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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

A high-performance lung-inspired ceramic 3D-printed heat exchanger for high-temperature energy-efficient systems

The thermal-to-electric conversion efficiency of next-generation supercritical carbon dioxide and concentrated solar power plants is significantly augmented by operating at temperatures exceeding 1000 °C if durable, compact, high-temperature heat exchangers (HXs) are developed. Whereas metal 3D-printed HXs fail to operate under extreme temperature conditions, ceramic 3D-printed HXs are deemed promising candidates for high-temperature, highly oxidizing environments. Ceramic 3D-printed HXs, however, exhibit a high gas permeability issue through hot and cold separating walls due to an excessive non-volatile photopolymer content utilized. Here, in this work, a novel leak-free lung-inspired ceramic 3D-printed HX employing a highly complex heat transfer topology is introduced for high-temperature energy-efficient systems. The high permeability issue of ceramic 3D-printed HXs is fully eliminated through a uniform zinc-based coating. It was determined that the effective thermal conductivity of the sintered ceramic heat exchangers is affected by the coated layer. The high-temperature thermal and hydraulic characteristics of the lung-inspired ceramic 3D-printed HX are comprehensively examined and compared against a millichannel 3D-printed HX module. Experimental results indicated that the lung-inspired 3D-printed ceramic HX significantly outperforms its millichannel counterpart. The lung-inspired HX shows a volume-based power density of 8.2 MW/m3 at a hot-side inlet air temperature of 700°C, a 71 % improvement compared with that of the millichannel HX. More importantly, the higher thermal duty of the lung-inspired 3D-printed HX is realized at a lower normalized pressure drop penalty of 510 Pa/W, 22 % lower than that of the millichannel ceramic HX. This study accelerates the advancement of high-performance ceramic 3D-printed HXs with complex topologies for high-temperature energy-efficient systems and/or corrosive environments.

42 ENGINEERING↗
DOE OSTI2021

Recent Developments in the Design of Vertical Borehole Ground Heat Exchangers for Cost Reduction and Thermal Energy Storage

Ground source (geothermal) heat pumps (GSHPs) can meet the thermal demands of buildings in an energy-efficient manner. The current high installation costs and long payback period limit the attractiveness of GSHP installation in the United States. Vertical borehole ground heat exchangers (VBGHEs), which are commonly used in GSHP systems, contribute most to the cost premium of GSHPs. Reducing the cost of VBGHEs could help increase market penetration of GSHP systems. This paper reviews recent developments for VBGHEs, including improvements in borehole heat transfer and borehole field layout, integration with thermal energy storage, and new design tools. Improvements in the borehole design and materials are more likely to be justified when the ground has high thermal conductivity. Integrating thermal energy storage can provide additional value to the GSHP system, especially when flexible electric demand at buildings becomes more valuable. Here, advanced design tools for VBGHEs that account for the thermal response of irregularly shaped borehole fields and that are more closely integrated with whole-building energy simulation programs may facilitate more innovations and optimization of GSHP system designs.

15 GEOTHERMAL ENERGY↗
DOE OSTI2022

Integration of Pumped Heat Energy Storage with Fossil-Fired Power Plant (Final Report)

