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DOE OSTI2021

Asymmetric temperature equilibration with heat flow from cold to hot in a quantum thermodynamic system

A model computational quantum thermodynamic network is constructed with two variable temperature baths coupled by a linker system, with an asymmetry in the coupling of the linker to the two baths. It is found in computational simulations that the baths come to “thermal equilibrium” at different bath energies and temperatures. In a sense, heat is observed to flow from cold to hot. Additionally, a description is given in which a recently defined quantum entropy S univ Q for a pure state “universe” continues to increase after passing through the classical equilibrium point of equal temperatures, reaching a maximum at the asymmetric equilibrium. Thus, a second law account Δ S univ Q ≥ 0 holds for the asymmetric quantum process. In contrast, a von Neumann entropy description fails to uphold the entropy law, with a maximum near when the two temperatures are equal, then a decrease Δ S v N < 0 on the way to the asymmetric equilibrium.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Effect of total and pair configurational entropy in determining dynamics of supercooled liquids over a range of densities

In this paper, we present a study of supercooled liquids interacting with the Lennard Jones potential and the corresponding purely repulsive (Weeks-Chandler-Andersen) potential, over a range of densities and temperatures, in order to understand the origin of their different dynamics in spite of their structures being similar. Using the configurational entropy as the thermodynamic marker via the Adam Gibbs relation, we show that the difference in the dynamics of these two systems at low temperatures can be explained from thermodynamics. At higher densities both the thermodynamical and dynamical difference between these model systems decrease, which is quantitatively demonstrated in this paper by calculating different parameters. The study also reveals the origin of the difference in pair entropy despite the similarity in the structure. Although the maximum difference in structure is obtained in the partial radial distribution function of the B type of particles, the rdf of AA pairs and AB pairs gives rise to the differences in the entropy and dynamics. This work supports the observation made in an earlier study [A. Banerjee et al., Phys. Rev. Lett. 113, 225701 (2014)] and shows that they are generic in nature, independent of density.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Strong Correlation Between the Magnetocaloric Properties of Nanotubes of La{sub 0.325}Pr{sub 0.3}Ca{sub 0.375}MnO{sub 3} and their Diameters

Under 0.01 T applied magnetic field variation, the calculation of magnetocaloric properties for 200 and 800 nm nanotubes of La{sub 0.325}Pr{sub 0.3}Ca{sub 0.375}MnO{sub 3} (LPCMO) perovskite such as magnetic entropy change, full-width at half-maximum (δT FWHM), relative cooling power, and magnetic specific heat change have been done. Magnetocaloric properties of 800-nm nanotubes of LPCMO is more than MCE of 200 nm ones. LPCMO nanotubes have hopeful application for magnetic refrigeration (MR) in an extended high-temperature range due to high values of δT{sub FWHM}. Therefore, nanotubes of LPCMO are very significant for MR applications, especially nitrogen liquefier.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Beyond the Holographic Entropy Cone via Cycle Flows

Motivated by bit threads, we introduce a new prescription for computing entropy vectors outside the holographic entropy cone. By utilizing cycle flows on directed graphs, we show that the maximum cycle flow associated to any subset of vertices, which corresponds to a subsystem, manifestly obeys purification symmetry. Furthermore, by restricting ourselves to a subclass of directed graphs, we prove that the maximum cycle flow obeys both subadditivity and strong subadditivity, thereby establishing it as a viable candidate for the entropy associated to the subsystem. Lastly, we demonstrate how our model generalizes the entropy vectors obtainable via conventional flows in undirected graphs, as well as conjecture that our model similarly generalizes the entropy vectors arising from hypergraphs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2014

Oscillating magnetocaloric effect of a multilayer graphene

The oscillating magnetocaloric effect of a multilayer graphene in Bernal and rhombohedral stacking is investigated to extend the previous knowledge of the effect on a single layer graphene. We started from results of a tight-binding model and obtained analytical expressions for the thermodynamic potential and for the entropy change. The last exhibits the same dependence on field and temperature observed for other diamagnetic systems; it oscillates with the inverse magnetic field and presents a maximum value at a given temperature. The amplitude of the oscillating entropy change decreases with the number of layers and the stacking sequence rules the magnetocaloric properties of the system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Magnetoelastic transition and magnetocaloric effect in induction melted Fe 100-x Rh x bulk alloys with x = 50, 51

