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DOE OSTI2023

LA100 Equity Strategies. Chapter 2: Procedural Justice

The LA100 Equity Strategies project synthesizes community guidance with robust research, modeling, and analysis to identify strategy options that can increase equitable outcomes in Los Angeles' clean energy transition. Grounded in the analysis of past and ongoing energy inequities and engagement with underserved communities, the project presents community-guided and community-tailored strategies that aim to operationalize recognition and procedural justice. This chapter focuses on procedural justice, examining priorities identified during the community engagement portion of the LA100 Equity Strategies project. This process, and our approach to partnering with community-based organizations (CBOs) and the communities they serve, was developed from the baseline analysis in Chapter 1, which centers on recognition justice, examining past and current inequities in LA. Recognition, procedural, and distributional justice are the three tenets of energy justice around which the LA100 Equity Strategies project is organized. Procedural justice prioritizes fair, equitable, and inclusive participation in the decision-making process. This tenet's practical application entails who is invited and able to participate, whose voices are considered as decisions are made, the co-development of procedures to inform this deliberative process, and who has access to formal measures of regulation and accountability. Engaging with Angelenos to examine the causes of inequities and identify impact areas and priorities that center community experiences, values, and goals represents a first step in developing energy equity strategies for the Los Angeles Department of Water and Power (LADWP) to achieve distributional justice - the just and equitable distribution of energy benefits and burdens in LA's energy transition. Equity, as community members insisted, is about making - and following through with - a commitment to prioritize historically underserved and overburdened communities. Community engagement is a principal method for operationalizing this commitment, guiding our analytic approach and potential equity strategies. Using procedural justice as an analytical tool, this chapter presents the LA100 Equity Strategies approach to community engagement from 2021 to 2023 and the results of this process in relation to community-identified barriers and burdens impacting procedural justice outcomes. We analyze the procedural elements of reaching the equity goals Angelenos set to inform future LADWP decision-making and program development.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2022

Approximate recoverability and relative entropy II: 2-positive channels of general von Neumann algebras

Abstract We generalize our results in paper I in this series to quantum channels between general von Neumann algebras, proving the approximate recoverability of states which undergo a small change in relative entropy through the channel. To this end, we derive a strengthened form of the quantum data processing inequality for the change in relative entropy of two states under a channel between two von Neumann algebras. Compared to the usual inequality, there is an explicit lower bound involving the fidelity between the original state and a recovery channel.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

JUST-R metrics for considering energy justice in early-stage energy research

We report achieving sustainable decarbonization of the energy sector requires implementing and improving energy technologies while simultaneously managing sources of social inequity in the energy system. Centering energy justice, which has "the goal of achieving equity in both the social and economic participation in the energy system, while also remediating social, economic, and health burdens on those historically harmed by the energy system," in the transition to clean energy has become an increasingly urgent priority for social scientists, policymakers, and community activists alike. However, late-stage consideration of social impacts of energy technologies may result in identifying inequities only after substantial time, money, and effort have been expended on research and development (R&D). This issue is exemplified by concerns over environmental and human health impacts related to cobalt in lithium-ion batteries, which has spurred research into alternatives only after decades of R&D and the establishment of supply chains, infrastructure, and markets for cobalt-containing chemistries. Other examples include issues with land use and resource consumption related to first-generation biofuel feedstocks as well as occupational hazards and pollution associated with photovoltaics manufacturing. In all these cases, subsequent R&D to improve technologies or processes cannot undo the effects already experienced. Incorporating energy justice from the earliest stage of R&D will enable more just technology implementation, but integrating justice considerations into early-stage research is a challenge due to a lack of tools to assess and manage them. To fill this gap, we center early-stage research to develop the Justice Underpinning Science and Technology Research (JUST-R) metrics framework - energy justice metrics specifically targeted at early-stage researchers to assess their work on an immediate timescale. By applying these metrics to a case study focused on materials for next-generation photovoltaics, we highlight potential benefits and barriers to implementing this framework in early-stage research and discuss necessary institutional and individual actions needed for researchers to effectively leverage the tool to incorporate justice-focused criteria into R&D decision making.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2021