The project team of Southwest Research Institute ® (SwRI ® ), Malta Inc. (Malta), and Luminant Generation Company LLC (Luminant) completed a feasibility study for the integration of a 100-MW, 10-hour (1000-MWh) Malta Pumped Heat Energy Storage (MPHES) system with multiple full-sized fossil-fired electricity generation units (EGU) in Luminant portfolio. MPHES is a long-duration, molten-salt-energy storage technology that uses turbomachinery and heat exchangers to transfer energy to a thermal storage media when charging, and removes the heat in a similar fashion when discharging. With high round trip efficiency (60-65%) and long lifespan (30+ years), MPHES provides economic benefits to the fossil-asset owners that can be scaled to integrate with assets across their portfolio. This technology uses hardware components, workforce personnel, and skillsets similar to those used by fossil EGUs, allowing for synergy when co-locating the two technologies. Luminant has approximately 39,000 megawatts of generation across 12 states, operating in six of the seven competitive markets in the U.S. and powered by a diverse portfolio of natural gas, nuclear, coal, and solar facilities. The DeCordova plant in Granbury, Texas, a simple cycle natural gas peaker power plant, was used as the fossil-fired asset in this project. The local market in Granbury, Texas has many influences, including several nearby power plants, a Luminant-owned nuclear plant (Comanche Peak), and substantial wind energy, which causes both negative pricing at night and high market volatility. Reducing false starts of the DeCordova plant and better responding to market volatility would be an economic advantage. Luminant is currently integrating battery storage plant on site to begin addressing these challenges. Integrating long-duration storage, like MPHES, would expand this capability beyond one hour of storage and have the potential to greatly reduce the total number of gas turbine starts. The MPHES charging requirement could help offset the overnight operating costs of Comanche Peak, which cannot load follow, and the nearby Luminant-owned Wise County combined cycle plant that cycles too often. Following the assessment of Luminant’s ERCOT-based portfolio for integration compatibility with Malta’s PHES system and the project tasks of conceptual study, technoeconomic analysis, technology gap assessment, and commercialization plan, the project team effort has resulted in several key outcomes: (1) Identification of market trends in a high-wind penetration market outside a major metropolitan area; (2) Creation of a dispatching model for the MPHES system and the pairing of Li-ion battery with a gas turbine in a real time market; (3) Revenue and cost estimations for operating MPHES alongside a gas peaker plant with real dispatching considerations and comparison with variations in the Malta implementation, including doubling the storage capacity and using two discharge drivetrains; (4) Potential carbon emission reductions possible by replacing gas turbine operation with Malta PHES operation; and (5) Summary of literature-based future market predictions for Texas.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2024

Exchange–correlation entropy from the generalized thermal adiabatic connection

Warm dense matter is a highly energetic phase characterized by strong correlations, thermal effects, and quantum mechanical electrons. Thermal density functional theory is commonly used in simulations of this challenging phase, driving the development of temperature-dependent approximations to the exchange–correlation free energy. Approaches using the adiabatic connection formula are well known at zero temperature and have been recently leveraged at non-zero temperatures as well. In this work, a generalized thermal adiabatic connection (GTAC) formula is proposed, introducing a fictitious temperature parameter. This allows extraction of the exchange–correlation entropy S XC using simulated interaction strength scaling. Here, this procedure uses a Hellmann–Feynman approach to express the exchange–correlation entropy in terms of a temperature- and interaction strength-dependent exchange–correlation potential energy. In addition, analysis of S XC as a function of interaction strength suggests new forms for approximations, and GTAC itself offers a new framework for exploring both the exact and approximate interplay of temperature, density, and interaction strength across a wide range of conditions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

National and Regional Initiatives to Promote Energy Efficiency and Renewable Energy Through State Energy Offices

The National Association of State Energy Officials (NASEO) worked with the U.S. Department of Energy’s (DOE) Office of Energy Efficiency and Renewable Energy (EERE), Weatherization and Intergovernmental Programs Office (WIP) over a ten year period to provide technical assistance, research and analyses, and enhanced coordination between DOE and the State and Territory Energy Offices. Over the life of the agreement, NASEO worked with WIP and the states to provide statewide strategic energy plan analyses and recommendations, including customized technical assistance to the states; peer to peer financing assistance via NASEO’s Financing Committee and supporting activities; training on core energy policies and programs, including dialogues and resources to support energy-air coordination, a training for new State Energy Office Directors, peer to peer exchange via a rural energy taskforce, and support to states to enhance buildings efficiency, home energy labeling, and technology deployment opportunities; support for State Energy Program metrics; and regional coordination via regional coordinators and peer exchange opportunities both in-person and online. Over the life of the project, the position and role of State Energy Offices within state government has changed, with now 80 percent of State Energy Office Directors serving as their Governor’s energy advisor, or reporting directly to their Governor’s energy advisor. This shift in stature has made it ever more crucial for State Energy Offices to receive timely and relevant technical assistance across a range of energy issue areas. NASEO, in collaboration with WIP, was able to deliver this technical assistance, and energy efficiency and renewable energy deployment has accelerated across the country. The State Energy Office Directors and their staff continue to engage in NASEO’s Committees – many of which were supported through this agreement – and have provided formal and informal feedback on the value of the programs supported through this award (e.g., reporting via survey increased understanding of their roles and technical assistance offerings provided by WIP and NASEO following the New Director Trainings). Moreover, resources developed through this award (e.g., Comprehensive State Energy Planning Guidelines, State Energy Loan Fund Database, Rural Data Resources for State Energy Planning and Programs, The Value of Adding home Energy Score to Low-Income Energy Efficiency Programs, etc.) have been cited by states as instrumental to their understanding of specific energy issue areas and in many cases led directly to enhanced program design within a state (e.g. Iowa citing their review of NASEO’s Comprehensive State Energy Planning Guidelines as a necessary first step in their planning process, later following may of the steps outlined in the guidelines). The priorities of the states and federal government have evolved over the last decade, with an increasing focus on climate mitigation and adaptation, equity impacts and considerations, energy security and resilience, and enhanced energy efficiency and renewable energy technology deployment, but the roots of these new priorities are based in the state and federal policies and programs, and research and analyses, that were supported in part through this award and other complementary initiatives. NASEO looks forward to continuing to support the states, and collaborate and coordinate with DOE, as we build on this important foundation in the years ahead.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2022