Magnetoelastic transitions (METs) in bulk in nearly equiatomic Fe-Rh alloys produced by arc melting may show poor reproducibility related to insufficient chemical homogeneity and presence of impurity phases in variable concentrations. To better understand the synthesis conditions that reliably yield bulk FeRh materials with reproducible MET characteristics, Fe 100-x Rh x alloys with x = 50, 50.5 and 51 at. % were prepared by induction melting and thermal annealing under identical conditions. The fabricated samples were cut into several slices, followed by characterization of METs in each of the slices using isothermal and isofield magnetization measurements, differential scanning calorimetry, and direct measurements of the magnetocaloric effect. All of the slices exhibit METs between the AFM and FM states, but the transitions are abrupt with nearly the same change of magnetization, ΔM, when x = 50.5 and 51, whereas for the x = 50 alloy the transition spreads over a wide temperature interval and ΔM may fluctuate by as much as 10 % from one specimen to another. A comparison of the magnetocaloric responses of x = 50 and 51 materials is presented. The clearly different effect of the magnetic field on the transition in both directions leads to significant differences in the reversibility and maximum values of the magnetic field-induced entropy and adiabatic temperature changes, as well as average hysteresis losses. In terms of reproducibility, our results suggest that induction melting is a more appropriate technique to prepare these binary alloys.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Hydrogen Plus Other Alternative Fuels Risk Assessment Models (HyRAM+) Version 4.1 Technical Reference Manual

The HyRAM+ software toolkit provides a basis for conducting quantitative risk assessment and consequence modeling for hydrogen, methane, and propane systems. HyRAM+ is designed to facilitate the use of state-of-the-art models to conduct robust, repeatable assessments of safety, hazards, and risk. HyRAM+ integrates deterministic and probabilistic models for quantifying accident scenarios, predicting physical effects, characterizing hazards (thermal effects from jet fires, overpressure effects from delayed ignition), and assessing impacts on people. HyRAM+ is developed at Sandia National Laboratories to support the development and revision of national and international codes and standards, and to provide developed models in a publicly-accessible toolkit usable by all stakeholders. This document provides a description of the methodology and models contained in HyRAM+ version 4.1. The two most significant changes for HyRAM+ version 4.1 from HyRAM+ version 4.0 are direct incorporation of unconfined overpressure into the QRA calculations and modification of the models for cryogenic liquid flow through an orifice. In QRA mode, the user no longer needs to input peak overpressure and impulse values that were calculated separately; rather, the unconfined overpressure is estimated for the given system inputs, leak size, and occupant location. The orifice flow model now solves for the maximum mass flux through the orifice at constant entropy while conserving energy, which does not require a direct speed of sound calculation. This does not affect the mass flow for all-gaseous releases; the method results in the same speed of sound for choked flow. However, this method does result in a higher (and more realistic) mass flow rate for a given leak size for liquid releases than was previously calculated.

08 HYDROGEN↗

DOE OSTI2015

Sensitivity of inertial confinement fusion hot spot properties to the deuterium-tritium fuel adiabat