On a nonlocal Cahn–Hilliard model permitting sharp interfaces

A nonlocal Cahn–Hilliard model with a non-smooth potential of double-well obstacle type that promotes sharp interfaces in the solution is presented. To capture long-range interactions between particles, a nonlocal Ginzburg–Landau energy functional is defined which recovers the classical (local) model as the extent of nonlocal interactions vanish. In contrast to the local Cahn–Hilliard problem that always leads to diffuse interfaces, the proposed nonlocal model can lead to a strict separation into pure phases of the substance. In this work, the lack of smoothness of the potential is essential to guarantee the aforementioned sharp-interface property. Mathematically, this introduces additional inequality constraints that, in a weak formulation, lead to a coupled system of variational inequalities which at each time instance can be restated as a constrained optimization problem. We prove the well-posedness and regularity of the semi-discrete and continuous in time weak solutions, and derive the conditions under which pure phases are admitted. Moreover, we develop discretizations of the problem based on finite element methods and implicit–explicit time-stepping methods that can be realized efficiently. Finally, we illustrate our theoretical findings through several numerical experiments in one and two spatial dimensions that highlight the differences in features of local and nonlocal solutions and also the sharp interface properties of the nonlocal model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Positivity from Cosmological Correlators

Abstract Effective field theories in flat space and in anti-de Sitter space are constrained by causality and unitarity, often in the form of positivity bounds. Similar bounds have been harder to demonstrate in cosmological backgrounds, where the roles of unitarity and causality are more obscure. Fortunately, the expansion of the universe ensures that late-time cosmological correlators are effectively classical and the role of unitarity is played by classical statistical inequalities. For multi-field inflation, the resulting positivity constraints have long been known in terms of the Suyama-Yamaguchi inequality. In this paper, we demonstrate that similar statistical bounds imply nontrivial constraints for massive fields in the early universe. We show that any real anomalous dimensions for principal series fields in de Sitter space must be positive. We also derive a limit on the amplitude of particular oscillatory signals from inflation, including those arising in cosmological collider physics. Finally, we demonstrate that these constraints manifest themselves directly in the two-point statistics of matter and galaxies that will be measured in upcoming surveys.

Physics↗
DOE OSTI2026

Exploring the holographic entropy cone via reinforcement learning

We develop a reinforcement learning algorithm to study the holographic entropy cone. Given a target entropy vector, our algorithm searches for a graph realization whose min-cut entropies match the target vector. If the target vector does not admit such a graph realization, it must lie outside the cone, in which case the algorithm finds a graph whose corresponding entropy vector most nearly approximates the target and allows us to probe the location of the facets. For the N = 3 cone, we confirm that our algorithm successfully rediscovers monogamy of mutual information beginning with a target vector outside the holographic entropy cone. We then apply the algorithm to the N = 6 cone, analyzing the 6 mystery extreme rays of the subadditivity cone from [1] that satisfy all known holographic entropy inequalities yet lacked graph realizations. We found realizations for 3 of them, proving they are genuine extreme rays of the holographic entropy cone, while providing evidence that the remaining 3 are not realizable, implying unknown holographic inequalities exist for N = 6.

