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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

A mathematical framework for thermodynamic computing with applications to chemical reaction networks

The widespread adoption of energy-intensive computing applications has led to a growing need for energy-efficient computing approaches. Thermodynamic computing offers a promising approach for low-energy computation by leveraging the intrinsic computational capabilities of physical, chemical, or biological systems. However, the mathematical foundations of thermodynamic computing require further development to fully realize the potential energy efficiencies, as well as to assess factors like noise and operational speed. In this paper, we establish a mathematical framework for utilizing thermodynamic processes to perform fundamental operations, including addition, subtraction, multiplication, and division. We highlight the use of chemical reactions as potential computational units and explore synthetic chemical and biochemical systems as practical implementations. Additionally, we demonstrate how these principles can be applied to solving complex mathematical problems, such as ordinary differential equations (ODEs) and suggest the necessary components to implement the thermodynamic computing framework using chemical reactions based in a microfluidic device. This work enhances our understanding of thermodynamic processes for natural computing as a basis for scalable, energy-efficient computation in paradigm disruptive next-generation systems.

Cannon, William R. [Pacific Northwest National Lab↗
DOE OSTI2022

Thermodynamics of electrolyte solutions near charged surfaces: Constant surface charge vs constant surface potential

Electric double layers are ubiquitous in science and engineering and are of current interest, owing to their applications in the stabilization of colloidal suspensions and as supercapacitors. While the structure and properties of electric double layers in electrolyte solutions near a charged surface are well characterized, there are subtleties in calculating thermodynamic properties from the free energy of a system with charged surfaces. These subtleties arise from the difference in the free energy between systems with constant surface charge and constant surface potential. In this work, we present a systematic, pedagogical framework to properly account for the different specifications on charged bodies in electrolyte solutions. Our approach is fully variational—that is, all free energies, boundary conditions, relevant electrostatic equations, and thermodynamic quantities are systematically derived using variational principles of thermodynamics. We illustrate our approach by considering a simple electrolyte solution between two charged surfaces using the Poisson–Boltzmann theory. Our results highlight the importance of using the proper thermodynamic potential and provide a general framework for calculating thermodynamic properties of electrolyte solutions near charged surfaces. Specifically, we present the calculation of the pressure and the surface tension between two charged surfaces for different boundary conditions, including mixed boundary conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Is stochastic thermodynamics the key to understanding the energy costs of computation?

The relationship between the thermodynamic and computational properties of physical systems has been a major theoretical interest since at least the 19th century. It has also become of increasing practical importance over the last half-century as the energetic cost of digital devices has exploded. Importantly, real-world computers obey multiple physical constraints on how they work, which affects their thermodynamic properties. Moreover, many of these constraints apply to both naturally occurring computers, like brains or Eukaryotic cells, and digital systems. Most obviously, all such systems must finish their computation quickly, using as few degrees of freedom as possible. This means that they operate far from thermal equilibrium. Furthermore, many computers, both digital and biological, are modular, hierarchical systems with strong constraints on the connectivity among their subsystems. Yet another example is that to simplify their design, digital computers are required to be periodic processes governed by a global clock. None of these constraints were considered in 20th-century analyses of the thermodynamics of computation. The new field of stochastic thermodynamics provides formal tools for analyzing systems subject to all of these constraints. We argue here that these tools may help us understand at a far deeper level just how the fundamental thermodynamic properties of physical systems are related to the computation they perform.

computation↗
DOE OSTI2019

Macroscopic Thermodynamic Reversibility in Quantum Many-Body Systems

The resource theory of thermal operations, an established model for small-scale thermodynamics, provides an extension of equilibrium thermodynamics to nonequilibrium situations. On a lattice of any dimension with any translation-invariant local Hamiltonian, we identify a large set of translation-invariant states that can be reversibly converted to and from the thermal state with thermal operations and a small amount of coherence. These are the spatially ergodic states, i.e., states that have sharp statistics for any translation-invariant observable, and mixtures of such states with the same thermodynamic potential. As an intermediate result, we show for a general state that if the gap between the min- and the max-relative entropies to the thermal state is small, then the state can be approximately reversibly converted to and from the thermal state with thermal operations and a small source of coherence. Our proof provides a quantum version of the Shannon-McMillan-Breiman theorem for the relative entropy and a quantum Stein’s lemma for ergodic states and local Gibbs states. In this work, our results provide a strong link between the abstract resource theory of thermodynamics and more realistic physical systems as we achieve a robust and operational characterization of the emergence of a thermodynamic potential in translation-invariant lattice systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Evolution of the Thermodynamic Properties of Clusters of Galaxies out to Redshift of 1.8