We determine the dependence of key Inertial Confinement Fusion (ICF) hot spot simulation properties on the deuterium-tritium fuel adiabat, here modified by addition of energy to the cold shell. Variation of this parameter reduces the simulation to experiment discrepancy in some, but not all, experimentally inferred quantities. Using simulations with radiation drives tuned to match experimental shots N120321 and N120405 from the National Ignition Campaign (NIC), we carry out sets of simulations with varying amounts of added entropy and examine the sensitivities of important experimental quantities. Neutron yields, burn widths, hot spot densities, and pressures follow a trend approaching their experimentally inferred quantities. Ion temperatures and areal densities are sensitive to the adiabat changes, but do not necessarily converge to their experimental quantities with the added entropy. This suggests that a modification to the simulation adiabat is one of, but not the only explanation of the observed simulation to experiment discrepancies. In addition, we use a theoretical model to predict 3D mix and observe a slight trend toward less mixing as the entropy is enhanced. Instantaneous quantities are assessed at the time of maximum neutron production, determined dynamically within each simulation. These trends contribute to ICF science, as an effort to understand the NIC simulation to experiment discrepancy, and in their relation to the high foot experiments, which features a higher adiabat in the experimental design and an improved neutron yield in the experimental results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Equation of State and Progenitor Dependence of Stellar-mass Black Hole Formation

The core collapse of a massive star results in the formation of a proto-neutron star (PNS). If enough material is accreted onto a PNS, it will become gravitationally unstable and further collapse into a black hole (BH). We perform a systematic study of failing core-collapse supernovae in spherical symmetry for a wide range of pre-supernova progenitor stars and equations of state (EOSs) of nuclear matter. We analyze how variations in progenitor structure and the EOS of dense matter above nuclear saturation density affect the PNS evolution and subsequent BH formation. Comparisons of core collapse for a given progenitor star and different EOSs show that the path traced by the PNS in mass-specific entropy phase space ${M}_{\mathrm{grav}}^{\mathrm{PNS}}-\tilde{s}$ is well correlated with the progenitor compactness and is almost EOS independent, apart from the final end point. Furthermore, BH formation occurs, to a very good approximation, soon after the PNS overcomes the maximum gravitational mass supported by a hot NS with constant specific entropy equal to $\tilde{s}$. These results show a path to constraining the temperature dependence of the EOS through the detection of neutrinos from a failed galactic supernova.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1972

Shock melting and vaporization of metals.

The effect of initial porosity on shock induction of melting and vaporization is investigated for Ba, Sr, Li, Fe, Al, U, and Th. For the less compressible of these metals, it is found that for a given strong shock-generation system (explosive in contact, or flyer-plate impact) an optimum initial specific volume exists such that the total entropy production, and hence the amount of metal liquid or vapor, is a maximum. Initial volumes from 1.4 to 2.0 times crystal volumes, depending on the metal sample and shock-inducing system, will result in optimum post-shock entropies.

Ahrens, T. J.↗

NASA NTRS1990

MHD intermediate shocks in coronal mass ejections

A simplified model of coronal mass ejections is considered in which at least a portion of the interaction with the background corona involves a shock wave, and the allowable shock solutions and their compressive signatures are examined. The MHD shock-jump equations have a maximum of three possible types of solutions with an entropy rise for fixed values of the physical variables (slow, intermediate, and fast shocks). However, one of the three solution classes (the intermediate shock) is widely believed to not occur in nature and is regarded as nonevolutionary or extraneous. Without the intermediate shock, there is no multiplicity of solutions in that only one shock (or none) can occur for given physical values. All three potential shock types are considered, and it is shown solely on the basis of the shock-jump equations, that intermediate shocks must exist along some segment of the shock front for certain parametric regimes and for conditions that probably occur in some coronal mass ejections.

Steinolfson, R. S.↗

DOE OSTI2018

First-principles study of vibrational entropy effects on the PbTe-SrTe phase diagram

We present first-principles calculations of the solid-state phase diagram of PbTe-SrTe that include both configurational and vibrational contributions to the free energy. These configurational and vibrational free energies were calculated using the cluster expansion (CE) approach and quasiharmonic phonon calculations, respectively. The coupled configurational and vibrational degrees of freedom were taken into account by including temperature-dependent CE interactions with the T = 0K values and temperature dependence of the interactions determined from total energies and phonon free energies, both calculated using density functional theory. This Hamiltonian was then employed in Monte Carlo simulations to obtain a quantitative prediction of the PbTe-SrTe phase diagram. The phase diagram consists of a miscibility gap with a maximum temperature of ~500 K, with the inclusion of the vibrational entropy resulting in a more than fourfold increase in the calculated solubility limits of SrTe in PbTe. Our results suggest that the equilibrium solubility of this system is likely much larger than previously thought and deserves further experimental investigation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2010

Transient stability and control of renewable generators based on Hamiltonian surface shaping and power flow control. Part II, analysis.

