe the flame chemistry of highly preheated mixtures at relatively low pressures that are often encountered in ram-based propulsion engine combustors.

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

Design of novel refractory equiatomic multi-principal elemental alloys based on Mo-Nb-Ti system for Gen IV reactor applications

Excellent irradiation damage resistance demonstrated by multi-principal elemental alloys (MPEAs) has sparked significant interest among researchers, prompting exploration into their vast compositional space, to validate their suitability for nuclear applications. A combined approach of thermodynamic and empirical parameters calculations alongside CALPHAD (CALculation of PHAse Diagrams) for phase formation predictions enable high-throughput material selection for sophisticated applications like nuclear, overcoming laborious and time-consuming experiments. Key thermodynamic and empirical parameters for eight novel equiatomic MPEAs, based on seven low thermal neutron cross section refractory elements, for predicting phase formation were calculated, and equilibrium and non-equilibrium simulations in CALPHAD were employed to comprehensively model the systems. Pseudo binary phase diagram simulations showed that Zr, V or equiatomic CrV additions to the base MoNbTi alloy (MoNbTi-Zr, MoNbTi-V and MoNbTi-CrV alloys) favor the formation of isomorphous body-centered cubic (BCC) phase at high temperatures, while Cr, Al, equiatomic ZrV, or equiatomic CrAl additions (MoNbTi-Cr, MoNbTi-Al, MoNbTi-ZrV or MoNbTi-CrAl alloys) limit the solubility of them. Equilibrium CALPHAD simulations at 750 oC were consistent with XRD results on MoNbTi, MoNbTiZr and MoNbTiCr alloys, and partially for others. Notably, elemental segregation observed in the backscattered electron (BSE) scanning electron microscopy (SEM) images of the alloys was accurately simulated through non-equilibrium Scheil solidification calculations in CALPHAD, further verified by experiments. The precipitation of TiCr2 Laves phase in Cr containing MoNbTiCr and MoNbTiCrAl was accurately predicted while discrepancies were noted in MoNbTiCrV. The equilibrium simulations also provided insights into phase compositions at specific temperatures offering a pathway for tailoring the desired microstructure and properties of these systems. Empirical parameters calculations successfully predicted random solid solution in the base MoNbTi alloy, and with an exception in MoNbTiV and MoNbTiAl, predicted intermetallic precipitation in the rest, especially, Laves phase precipitation in Cr containing alloys.

36 - MATERIALS SCIENCE↗
DOE OSTI2025

Pseudo-equilibrium theory for extrinsic doping control of the topological semimetal Cd 3 As 2

The standard approach for predicting defect equilibria from first principles assumes that the solid-state system is initially in a thermodynamic equilibrium with the external atomic reservoirs. This “growth step” is then often followed by a temperature quench in a “pseudo-equilibrium” in which some or all defect concentrations are frozen in until only the Fermi level E F remains to be equilibrated. However, this protocol does not account for the possibility of site exchanges which can create important defect redistributions as long as short-range defect migration is kinetically permissible. To model this redistribution, we developed an approach to solve for the non-equilibrium chemical potentials as a function of temperature while maintaining the overall defect stoichiometry. We then apply this approach to the Dirac semimetal Cd 3 As 2 to model extrinsic doping with group 1/11 and 14 elements. Undoped Cd 3 As 2 exhibits an undesirable mismatch between E F and the Dirac point. This unintentional electron doping originates from intrinsic defects and is difficult to overcome through adjustment of synthesis conditions alone. Employing our pseudo-equilibrium modeling, we identify extrinsic doping strategies for realizing doping-balanced Cd 3 As 2 at the relatively low temperatures accessible in thin-film growth of this material.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Thermodynamic consistency and fluctuations in mesoscopic stochastic simulations of reactive gas mixtures

It is essential that mesoscopic simulations of reactive systems reproduce the correct statistical distributions at thermodynamic equilibrium. By considering a compressible fluctuating hydrodynamics (FHD) simulation method of ideal gas mixtures undergoing reversible reactions described by the chemical Langevin equations, we show that thermodynamic consistency in reaction rates and the use of instantaneous temperatures for the evaluation of reaction rates is required for fluctuations for the overall system to be correct. We then formulate the required properties of a thermodynamically consistent reaction (TCR) model. As noted in the literature, while reactions are often discussed in terms of forward and reverse rates, these rates should not be modeled independently because they must be compatible with thermodynamic equilibrium for the system. Using a simple TCR model where each chemical species has constant heat capacity, we derive the explicit condition that the forward and reverse reaction rate constants must satisfy in order for the system to be thermodynamically consistent. We perform equilibrium and non-equilibrium simulations of ideal gas mixtures undergoing a reversible dimerization reaction to measure the fluctuational behavior of the system numerically. We confirm that FHD simulations with the TCR model give the correct static structure factor of equilibrium fluctuations. For the statistically steady simulation of a gas mixture between two isothermal walls with different temperatures, we show using the TCR model that the temperature variance agrees with the corresponding thermodynamic-equilibrium temperature variance in the interior of the system, whereas noticeable deviations are present in regions near walls, where chemistry is far from equilibrium.

Polimeno, Matteo [University of California, Merced↗