The thermodynamic properties of the hot plasma in galaxy clusters retains information on the processes leading to the formation and evolution of the gas in their deep, dark matter potential wells. These processes are dictated not only by gravity but also by gas physics, e.g. AGN feedback and turbulence. Here, we study the thermodynamic properties, e.g. density, temperature, pressure, and entropy, of the most massive and the most distant (z > 1.2) SPT-selected clusters, and compare them with those of the nearby clusters (z < 0.1) to constrain their evolution as a function of time and radius. We find that thermodynamic properties in the outskirts of high redshift clusters are remarkably similar to the low redshift clusters, and their evolution follows the prediction of the self-similar model. Their intrinsic scatter is larger, indicating that the physical properties that lead to the formation and virialization of cluster outskirts show evolving variance. On the other hand, thermodynamic properties in the cluster cores deviates significantly from self-similarity indicating that the processes that regulate the core are already in place in these very high redshift clusters. This result is supported by the unevolving physical scatter of all thermodynamic quantities in cluster cores.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Classifying thermodynamic cloud phase using machine learning models

Vertically resolved thermodynamic cloud-phase classifications are essential for studies of atmospheric cloud and precipitation processes. The Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) Thermodynamic Cloud Phase (THERMOCLDPHASE) value-added product (VAP) uses a multi-sensor approach to classify the thermodynamic cloud phase by combining lidar backscatter and depolarization, radar reflectivity, Doppler velocity, spectral width, microwave-radiometer-derived liquid water path, and radiosonde temperature measurements. The measured pixels are classified as ice, snow, mixed phase, liquid (cloud water), drizzle, rain, and liq_driz (liquid+drizzle). We use this product as the ground truth to train three machine learning (ML) models to predict the thermodynamic cloud phase from multi-sensor remote sensing measurements taken at the ARM North Slope of Alaska (NSA) observatory: a random forest (RF), a multi-layer perceptron (MLP), and a convolutional neural network (CNN) with a U-Net architecture. Evaluations against the outputs of the THERMOCLDPHASE VAP with 1 year of data show that the CNN outperforms the other two models, achieving the highest test accuracy, F1 score, and mean intersection over union (IOU). Analysis of ML confidence scores shows that ice, rain, and snow have higher confidence scores, followed by liquid, while mixed, drizzle, and liq_driz have lower scores. Feature importance analysis reveals that the mean Doppler velocity and vertically resolved temperature are the most influential data streams for ML thermodynamic cloud-phase predictions. Lidar measurements exhibit lower feature importance due to rapid signal attenuation caused by the frequent presence of persistent low-level clouds at the NSA site. The ML models' generalization capacity is further evaluated by applying them at another Arctic ARM site in Norway using data taken during the ARM Cold-Air Outbreaks in the Marine Boundary Layer Experiment (COMBLE) field campaign. The models demonstrated similar performance to that observed at the NSA site. Finally, we evaluate the ML models' response to simulated instrument outages and signal degradation and show that a CNN U-Net model trained with input channel dropouts performs better when input fields are missing.