The swing equations for renewable generators connected to the grid are developed and a wind turbine is used as an example. The swing equations for the renewable generators are formulated as a natural Hamiltonian system with externally applied non-conservative forces. A two-step process referred to as Hamiltonian Surface Shaping and Power Flow Control (HSSPFC) is used to analyze and design feedback controllers for the renewable generators system. This formulation extends previous results on the analytical verification of the Potential Energy Boundary Surface (PEBS) method to nonlinear control analysis and design and justifies the decomposition of the system into conservative and non-conservative systems to enable a two-step, serial analysis and design procedure. The first step is to analyze the system as a conservative natural Hamiltonian system with no externally applied non-conservative forces. The Hamiltonian surface of the swing equations is related to the Equal-Area Criterion and the PEBS method to formulate the nonlinear transient stability problem. This formulation demonstrates the effectiveness of proportional feedback control to expand the stability region. The second step is to analyze the system as natural Hamiltonian system with externally applied non-conservative forces. The time derivative of the Hamiltonian produces the work/rate (power flow) equation which is used to ensure balanced power flows from the renewable generators to the loads. The Second Law of Thermodynamics is applied to the power flow equations to determine the stability boundaries (limit cycles) of the renewable generators system and enable design of feedback controllers that meet stability requirements while maximizing the power generation and flow to the load. Necessary and sufficient conditions for stability of renewable generators systems are determined based on the concepts of Hamiltonian systems, power flow, exergy (the maximum work that can be extracted from an energy flow) rate, and entropy rate. This paper will present the analysis and numerical simulation results for two nonlinear control design examples that include: (1) the One-Machine Infinite Bus (OMIB) system with a Unified Power Flow Controller (UPFC) and (2) the swing equation for a wind turbine connected to an infinite bus through a UPFC to determine the required performance of the UPFC to enable the maximum power output of a wind turbine subject to stochastic inputs while meeting the power system constraints on frequency and phase. The energy storage requirements will also be identified from the UPFC and/or FACTS devices while working in combination with the wind turbine.

17 WIND ENERGY↗

DOE OSTI2022

Liquid fragility maximum in lithium borate glass‐forming melts related to the local structure

Abstract The structure of liquid lithium pyroborate, Li 4 B 2 O 5 ( J = Li/B = 2), has been measured over a wide temperature range by high‐energy X‐ray diffraction, and compared to that of its glass and borate liquids of other compositions. The results indicate a gradual increase in tetrahedral boron fraction from 3(1)% to 6(1)% during cooling from T = 1271(15) to 721(8) K, consistent with the larger N 4 = 10(1)% found for the glass, and literature 11 B nuclear magnetic resonance measurements. van't Hoff analysis based on a simple boron isomerization reaction BØ 3 O 2 – ⇌ BØO 2 2– yields Δ H = 13(1) kJ mol –1 and Δ S = 40(1) J mol –1 K –1 for the boron coordination change from 4 to 3, which are, respectively, smaller and larger than found for singly charged isomers for J ≤ 1. With these, we extend our model for N 4 ( J , T ), nonbridging oxygen fraction f nbr ( J , T ), configurational heat capacity , and entropy S conf ( J , T ) contributions up to J = 3. A maximum is revealed in at J = 1, and shown semi‐quantitatively to lead to a corresponding maximum in fragility contribution, akin to that observed in the total fragilities by temperature‐modulated differential scanning calorimetry. Lithium is bound to 4.6(2) oxygen in the pyroborate liquid, with 2.7(1) bonds centered around 1.946(8) Å and 1.9(1) around 2.42(1) Å. In the glass, n LiO = 5.4(4), the increase being due to an increase in the number of short Li–O bonds.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Fluid dynamic and thermal performance of a slotted cylinder at low Reynolds number