Importance of imposing gauge invariance in time-dependent density functional theory calculations with meta-generalized gradient approximations

It has been known for more than a decade that the gauge variance of the kinetic energy density τ leads to additional terms in the magnetic orbital rotation Hessian used in linear-response time-dependent density functional theory (TDDFT), affecting excitation energies obtained with τ-dependent exchange–correlation functionals. While previous investigations found that a correction scheme based on the paramagnetic current density has a small effect on benchmark results, we report more pronounced effects here, in particular, for the popular M06-2X functional and for some other meta-generalized gradient approximations (mGGAs). In the first part of this communication, this is shown by a reassessment of a set of five Ni(II) complexes for which a previous benchmark study that did not impose gauge invariance has found surprisingly large errors for excitation energies obtained with M06-2X. These errors are more than halved by restoring gauge invariance. The variable importance of imposing gauge invariance for different mGGA-based functionals can be rationalized by the derivative of the mGGA exchange energy integrand with respect to τ. In the second part, a large set of valence excitations in small main-group molecules is analyzed. For M06-2X, several selected n → π* and π→π$^{*}_{⊥}$ excitations are heavily gauge-dependent with average changes of –0.17 and –0.28 eV, respectively, while π→π$^{*}_{∥}$ excitations are marginally affected (–0.04 eV). Similar patterns, but of the opposite signs, are found for SCAN0. Here, the results suggest that reevaluation of previous gauge variant TDDFT results based on M06-2X and other mGGA functionals is warranted.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Narrow-Channel, Fluidized Beds for Effective Particle Thermal Energy Transport and Storage

Colorado School of Mines (Mines) led this program in collaboration with Sandia National Laboratories (Sandia) to characterize narrow-channel fluidized beds of aluminosilicate particles – supplied by Carbo Ceramics – as a means for releasing high-temperature thermal energy in particle heat exchangers and for capturing concentrated solar energy in indirect particle receivers. Single-channel, heat transfer experiments at Mines and reduced-order 1-D models and 3-D two-fluid, CFD models explored many aspects of counterflow, bubbling fluidized beds (net downward particle flow and upward gas flow) for enhancing particle-wall heat transfer at elevated temperatures. Results at Mines on single-channel test sections consistently showed that mild bubbling fluidization increases particle-wall heat transfer coefficients (h T,w ) regularly by more than 4.0x over h T,w values without fluidization at similar conditions (mean particle diameter d p , bed depth Δz b , and bed particle temperatures T p ). Insights from lab-scale tests and modeling studies provided Nusselt number correlations for h T,w and informed the design and fabrication (by Vacuum Process Engineering) of a nominal 40-kWth, particle-sCO 2 plate heat exchanger (HX) with 12 parallel narrow-channel, fluidized beds bounded by stainless-steel walls with embedded microchannels for high-pressure sCO 2 flows. Tests of the 40-kW th HX at the particle-sCO 2 HX test stand at Sandia's National Solar Thermal Test Facility (NSTTF) were limited, due to HX design, to particle inlet temperatures T p,in ≤ 520°C with maximum sCO 2 outlet temperatures T sCO2,out ≈ 440°C, which are well below design conditions for a primary HX in a sCO 2 power cycle for a Gen-3 concentrating solar power (CSP) plant. Total heat transfer $\dot{Q}_{HX}$ remains relatively constant with increased fluidization for fixed particle and sCO 2 inlet conditions because higher h T,w due to fluidization is offset by increased axial dispersion, which suppresses temperature differences between the particles and sCO 2 in the counterflow configuration. The axial dispersion reduces the effective overall heat transfer coefficient U based on T p,in to values around 200 W m -2 K -1 .