ARM Aerial Facility↗
DOE OSTI2020

Evolution of the Thermodynamic Properties of Clusters of Galaxies out to Redshift of 1.8

The thermodynamic properties of the hot plasma in galaxy clusters retains information on the processes leading to the formation and evolution of the gas in their deep, dark matter potential wells. These processes are dictated not only by gravity but also by gas physics, e.g. AGN feedback and turbulence. In this work, we study the thermodynamic properties, e.g. density, temperature, pressure, and entropy, of the most massive and the most distant ($z > 1.2$) SPT-selected clusters, and compare them with those of the nearby clusters ($z<0.1$) to constrain their evolution as a function of time and radius. We find that thermodynamic properties in the outskirts of high redshift clusters are remarkably similar to the low redshift clusters, and their evolution follows the prediction of the self-similar model. Their intrinsic scatter is larger, indicating that the physical properties that lead to the formation and virialization of cluster outskirts show evolving variance. On the other hand, thermodynamic properties in the cluster cores deviates significantly from self-similarity indicating that the processes that regulate the core are already in place in these very high redshift clusters. This result is supported by the unevolving physical scatter of all thermodynamic quantities in cluster cores.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Inverse Thermodynamics: Designing Interactions for Targeted Phase Behavior

The traditional goal of inverse self-assembly is to design interactions that drive particles toward a desired target structure. However, achieving successful self-assembly also requires tuning the thermodynamic conditions under which the structure is stable. In this work, we extend the inverse design paradigm to explicitly address this challenge by developing a framework for inverse thermodynamics, i.e., the design of interaction potentials that realize specific thermodynamic behavior. As a step in this direction, using patchy particle mixtures as a model system, we demonstrate how precise control over both bonding topology and bond energetics enables the programming of targeted phase behavior. In particular, we establish design principles for azeotropic demixing and show how to create mixtures that exhibit azeotropy at any prescribed composition. Our predictions are validated through Gibbs-ensemble simulations [Panagiotopoulos, Mol. Phys. 1987, 61, 813−826]. These results highlight the necessity of coupling structural design with thermodynamic engineering, and provide a blueprint for controlling complex phase behavior in multicomponent systems.

Azeotropes↗
DOE OSTI2022

Quantum thermodynamic devices: From theoretical proposals to experimental reality

Thermodynamics originated in the need to understand novel technologies developed by the Industrial Revolution. However, over the centuries, the description of engines, refrigerators, thermal accelerators, and heaters has become so abstract that a direct application of the universal statements to real-life devices is everything but straight forward. Furthermore, the recent, rapid development of quantum thermodynamics has taken a similar trajectory, and, e.g., “quantum engines” have become a widely studied concept in theoretical research. However, if the newly unveiled laws of nature are to be useful, we need to write the dictionary that allows us to translate abstract statements of theoretical quantum thermodynamics to physical platforms and working mediums of experimentally realistic scenarios. To assist in this endeavor, this review is dedicated to provide an overview over the proposed and realized quantum thermodynamic devices and to highlight the commonalities and differences of the various physical situations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

On Gibbs Equilibrium and Hillert Nonequilibrium Thermodynamics

During his time at Royal Institute of Technology (Kungliga Tekniska högskolan) in Sweden, the present author learned nonequilibrium thermodynamics from Mats Hillert. The key concepts are the separation of internal and external variables of a system and the definitions of potentials and molar quantities. In equilibrium thermodynamics derived by Gibbs, the internal variables are not independent and can be fully evaluated from given external variables. While irreversible thermodynamics led by Onsager focuses on internal variables though often mixed with external variables. Hillert integrated them together by first emphasizing their differences and then examining their connections. His philosophy was reflected by the title of his book “Phase Equilibria, Phase Diagrams and Phase Transformations” that puts equilibrium, nonequilibrium, and internal processes on equal footing. Here, in the present paper honoring Hillert, the present author reflects his experiences with Hillert and his work in last 40 years and expresses his gratitude for all the wisdom and support from him in terms of “Hillert nonequilibrium thermodynamics” and discusses some recent topics that the present author has been working on.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Null geodesics and thermodynamic phase transition of four-dimensional Gauss–Bonnet AdS black hole

