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DOE OSTI2026

Equilibrium and non-equilibrium effects in high pressure phase transformations of carbon

The behavior of carbon in the range 1–100 GPa and 1–10 kK is central to problems in planetary interiors, inertial confinement fusion targets, and high-pressure synthesis of carbon-based materials, but experiments in this regime are difficult and often provide only indirect constraints on phase behavior. As a result, phase boundary loci, structure, and limits of metastability at high pressure remain uncertain. In this work, machine-learning enhanced atomistic simulations are used to address this knowledge gap. We determine the melt line up to 100 GPa, the graphite-diamond phase boundary up to the melt line, and analyze structure of the coexisting phases. We show that the coexisting liquid evolves smoothly with pressure without evidence for a first-order liquid–liquid transition. Orientation-resolved graphite melting simulations indicate that basal-plane interfaces develop a dewetting layer and undergo layer-by-layer melting, producing kinetic hysteresis and an apparent orientation dependence of the melt line. Non-equilibrium quenches from the melt are used to construct a kinetically limiting graphite–diamond phase boundary for rapid quenches from above the melt line, and show that graphite is metastable at pressures of up to ≈ 25 GPa. These results provide bounds on equilibrium and metastable behavior in carbon relevant for interpreting high-pressure experiments and for designing synthesis pathways to specific carbon microstructures.

Lyu, Yanjun [Department of Materials Science and E↗

DOE OSTI2025

Non-Equilibrium Effects in Quantum Magnets

While most often the state of a material will tend toward an equilibrium determined by its environment, there are many cases of scientific and technological interest where materials are manipulated to be or are found in non-equilibrium configurations. For example, data can be stored in hard drives by deliberately altering the magnetic orientation in a material to store information in non-equilibrium pattern. In this project, the main goals were studies of non-equilibrium properties of quantum magnets using neutron scattering as the primary experimental method. Neutron scattering allows characterization of magnetic correlation lengths sensitive to the presence of defects. It can also be used to distinguish equilibrium from non-equilibrium states via energy transfer rates. Typical bulk state magnetization relaxation times are too short to perform many neutron scattering measurements of interest. To enable the study of non-equilibrium conditions, materials with longer magnetic relaxation times were targeted. CoNb 2 O 6 was used in two experiments related to non-equilibrium physics. In the first, evidence for defects created via the Kibble-Zurek mechanism (KZM) was sought by quenching across a magnetic field-dependent phase transition. Somewhat unexpectedly, clear evidence for KZM-induced defects was absent. Additional measurements of CoNb 2 O 6 were made to better characterize its crystal field and other properties to provide a better theoretical understanding to enable more effective non-equilibrium physics measurements. In another project, LiHo 0.45 Y 0.55 F 4 was used to compare a quantum annealing protocol to a thermal annealing one since magnetic fields can be used to control the thermal fluctuations in LiHo 0.45 Y 0.55 F 4 . In addition, a new pulsed magnet power supply and new techniques were developed suitable for neutron scattering experimental environments to enable faster magnetic field changes for producing non-equilibrium conditions. The power supply developed for this project has wider technological applications in addition to faster magnetic field ramps.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Non-equilibrium critical scaling and universality in a quantum simulator

Universality and scaling laws are hallmarks of equilibrium phase transitions and critical phenomena. However, extending these concepts to non-equilibrium systems is an outstanding challenge. Despite recent progress in the study of dynamical phases, the universality classes and scaling laws for non-equilibrium phenomena are far less understood than those in equilibrium. In this work, using a trapped-ion quantum simulator with single-spin resolution, we investigate the non-equilibrium nature of critical fluctuations following a quantum quench to the critical point. We probe the scaling of spin fluctuations after a series of quenches to the critical Hamiltonian of a long-range Ising model. With systems of up to 50 spins, we show that the amplitude and timescale of the post-quench fluctuations scale with system size with distinct universal critical exponents, depending on the quench protocol. While a generic quench can lead to thermal critical behavior, we find that a second quench from one critical state to another (i.e. a double quench) results in a new universal non-equilibrium behavior, identified by a set of critical exponents distinct from their equilibrium counterparts. Our results demonstrate the ability of quantum simulators to explore universal scaling beyond equilibrium.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Feedforward equilibrium trajectory optimization with GSPulse