AdS-CFT correspondence↗
DOE OSTI2025

Cosmohedra

It has been a long-standing challenge to find a geometric object underlying the cosmological wavefunction for Tr(ϕ 3 ) theory, generalizing associahedra and surfacehedra for scattering amplitudes. In this note, we describe a new class of polytopes — “cosmohedra” — that provide a natural solution to this problem. The faces of associahedra capture the combinatorics of non-overlapping chords of the momentum polygon, reflecting all partial factorizations of amplitudes. Cosmohedra are far richer — instead of non-overlapping chords, their faces capture the “russian doll” structure of non-overlapping subpolygons that determine the wavefunction. We show that cosmohedra are intimately related to associahedra, obtained by “blowing up” faces of the associahedron in a simple way. We give a full combinatorial description of cosmohedron faces and their factorization properties, and provide an explicit realization in terms of facet inequalities that further “shave” the facet inequalities of the associahedron. We also discuss a novel way for computing the wavefunction from cosmohedron geometry that extends the usual connection with polytope canonical forms. We illustrate cosmohedra with examples at tree-level and one loop; the close connection to surfacehedra suggests the generalization to all loop orders. Moving beyond the wavefunction, we briefly describe “cosmological correlahedra” for full correlators, which are one higher-dimensional polytopes, interpolating between associahedra and cosmohedra on opposite facets in an extra direction associated with the total energy. We speculate on how the existence of cosmohedra might suggest a “stringy” formulation for the cosmological wavefunction/correlators, generalizing the way in which the Minkowski sum decomposition of associahedra naturally extend particle to string amplitudes.

Scattering Amplitudes↗
DOE OSTI2023

Minimizing Optimal Transport for Functions with Fixed-Size Nodal Sets

Consider the class of zero-mean functions with fixed L ∞ and L 1 norms and exactly N ϵ N nodal points. Which functions f minimize W p (f + ,f – ), the Wasserstein distance between the measures whose densities are the positive and negative parts? We provide a complete solution to this minimization problem on the line and the circle, which provides sharp constants for previously proven “uncertainty principle”-type inequalities, i.e., lower bounds on N • W p (f + ,f – ). We further show that, while such inequalities hold in many metric measure spaces, they are no longer sharp when the non-branching assumption is violated; indeed, for metric star-graphs, the optimal lower bound on W p (f + ,f – ) is not inversely proportional to the size of the nodal set, N. Here, based on similar reductions, we make connections between the analogous problem of minimizing W p (f + ,f – ) for f defined on Ω C R d with an equivalent optimal domain partition problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Electron–phonon interaction in Kondo lattice systems

Highlights: • Rigorous study of ground state properties of the Kondo lattice model with an electron–phonon. • The ground state is proved to be unique. • The total spin of the ground state is determined according to the lattice structure. • Novel applications of order preserving operator inequalities. We study ground state properties of the Kondo lattice model with an electron–phonon interaction. The ground state is proved to be unique; in addition, the total spin of the ground state is determined according to the lattice structure. To prove the assertions, an extension of the method of spin reflection positivity is given in terms of order preserving operator inequalities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Extreme events, energy security and equality through micro- and macro-levels: Concepts, challenges and methods

Low-income households face long-standing challenges of energy insecurity and inequality (EII). During extreme events (e.g., disasters and pandemics) these challenges are especially severe for vulnerable populations reliant on energy for health, education, and well-being. However, many EII studies rarely incorporate the micro- and macro-perspectives of resilience and reliability of energy and internet infrastructure and social-psychological factors. To remedy this gap, we first address the impacts of extreme events on EII among vulnerable populations. Second, we evaluate the driving factors of EII and how they change during disasters. Third, we situate these inequalities within broader energy systems and pinpoint the importance of equitable infrastructure systems by examining infrastructure reliability and resilience and the role of renewable technologies. Then, we consider the factors influencing energy consumption, such as energy practices, socio-psychological factors, and internet access. Finally, we propose interdisciplinary research methods to study these issues during extreme events and provide recommendations.

Chen, CF↗
DOE OSTI2024

A phase-field diffraction model for thermo-hydro-mechanical propagating fractures