Highlights: • Modified gravity theories. • Null geodesics and the thermodynamic phase transition. • Four-dimensional Gauss–Bonnet AdS black hole. • Correlation between gravity and thermodynamics. Modified gravity theories are of great interest in both observational and theoretical studies. In this article, we study the correlation between the null geodesics and the thermodynamic phase transition of a four-dimensional Gauss–Bonnet AdS black hole. Firstly, we study the phase structure of the black hole, using the coexistence and spinodal curves, to understand the phase transition in an extended phase space. The imprints of these phase transition features can be clearly observed from the functional dependence of photon orbit radius and minimum impact parameter with respect to the Hawking temperature and pressure. The change in these two quantities during the phase transition serve as order parameters which characterise the critical behaviour. The correlation shows that thermodynamic phase transition can be studied by observing the effects of strong gravitational field on the photon orbit and vice versa.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Thermodynamics of monoclinic and tetragonal hafnium dioxide (HfO 2 ) at ambient pressure

Accurate and precise thermodynamic models of oxide compounds and their phases are important for calculating the phase stability of oxide materials. We develop and use a coupled quantum mechanical and molecular dynamics approach to create thermodynamic models of hafnia (HfO2) polymorphs from 0 K to 3000 K at ambient pressure. The approach is based on the quasi-harmonic approximation below the Debye temperature and on ab-initio molecular dynamics calculations above the Debye temperature to predict constant pressure heat capacities (C-p). A Bayesian model provides interpolated values between these regimes. As a case study, we develop thermodynamic models of monoclinic and tetragonal HfO2 polymorphs. The predicted heat capacities are in excellent agreement with experiment, and the predicted temperature of the monoclinic to tetragonal phase transition (2173 K) is in good agreement with the experimental value (2078K). These results provide a comprehensive and accurate thermodynamic model of the monoclinic and tetragonal phases of hafnia on a broad range of temperatures and can serve as input to CALPHAD assessment of multi-component hafnia-based phase diagrams.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Thermodynamic re-modeling of the Yb-Sb system aided by first-principles calculations

Here, the thermodynamic description of the Yb-Sb binary system is developed by means of the CALculations of PHAse Diagrams (CALPHAD) method by combining experimental data in the literature and predictions from first-principles calculations based on density functional theory (DFT) in the literature and the present work. Two pseudopotentials of Yb are compared in the present DFT-based calculations with 14 and 13 f-electrons frozen in the core, i.e., 5p 6 6s 2 and 5p 6 6s 2 5 d 1 electrons as valence electrons, termed Yb_2 and Yb_3, respectively. It is shown that the phonon spectrum of the YbSb phase calculated using the Yb_3 pseudopotential does not have imaginary phonon modes and is subsequently used to predict its temperature dependent thermodynamic properties by the DFT-based quasiharmonic phonon calculations. The present thermodynamic database includes the Yb 16 Sb 11 phase in addition to five intermetallic phases that were considered in previous modeling studies, i.e., YbSb 2 , YbSb, Yb 11 Sb 10 , Yb 4 Sb 3 , and Yb 5 Sb 3 . The high temperature orthorhombic structure of the Yb 5 Sb 3 phase is not considered in the present work as it was stabilized by hydrogen. The associate solution model is used to describe the short-range ordering behavior in the liquid phase. The calculations from the present thermodynamic model show good agreement with thermochemical and phase equilibrium data from both the present work and the literature.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Extended thermodynamic model for high salinity produced waters

To support the development of desalination processes for high salinity produced waters, we developed a comprehensive thermodynamic model that reliably predicts the thermodynamic properties and phase behavior of produced water. Here this study extends a previously developed thermodynamic model for the aqueous hexary oceanic salt system by incorporating the Sr 2+ and Ba 2+ ions. Based on the electrolyte nonrandom two-liquid theory, the model requires two adjustable binary interaction parameters for each water-electrolyte and electrolyte-electrolyte pair that has a common ion. The binary interaction parameters for the electrolyte-electrolyte pairs involving Sr 2+ and Ba 2+ ions were identified using thermodynamic and salt solubility data. The model was validated for temperatures from 273.15 K to 473.15 K and electrolyte concentrations from infinite dilution to salt saturation. Extension of the model to include HCO 3 − , CO 3 2− , and CO 2 is currently in progress.