One of the common tasks required for designing new plasma scenarios or evaluating capabilities of a tokamak is to design the desired equilibria using a Grad-Shafranov (GS) equilibrium solver. However, most standard equilibrium solvers are time-independent and do not include dynamic effects such as plasma current flux consumption, induced vessel currents, or voltage constraints. Another class of tools, plasma equilibrium evolution simulators, do include time-dependent effects. These are generally structured to solve the forward problem of evolving the plasma equilibrium given feedback-controlled voltages. In this work, we introduce GSPulse, a novel algorithm for equilibrium trajectory optimization, that is more akin to a pulse planner than a pulse simulator. GSPulse includes time-dependent effects and solves the inverse problem: given a user-specified set of target equilibrium shapes, as well as limits on the coil currents and voltages, the optimizer returns trajectories of the voltages, currents, and achievable equilibria. This task is useful for scoping performance of a tokamak and exploring the space of achievable pulses. The computed equilibria satisfy both Grad-Shafranov force balance and axisymmetric circuit dynamics. The optimization is performed by restructuring the free-boundary equilibrium evolution equations into a form where it is computationally efficient to optimize the entire dynamic sequence. GSPulse can solve for hundreds of equilibria simultaneously within a few minutes. GSPulse has been validated against NSTX-U and MAST-U experiments and against SPARC feedback control simulations, and is being used to perform scenario design for SPARC. The computed trajectories can be used as feedforward inputs that are connected to the feedback controller to inform and improve feedback performance. The code for GSPulse is available open-source at github.com/jwai-cfs/GSPulse_public.

equilibrium↗

DOE OSTI2026

Pre-Equilibrium De-Excitations for Neutrino-Nucleus Interactions

The Deep Underground Neutrino Experiment (DUNE) is sensitive to MeV-scale energy depositions from low-energy astrophysical neutrinos, including those from core-collapse supernovae. Interpreting these detector signals requires accurate modeling of the nuclear de-excitation that follows from the neutrino-nucleus interaction. The MARLEY (Model of Argon Reaction Low-Energy Yields) event generator specializes in the low-energy regime. MARLEY currently assumes the residual nucleus equilibrates immediately after the primary interaction. This omits the intermediate pre-equilibrium stage in which energy redistributes among nucleons until statistical equilibrium is reached. While pre-equilibrium effects are well established for nucleon-induced reactions, they have not previously been studied for neutrino-nucleus interactions. This work addresses that gap by implementing a two-component exciton model, which is the first dedicated treatment of pre-equilibrium de-excitation for neutrino-nucleus interactions, restructured around MARLEY's existing class hierarchy to prepare for direct integration, including particle-hole state densities, internal transition rates, and pre-equilibrium particle emission. The calculations show encouraging agreement with the TALYS-2.2 nuclear reaction code for neutron-nucleus interactions. We further propose a concrete integration path into the full MARLEY event generator, including derived class structure and an extended event record for pre-equilibrium vertices in support of future reweighting. Remaining work focuses on refining the emission width calculation, adding $\gamma$-ray emission, and completing this integration to quantify the impact of pre-equilibrium effects on the expected low-energy neutrino signals in DUNE and similar experiments.

Visser, Erin [Michigan State U., East Lansing (mai↗

DOE OSTI2026

A lumped particle direct simulation Monte-Carlo method combined with the collisional-radiative model for simulations of non-equilibrium laser-induced plasma plumes

Collisional plasma plumes induced by laser irradiation of material targets exhibit large variations in local density as well as ionization and excitation states, making purely hydrodynamic or kinetic simulations inaccurate or infeasible. To address this challenge and capture non-equilibrium effects in laser-induced plasma plumes at arbitrary degrees of ionization, we develop a hybrid computational approach that combines the kinetic direct simulation Monte Carlo (DSMC) method with a collisional-radiative model (CRM). This ℓDSMC-CRM approach utilizes a lumped particle method to represent minor fractions of excited ions in particle-based simulations and a special coarse-graining technique for atomic spectra and photoionization rates, ensuring numerical convergence at reduced computational cost. The hybrid approach is applied to simulate spatially homogeneous relaxation as well as one- and two-dimensional expansions of plasma plumes induced by irradiation of a copper target by a nanosecond laser pulse in a vacuum or background gas. The comparison with an equilibrium model, where local Saha-Boltzmann equilibrium is enforced, shows that the non-equilibrium effects play a dominant role. The equilibrium model can fail to predict the flow structure and strongly underestimate the degree of absorption of laser radiation by the plume. The ℓDSMC-CRM approach is validated against experimental data demonstrating reasonable agreement with the experimental electron density and temperature, while the equilibrium model is found to dramatically underestimate electron density and temperature. The flexibility of the ℓDSMC-CRM approach allows for its seamless integration into existing DSMC frameworks, making it a valuable tool for high-fidelity plasma modeling in laser-material interactions, laser-based manufacturing, and beyond.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Effects of non-equilibrium ionization and excitation on radiation absorption in plasma plumes induced by ablation of metal targets with nanosecond laser pulses