This paper introduces a novel diffraction based thermo-hydraulic–mechanical (THM) model for fracture propagation using a phase-field fracture (PFF) approach. The key innovation of the THM-PFF model lies in its integrated treatment of four solution variables—displacements, phase-field, pressure, and temperature—each governed by a combination of conservation of momentum (mechanics problem), a variational inequality (constrained minimization problem), mass conservation (pressure problem), and energy conservation (temperature problem). This leads to a new formulation of a coupled variational inequality system. A major advancement is the development of an extended fixed-stress algorithm, where displacements, phase-field, pressures, and temperatures are solved in a staggered sequence. An important aspect of this work is the global coupling of pressures and temperatures across the domain using diffraction systems, with diffraction coefficients defined by material parameters weighted by the diffusive phase-field variable. To ensure robust local mass conservation, we employ enriched Galerkin finite elements (EG) for both pressure and temperature diffraction equations. By enriching the continuous Galerkin basis functions with discontinuous piecewise constants, EG accurately represents solution and parameter discontinuities while preserving local mass and energy conservation—crucial aspects for THM problems and realistic behavior. Moreover, the use of a predictor–corrector local mesh adaptivity scheme is employed, allowing the model to handle small phase-field length-scale parameters while maintaining high numerical accuracy and reasonable computational cost. Furthermore, these new model and algorithmic developments represent significant advances in the field and have been substantiated through rigorous numerical tests.

Diffraction systems↗
DOE OSTI2023

On the convexity of phase-field fracture formulations: Analytical study and comparison of various degradation functions

Efficient and accurate fracture modeling is of great importance in applications where catastrophic outcomes under extreme scenarios are possible. The phase-field (PF) approach to fracture received significant attention over the past decade, due to its capability to capture complicated fracture patterns (e.g., crack merging and branching). Specifically, crack initiation and propagation are modeled via minimization of the total energy functional, which is regularized with the aid of a phase field. Despite the promising results and modeling capabilities of the PF method in many applications, the solution of fracture problems remains computationally challenging mainly due to the non-convexity of the total energy functional with respect to the combined unknown (phase field and displacement) fields. Understanding the effects of their coupling on convexity is crucial in order to address frequently encountered hurdles in fracture modeling (e.g., inefficient solvers and non-physical crack nucleation). In this paper, we develop convexity criteria for a wide class of PF fracture formulations. For this class of formulations, the second variation of the total energy functional is expressed in terms of Hessian matrices (evaluated at individual material points). Depending on the choice of geometric crack functions and degradation functions, we classify the formulations into three categories and analytically study each one separately. To study the sign of the second variation, we derive inequalities which are satisfied at material points when the Hessian matrix is locally positive semi-definite. These inequalities provide objective criteria for comparing degradation functions. Finally, the applicability of the proposed convexity criteria is demonstrated in the context of a one-dimensional problem, solved using a conventional monolithic solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Entropy stable modal discontinuous Galerkin schemes and wall boundary conditions for the compressible Navier-Stokes equations

Entropy stable schemes ensure that physically meaningful numerical solutions also satisfy a semi-discrete entropy inequality under appropriate boundary conditions. Here in this work, we describe a discretization of viscous terms in the compressible Navier-Stokes equations which enables a simple and explicit imposition of entropy stable no-slip and reflective (symmetry) wall boundary conditions for discontinuous Galerkin (DG) discretizations. Specifically, we derive methods for imposing adiabatic no-slip and reflective (symmetry) boundary conditions for modal entropy stable DG formulations which preserve a semi-discrete entropy inequality. Numerical results confirm the robustness and accuracy of the proposed approaches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Residential segregation and outdoor urban moist heat stress disparities in the United States

The combined impact of urbanization-induced warming and drying on large-scale heat stress disparities remains unknown, with multicity studies using satellite-derived land surface temperature as a proxy for these disparities. Here, using high-resolution urban-resolving numerical model simulations for 2014–2018, we find pervasive disparities in all-sky average maximum summertime air temperature and moist heat stress metrics across US cities, with higher outdoor heat stress exposure in poorer and primarily non-white census tracts. Ninety-four percent of the US urban population (228 million) live in cities where heat stress burdens the poor, with heat stress inequities between white and non-white populations strongly associated with residential segregation. Similarly, historically redlined neighborhoods show higher heat stress than their non-redlined counterparts, demonstrating how historical segregation relates to present-day environmental inequalities. Our results provide quantitative estimates of physiologically relevant heat stress disparities at the US national scale and highlight potential biases when using satellites as a proxy for these.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