42 ENGINEERING↗
DOE OSTI2025

A thermodynamically consistent discretization of 1D thermal-fluid models using their metriplectic 4-bracket structure

Thermodynamically consistent models in continuum physics, i.e. models which satisfy the first and second laws of thermodynamics, may be expressed using the metriplectic formalism. In this work, we leverage the structures underlying this modeling formalism to preserve thermodynamic consistency in discretizations of a fluid model. The procedure relies (1) on ensuring that the spatial semi-discretization retains certain symmetries and degeneracies of the Poisson and metriplectic 4-brackets, and (2) on the use of an appropriate energy conserving time-stepping method. Here, the minimally simple yet nontrivial example of a one-dimensional thermal-fluid model is treated. It is found that preservation of the requisite symmetries and degeneracies of the 4-bracket is relatively simple to ensure in Galerkin spatial discretizations, suggesting a path forward for thermodynamically consistent discretizations of more complex fluid models using more specialized Galerkin methods.

Hamiltonian structure↗
DOE OSTI2020

Critical evaluation and thermodynamic modeling of the Pd–Sn system

The single crystalline material PdSn 4 , a homologue of the Dirac nodal arc semimetal PtSn 4 , is a promising candidate to search for new topological states with fascinating quantum physical properties. In the present work, the thermochemistry and phase diagram information of the Pd–Sn system published in the literature was collected and critically reviewed, two thermodynamic reassessments of the Pd–Sn system were carried out in the frame of the CALPHAD approach to optimize the Gibbs free energy of each phase presented in the system. The liquid phase was described using respectively the Bragg-Williams random mixing model and the associate solution model. All the reliable thermodynamic property and phase equilibria data can be generally described using the presently obtained thermodynamic descriptions of the Pd–Sn system. Issues related to the further improvement of the thermodynamic descriptions of the Pd–Sn system are discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Complementing a continuum thermodynamic approach to constitutive modeling with symbolic regression

Here, an interpretable machine learning method, physics-informed genetic programming-based symbolic regression (P-GPSR), is integrated into a continuum thermodynamic approach to developing constitutive models. The proposed strategy for combining a thermodynamic analysis with P-GPSR is demonstrated by generating a yield function for an idealized material with voids, i.e., the Gurson yield function. First, a thermodynamic-based analysis is used to derive model requirements that are exploited in a custom P-GPSR implementation as fitness criteria or are strongly enforced in the solution. The P-GPSR implementation improved accuracy, generalizability, and training time compared to the same GPSR code without physics-informed fitness criteria. The yield function generated through the P-GPSR framework is in the form of a composite function that describes a class of materials and is characteristically more interpretable than GPSR-derived equations. The physical significance of the input functions learned by P-GPSR within the composite function is acquired from the thermodynamic analysis. Fundamental explanations of why the implemented P-GPSR capabilities improve results over a conventional GPSR algorithm are provided.

42 ENGINEERING↗
DOE OSTI2024

Thermodynamically consistent Cahn–Hilliard–Navier–Stokes equations using the metriplectic dynamics formalism

Cahn–Hilliard–Navier–Stokes (CHNS) systems describe flows with two-phases, e.g., a liquid with bubbles. Obtaining constitutive relations for general dissipative processes for such systems, which are thermodynamically consistent, can be a challenge. We show how the metriplectic 4-bracket formalism (Morrison and Updike, 2024) achieves this in a straightforward, in fact algorithmic, manner. First, from the noncanonical Hamiltonian formulation for the ideal part of a CHNS system we obtain an appropriate Casimir to serve as the entropy in the metriplectic formalism that describes the dissipation (e.g. viscosity, heat conductivity and diffusion effects). General thermodynamics with the concentration variable and its thermodynamics conjugate, the chemical potential, are included. Having expressions for the Hamiltonian (energy), entropy, and Poisson bracket, we describe a procedure for obtaining a metriplectic 4-bracket that describes thermodynamically consistent dissipative effects. The 4-bracket formalism leads naturally to a general CHNS system that allows for anisotropic surface energy effects. Furthermore, this general CHNS system reduces to cases in the literature, to which we can compare.

Cahn–Hilliard↗