Ionization and radiation absorption in nanosecond laser-induced plasma plumes are routinely modeled using the Saha–Boltzmann equilibrium ionization model (EQM). However, the equilibrium assumption can be inaccurate during the laser pulse when non-equilibrium effects significantly impact radiation absorption. In the present work, the EQM and non-equilibrium collisional-radiative model (CRM) are compared to reveal the effect of plasma non-equilibrium on radiation absorption in non-homogeneous plumes and degree of plasma shielding. Simulations of plume expansion induced by irradiation of a copper target in 1 atm argon background gas with a 10 ns Gaussian pulse at a fluence from 8 Jcm −2 to 14 Jcm −2 are performed with a hybrid computational model that couples a lumped particle direct simulation Monte Carlo method with either CRM or EQM. The simulations show that the EQM strongly underestimates the effects of ionization and radiation absorption compared to CRM and, contrary to the CRM, predict strong ionization of the background gas. The differences between the models are explained by the qualitatively different coupling between plume expansion and dynamics of ionization and exitation processes in the CRM and EQM under conditions when the characteristic times for most radiation- and electron-induced processes are longer than the pulse duration. The CRM-based predictions are also found to agree much better with available experimental data. In conclusion, these results indicate that the model of Saha–Boltzmann equilibrium cannot be used for reliable prediction of the degree of plasma shielding in plumes induced by nanosecond laser pulses or for processing results of spectroscopic measurements at early stages of expansion of such plumes.

Physics - Plasma physics↗

DOE OSTI2025

Stable isotope equilibria in the dihydrogen-water-methane-ethane-propane system. Part 2: Experimental determination of hydrogen isotopic equilibrium for ethane-H2 from 30 to 200 °C and propane-H2 from 75 to 200 °C

The stable isotopic compositions of light n-alkanes, including methane, ethane, and propane, are often used to identify the sources and thermal maturity of natural gas samples. Though stable isotopic compositions of these molecules are commonly assumed to be controlled by kinetic isotope effects, recent studies have proposed both carbon and hydrogen isotopic equilibrium may also occur in some samples. Assessing whether samples are in isotopic equilibrium requires knowledge of light alkane equilibrium fractionation factors over geologically relevant temperatures for formation and storage (up to ∼300 °C). In this study, we report experimental results of hydrogen isotopic equilibrium between ethane and H2 from 30 to 200 °C and propane and H2 from 75 to 200 °C. We compare these results with high-level theoretical calculations and provide a preferred polynomial fit to describe equilibrium fractionation factors. Comparison of these fractionation factors with a compilation of ∼500 compiled environmental gas samples supports the proposal that many (∼50%) of these natural gas samples exhibit hydrogen isotopic compositions consistent with having formed in or attained methane-ethane-propane hydrogen isotopic equilibrium over geologically relevant temperatures for formation and storage (50–300 °C).

Turner, Andrew C↗

DOE OSTI2025

Temperature sensitivity of the equilibrium neutronics and accident analysis of the HTR-10