The fluid dynamic and thermal performance of a circular cylinder with a slot parallel to the flow is numerically investigated. The study utilized the semi-implicit finite volume multi-material algorithm MPM-ICE, a component of the Uintah framework. The normalized slot width s/D ranges from 0.1 - 0.3, introducing an additional heat transfer surface area between ~ 10 and ~ 50%, and a mass reduction between ~ 13 and ~ 38% in the cylinder. We assumed two-dimensional incompressible flow and simulated a Reynolds number Re D between 100 and 1000. The slotted cylinders are found to have a total drag force reduction up to ~ 45%, compared to a solid cylinder despite the additional viscous drag force in the slot. Convection heat transfer is enhanced up to ~ 70%. Further, the slotted cylinder performance index, defined as the ratio of the heat rate to the drag force, increases up to maximum of ~ 3, indicating better overall thermal fluid performance. An entropy analysis showed the best performance index occurs at the highest Re D . Correlations for drag coefficient and Nusselt number are proposed along with an entropy optimization method.

42 ENGINEERING↗

DOE OSTI2021

Adaptive hyperparameter updating for training restricted Boltzmann machines on quantum annealers

Restricted Boltzmann Machines (RBMs) have been proposed for developing neural networks for a variety of unsupervised machine learning applications such as image recognition, drug discovery, and materials design. The Boltzmann probability distribution is used as a model to identify network parameters by optimizing the likelihood of predicting an output given hidden states trained on available data. Training such networks often requires sampling over a large probability space that must be approximated during gradient based optimization. Quantum annealing has been proposed as a means to search this space more efficiently which has been experimentally investigated on D-Wave hardware. D-Wave implementation requires selection of an effective inverse temperature or hyperparameter (β) within the Boltzmann distribution which can strongly influence optimization. Here, we show how this parameter can be estimated as a hyperparameter applied to D-Wave hardware during neural network training by maximizing the likelihood or minimizing the Shannon entropy. We find both methods improve training RBMs based upon D-Wave hardware experimental validation on an image recognition problem. Neural network image reconstruction errors are evaluated using Bayesian uncertainty analysis which illustrate more than an order magnitude lower image reconstruction error using the maximum likelihood over manually optimizing the hyperparameter. The maximum likelihood method is also shown to out-perform minimizing the Shannon entropy for image reconstruction.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2011

Asymmetric (1+1)-dimensional hydrodynamics in high-energy collisions

The possibility that particle production in high-energy collisions is a result of two asymmetric hydrodynamic flows is investigated using the Khalatnikov form of the (1+1)-dimensional approximation of hydrodynamic equations. The general solution is discussed and applied to the physically appealing ''generalized in-out cascade'' where the space-time and energy-momentum rapidities are equal at initial temperature but boost invariance is not imposed. It is demonstrated that the two-bump structure of the entropy density, characteristic of the asymmetric input, changes easily into a single broad maximum compatible with data on particle production in symmetric processes. A possible microscopic QCD interpretation of asymmetric hydrodynamics is proposed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2019

Photon entanglement entropy as a probe of many-body correlations and fluctuations

Recent theories and experiments have explored the use of entangled photons as a spectroscopic probe of physical systems. In this work, we describe here a theoretical description for entropy production in the scattering of an entangled biphoton Fock state within an optical cavity. We develop this using perturbation theory by expanding the biphoton scattering matrix in terms of single-photon terms in which we introduce the photon-photon interaction via a complex coupling constant, ξ. We show that the von Neumann entropy provides a concise measure of this interaction. We then develop a microscopic model and show that in the limit of fast fluctuations, the entanglement entropy vanishes, whereas in the limit of slow fluctuations, the entanglement entropy depends on the magnitude of the fluctuations and reaches a maximum. In conclusion, our result suggests that experiments measuring biphoton entanglement give microscopic information pertaining to exciton-exciton correlations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