A framework to centre justice in energy transition innovations

The important role of justice in energy transition technologies has been a topic of increasing interest in recent years. However, key questions remain about how inequities influence energy transition innovations (ETIs) from their design to their widespread use, which ETIs receive more funding, and who controls ETI research, prototyping and deployment. Here, in this work, we propose a framework to centre justice in energy transition innovations (CJI) and examine how three tenets of justice (recognition, procedural and distributional justice) influence each level of ETI, including niche, regime and landscape levels. We examine wind energy in Mexico and multiple ETIs in Los Angeles as use cases to show how our CJI framework can help reveal the specific inequities undermining just energy transitions at crucial analytical levels of ETI in practice. Our CJI framework offers a path for promoters, practitioners and underserved communities to target the problems these groups face and create ETIs that better address their specific aspirations, needs and circumstances.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2023

A comparative analysis of US state-level policies and programs to advance energy justice

Abstract The US energy system is undergoing massive changes that have environmental, technological, and societal implications. Decisions and actions taken now will dramatically alter the trajectory of our future energy system. Though new technologies can lessen the dangers of anthropogenic climate change, an effective and sustainable transition requires addressing social justice issues as a priority. To this end, many states have implemented policies and programs that address energy justice. A formal survey of state-level energy justice policies and programs is needed to better understand the methods used to assist communities targeted and the impacts of these efforts. Such an analysis should include an analysis of the metrics used to judge the effectiveness of the enacted policies and programs. In this paper, we analyze the energy justice policies and programs of seven different US states. From this analysis, we identify three important aspects of state energy policies. First, most policies and programs do not articulate their goals, nor cite metrics to judge their successes. This lack of transparency and accountability is a major roadblock to truly just solutions. Second, states focus on a very narrow range of solutions for energy justice issues. The most prevalent being utility bill assistance, which does not address the systemic and enduring challenges faced by many low-income or historically marginalized communities. Lastly, comprehensive energy policy does not acknowledge and address housing, employment, education, and healthcare inequities that exacerbate energy system inequities. The work presented in this paper sheds light on the progress of state-level energy justice policies and programs across the United States, and we argue more work needs to be done to understand best practices in energy justice policymaking.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2024

Causal and stable first-order chiral hydrodynamics

We derive the set of inequalities that is necessary and sufficient for nonlinear causality and linear stability of first-order relativistic hydrodynamics with either a U ( 1 ) V conserved current or a U ( 1 ) A current with a chiral anomaly or both. Our results apply to generic hydrodynamic frames in which no relations among the transport parameters are imposed. Furthermore, our analysis yields, to the best of our knowledge, the first theory of viscous chiral hydrodynamics proven to be causal and stable. We find that causality demands the absence of vorticity-induced heat flux, forcing a departure from the thermodynamic frame in the chiral case. The inequalities for causality and stability define a hypervolume in the space of transport parameters, wherein each point corresponds to a consistent formulation. Notably, causality is determined by just three combinations of transport parameters. We present our results in a form amenable to numerical hydrodynamic simulations. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2025

Locality in collider tests of quantum mechanics with top quark pairs

Tests of quantum properties of fundamental particles in high energy colliders are starting to appear. Entanglement and Bell inequality violation in top and antitop quark system is of particular interest since top quarks are unstable particles that undergo a cascade decay. We argue for criteria for the spacelike separation between top and antitop quarks at their different decay stages. We considered causal separation at three different instances: at the top quark decay, at the 𝑊 boson decay, and at the lepton/jet contact with the macroscopic apparatus. We showed that the spacelike fraction of events is the smallest, when requiring that both top quarks and 𝑊 bosons decay within the spacelike interval. For high invariant masses, typically required for the Bell inequality violation, this is almost identical to just the top quark decay requirement. We also include an option for the angular correlation of the 𝑏 quarks from top quark decay to be used for the spin correlation measurement. We require that both top quark and 𝑏 hadron decays are spacelike separated. Again, we find that at high invariant masses it is almost identical to just the requirement of spacelike separation between top and antitop quarks. We provide numerical values for our proposed criteria. If such a criterion is satisfied, the system is guaranteed to not be in a causal connection.

Entanglement in field theory↗