Pebble-Bed High-Temperature Gas-cooled Reactors (PB-HTGR) are moderated by the graphite in the fuel pebbles and the graphite reflector surrounding the pebble-bed. Because graphite is by far the most abundant material in PB-HTGRs and the primary moderator, accurate modeling of the graphite material, including density, impurities, and temperatures, is crucial for accurate computational modeling and simulation of these reactors. While main characteristics of the graphite components are often known, the local temperature is less well known and often averaged over all components. Here, this work studies the impact of considering accurate temperature profiles in the graphite material on the generation of a small PB-HTGR model at the state of equilibrium operation and on short-term accident progression. The fuel compositions for the PB-HTGR were determined using a jump-in equilibrium modeling method, the Axial Radial Zone Equilibrium Modeling (AR-ZEM) method. In contrast to previous work, the AR-ZEM method was used considering thermal-hydraulic feedback from the MELCOR code to determine temperatures of the fuel pebbles and the surrounding graphite reflector. The consideration of an axial and radial temperature profile in the core and reflector, as opposed to uniform material temperatures, had an impact of almost 1,300 pcm on the equilibrium core eigenvalue and caused significant differences in the discharged plutonium fuel inventory with up to 4.9% and 11.0% for Pu-239 and Pu-242, respectively. To assess the impact on short-term accident progression, two Anticipated Transient Without SCRAM (ATWS) events, a Pressurized Loss of Forced Coolant (PLOFC) and a Control Rod Withdrawal (CRW) with loss of flow, were simulated with MELCOR. The use of temperature profiles in the equilibrium core models did not reveal a significant impact on the temperature, power, or reactivity responses during the transients. In conclusion, a need for consideration of accurate temperature profiles, in particular for the graphite reflector, was found for the generation of equilibrium PB-HTGRs core models using jump-in methods, but detailed temperature profiles may not be necessary when performing conservative transient analysis.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2025

Self-consistent equilibrium and transport simulations for NSTX-U plasmas enhanced via machine learning surrogate models

The Control-Oriented Transport SIMulator (COTSIM) is an advanced equilibrium and transport code designed for simulating tokamak discharges at computational speeds suitable for control applications. COTSIM’s modular framework enables users to select models that balance accuracy with speed according to specific needs, allowing the code to operate from fast to faster-than-real-time performance levels. This work presents recent enhancements to COTSIM’s predictive accuracy for NSTX-U scenarios, achieved by integrating neural-network-based surrogate models and self-consistent equilibrium calculations. To improve source deposition predictions, a surrogate model for NUBEAM has been incorporated. Additionally, a surrogate model for the Multi-Mode Module (MMM) now supports predictions of anomalous thermal, momentum, and particle diffusivities—key factors for modeling the evolution of temperature and rotation. Each surrogate model was specifically trained for the NSTX-U operational regime to enhance COTSIM’s accuracy while maintaining computational efficiency. Moreover, COTSIM now couples fixed-boundary equilibrium solvers with its transport solvers, enabling self-consistent predictions of plasma profiles and equilibrium evolution over the discharge. Simulation results demonstrate strong agreement between COTSIM and TRANSP predictions for NSTX-U discharges. These substantial advancements expand COTSIM’s utility in model-based control applications for NSTX-U. Potential applications include simultaneous optimization of equilibrium and transport scenarios, integration into digital twins, real-time profile estimation (e.g., temperature and rotation) from limited or noisy measurements, and advanced feedback-based scenario control.

Equilibrium and transport modeling↗

NASA NTRSDate not supplied

Construction of an Exact Pressure-Equilibrium Scheme for the Five-Equation Two-Phase Flow Model With Thermal Relaxation

Numerical simulation of compressible multiphase flows based on the four-equation (homogeneous relaxation) model is known to suffer from two fundamental difficulties with (a) wave propagation and (b) pressure equilibrium preservation. First, the mixture sound speed exhibits non-monotonic dependency with respect to the volume fraction, which leads to robustness issues in the resolution of shocks and acoustic wave propagation across two-phase regions. This difficulty can be mitigated by solving Allaire’s five-equation model augmented with infinitely fast phasic temperature equilibrium, from which solutions of the four-equation model can be recovered. However, when temperature is non-uniform, this augmented five-equation formulation still fails to preserve pressure equilibrium across material interfaces. In this work, we propose a fully conservative numerical scheme that exactly preserves pressure equilibrium at the discrete level for the augmented five-equation model, for arbitrary initial distributions of temperature and volume fraction. Combined with the monotonic sound speed property of the five-equation formulation, the proposed pressure-equilibrium preserving scheme significantly improves robustness in the presence of strong multiphase interactions, including shock–interface interactions and advection of material interfaces.

ESG↗

DOE OSTI2025

Equilibrium Fe isotope fractionation between olivine, pyroxene, spinel and MORB glass: Implications for mantle partial melting to generate MORBs

Primitive mid-ocean ridge basalts (MORBs) exhibit Fe isotopic compositions heavier than the upper mantle by +0.074 ± 0.028 ‰ for δ 56 Fe. The processes responsible for this isotopic difference remain unclear. Modeling of Fe isotope fractionation during mantle partial melting requires reliable equilibrium Fe isotope fractionation factors between minerals and melts, for which consistent data are still lacking. Here, in this study, we used Nuclear Resonant Inelastic X-ray Scattering (NRIXS) technique to measure Fe force constants for a MORB glass (ALV 519-4-1) and natural mantle minerals (olivine, orthopyroxene, clinopyroxene, and spinel) to determine the equilibrium Fe isotope fractionation factors between them. The force constants determined in this study, in increasing order, are 167 ± 26 N/m for spinel, 175 ± 17 N/m for olivine, 176 ± 20 N/m for MORB glass, 205 ± 26 N/m for clinopyroxene, and 219 ± 36 N/m for orthopyroxene. We evaluated the previously proposed mechanisms for the heavy Fe isotopic composition of MORBs, including (i) mantle partial melting, (ii) mantle lithological heterogeneity, with pyroxenite in the source, (iii) mantle metasomatism by low-degree melts, and (iv) fractional crystallization of olivine from melts. For (i), we used the pMELTS program to simulate adiabatic decompression melting of mantle peridotites, and calculated Fe isotope fractionation based on Fe 3+ –Fe 2+ equilibrium-controlled fractionation, where Fe 3+ forms stronger bonds and is more incompatible than Fe 2+ . At 10 wt% peridotite melting, corresponding to MORB generation, only +0.03 ‰ Fe isotope fractionation between the melt and the original bulk composition (Δ 56 Fe = δ 56 Fe melt - δ 56 Fe 0 ) was produced, insufficient to account for the observed MORB-upper mantle difference. For (ii), melting of pyroxenites yields smaller Fe isotope fractionation than melting of peridotites, making it unlikely the cause for the MORB-upper mantle isotopic difference. For (iii), both the Fe 3+ /ΣFe ratio and the δ 56 Fe of melts increase with the degree of partial melting, indicating that low-degree melts are not isotopically heavy enough to significantly alter the isotopic composition of lithospheric mantle through metasomatism. For (iv), equilibrium isotope fractionation between olivine and melt is near zero. These results suggest that equilibrium Fe isotope fractionation alone cannot explain the MORB isotopic signature, highlighting the potential role of kinetic isotope fractionation. Using a diffusion model, we calculated kinetic Fe and Mg isotope fractionations associated with (iv) olivine crystallization from a melt, and found that the predicted Fe and Mg isotope fractionations were inconsistent with observations in MORBs. Qualitatively, two processes could have induced kinetic Fe isotope fractionation during MORB generation: (a) Fe-Mg interdiffusion between melt and solid during melt migration and (b) reactive melt-rock interactions during melt focusing. However, a quantitative understanding of their role in modifying the melt isotopic composition remains limited and requires further investigation.

Fe isotopes↗

DOE OSTI2026

Two-dimensional non-equilibrium melting of charged colloids

Thermodynamic two-dimensional melting has been extensively studied in experiments and simulations, and is well predicted by theory. For systems in equilibrium, this transition is well described by the Kosterlitz–Thouless–Halperin–Nelson–Young theory, where melting is directly linked to the unbinding of topological defects. For driven, non-equilibrium melting and other non-equilibrium phase transitions, the picture is less clear. Here, in this work, we study the two-dimensional melting of a crystal of charged colloids. By randomly replacing some charged colloids with magnetic colloids, we can melt our system by rotating a fraction of the particles to create non-equilibrium, hydrodynamic random flows and local stresses. We can also melt it thermally by changing the particle number density. We find that an effective temperature approach cannot explain the results of our driven system. Rather, in both experiments and simulations, we observe that plotting the hexatic order parameter and the hexatic correlation’s exponent versus the density of disclinations and dislocations, respectively, yields universal curves. This implies that in our systems, two-dimensional melting depends directly on the density of topological defects and is independent of whether thermal or non-equilibrium forces generate them.

critical phenomena↗

DOE OSTI2025

Experimental evidence of non-equilibrium phase separation in supercritical fluids

Supercritical fluids (SCFs), widely utilized in many industries, have long been regarded as homogeneous single-phase media. Recent simulation studies identified different phases (more gas-like or liquid-like) in SCFs at equilibrium, expanding the previous notion but still not addressing non-equilibrium properties of SCFs. Here we reveal the existence of long-lived liquid-like clusters in non-equilibrium SCFs by time-resolved small-angle neutron scattering measurements. Since SCFs in industrial applications frequently operate under dynamic, non-equilibrium conditions rather than strict thermodynamic equilibrium, our findings offer crucial information for improving the use of SCFs in industrial settings, like semiconductor cleaning and plant thermal-hydraulic engineering.

Lee, Juho [Pohang Univ. of Science and Technology ↗

DOE OSTI2025

Equilibrium Core Model for Micro Pebble Bed Reactors Using OpenMC

Estimating the equilibrium state for pebble bed reactors (PBRs) presents complex challenges as it requires simultaneous consideration of changes in the pebbles’ movement as well as their fuel compositions. Whereas traditional approaches use multigroup diffusion codes for neutronics calculations of PBRs’ equilibrium state, the double-heterogeneity of PBRs complicates neutron cross-section generation. Continuous-energy Monte Carlo (MC) methods are better suited for detailed PBR analysis because of their natural handling of double-heterogeneity, but they demand substantially more computational resources. Here, this study introduces a novel method for efficiently estimating the equilibrium state in small and micro PBRs with reduced computational cost. The method is anticipated to accelerate the processes of core design and performing parametric studies for utilizing advanced fuel and structural materials. The HTR-10 reactor design was used for validating the method’s predictions and evaluating its computational efficiency. When compared to reference calculation values from the literature, criticality (k-effective) was predicted to be approximately within the margin of error of the MC transport calculation, average core power density (in megawatts per cubic meter) was predicted within 2.5% relative error, and maximum thermal flux (10 13 n/cm 2 .s −1 ) was predicted within 1.8% relative error. The calculated inventory of fission products and fuel composition in the equilibrium core were within 15% and 16.6%, respectively, when compared to reported values from the literature. The difference is attributed to variance in the considered values of the core temperature, which was found to significantly affect the depletion analyses.

Equilibrium core↗

DOE OSTI2025

Effects of equilibrium pressure on plasma response to RMPs in a spherical tokamak

This study presents a comprehensive analysis of the equilibrium pressure on the plasma response to resonant magnetic perturbations (RMPs) in the spherical tokamak (ST) MAST-U, employing both single-fluid and MHD-kinetic hybrid models (implemented via the MARS-F/K codes). As a key finding, the study identifies two different pressure-driven eigenmodes, exhibiting Sturmian property, that affect the Troyon no-wall limits for the onset of the n = 1 and n = 2 ( n is the toroidal mode number) ideal external kink instabilities as well as the corresponding plasma response to the applied RMP. With increasing equilibrium pressure, the plasma response to RMPs is significantly enhanced in the ST plasma, particularly in the high-pressure regime where kinetic effects strongly stabilize the external kink instability. The Troyon no-wall limit divides the plasma response into two regions: well below the limit, the response amplitudes and trends (versus pressure) are similar between the fluid and kinetic models; as the equilibrium pressure approaches the Troyon limit, the kinetic model predicts significant amplification of the RMP field, up to 30 times for cases considered. A relatively weak dependence of the optimal coil phasing on the equilibrium pressure is computed in this ST plasma, similar to the trend obtained for the conventional aspect ratio devices. These findings underscore the importance of incorporating kinetic effects in accurate prediction of the plasma response to RMPs in high-pressure ST tokamak plasmas and provide a theoretical basis for optimizing RMP-based control of the edge-localized modes in future ST devices.

RMP↗

DOE OSTI2026

Equilibrium spin polarization arising from chirality

Chirality-induced spin selectivity (CISS) describes how chiral molecules and materials generate spin polarization even at thermal equilibrium. This observation has challenged established principles of microscopic reversibility and Onsager reciprocity. We resolve this paradox by formulating a pseudo-Hermitian quantum framework that separates thermodynamic equilibrium from time-reversal symmetry. Within this approach, structural chirality and electron correlations, irrespective of their microscopic origin, are sufficient to produce CISS observables. Chirality enters through a non-local metric η that couples spin and spatial motion, leading to real spectra, unitary evolution, and thermodynamic consistency. The framework predicts a chirality-induced spin magnetic ordering characterized by a spin-displacement order, which reconciles equilibrium spin polarization with detailed balance and explains the persistence of CISS in materials composed of light elements. We derive generalized Onsager-Casimir relations that respect the observed CISS symmetry, i.e., parity $(\mathscr{P})$-odd and time-reversal $(\mathscr{T})$-odd, but exhibiting $\mathscr{PT}$-even symmetry. This approach establishes a coherent foundation for equilibrium CISS and provides a route to link chemical chirality with measurable spin-to-charge conversion effects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

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↗