14 SOLAR ENERGY↗
DOE OSTI2023

The Predictive Power of Exact Constraints and Appropriate Norms in Density Functional Theory

Ground-state Kohn-Sham density functional theory provides, in principle, the exact ground-state energy and electronic spin densities of real interacting electrons in a static external potential. In practice, the exact density functional for the exchange-correlation (xc) energy must be approximated in a computationally efficient way. About 20 mathematical properties of the exact xc functional are known. In this work, we review and discuss these known constraints on the xc energy and hole. By analyzing a sequence of increasingly sophisticated density functional approximations (DFAs), we argue that (a) the satisfaction of more exact constraints and appropriate norms makes a functional more predictive over the immense space of many-electron systems and (b) fitting to bonded systems yields an interpolative DFA that may not extrapolate well to systems unlike those in the fitting set. We discuss both how the class of well-described systems has grown along with constraint satisfaction and the possibilities for future functional development.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Pressure-Dependent Magnetic Properties of Quasi-2D Cr 2 Si 2 Te 6 and Mn 3 Si 2 Te 6

Recently, pressure has been used to induce structural and magnetic phase transitions in many layered quantum materials whose layers are linked by van der Waals forces. Materials with such weakly held layers allow for relatively easy manipulation of the superexchange mechanism, which can give rise to novel magnetic behavior. Here, using hydrostatic pressure as a disorderless means to manipulate the interlayer coupling, we applied pressure on two quasi-2D sister compounds, namely, Cr 2 Si 2 Te 6 (CST) and Mn 3 Si 2 Te 6 (MST), up to ~1 GPa. Magnetic property measurements with the application of pressure revealed that the ferromagnetic transition temperature decreases in CST, while the opposite occurs for the ferrimagnetic MST. In MST, magnetization decreases with the increase in pressure, and such a trend is not clearly observed within the pressure range studied for CST. The overall pressure effect on magnetic characteristics such as exchange couplings and magnetic anisotropy energies is also examined theoretically using density functional theory. Exchange coupling in MST is strongly frustrated, and the first nearest neighbor interaction is the most dominant of the components with the strongest pressure dependence. In CST, the exchange coupling parameters exhibit very little dependence on pressure. This combined experimental and theoretical work has the potential to expand to other relevant quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Development, Monitoring, and Control of Fracture Thermal Energy Storage in Crystalline Rock Formations (DEMO-FTES) [Abstract]

Approximately half of global energy consumption is used for heating and cooling. Because fossil fuels are used to meet most of this demand, heating and cooling of buildings produces a large portion of global greenhouse gas (GHG) emissions. The proposed project seeks to demonstrate the feasibility of a seasonal thermal energy storage concept called fracture thermal energy storage (FTES), which has the potential to dramatically lower energy requirements for heating and cooling and improve the resilience of building energy systems. FTES is a technique for building a highly efficient heat exchanger by creating a carefully designed set of fractures in the ground below a building. This heat exchanger allows thermal energy to be stored over seasonal timeframes—for example, hot thermal energy that is easily captured in the summer or energy from waste heat sources—to meet heating needs during colder months. FTES offers a solution with a relatively small footprint and lower cost compared to currently operating aquifer thermal energy storage (ATES) systems and could be used in the many areas without aquifers suitable for ATES. If commercialized, FTES systems could exceed the 2.5 TWh of energy storage per year from the more than 2,800 ATES systems in operation worldwide, which range from 0.1 MW to 30 MW. The savings in CO2 emissions per year are also expected to match or exceed individual ATES projects, with the largest, a 30 MW system used to provide heating and cooling to the University of Technology in Eindhoven in the Netherlands, estimated to save 13,000 tons of CO2 emissions per year. FTES utilizes mature drilling and fracturing technology and therefore has the potential to be rapidly commercialized once demonstrated. The ability to construct and establish flow through an FTES heat exchanger has been demonstrated by a previous project and the potential for efficient, large-capacity energy storage has been shown using numerical models. However, no experimental validation of these numerical estimates of thermal energy storage has been made. The first crucial need to advance FTES technology is to identify the sensitivity of key metrics such as thermal energy storage and production rates, capacities, and efficiencies to design parameters such as the number of fractures, depth/temperature of fractures, size of fractures, and circulation rates. The second crucial need is experimental testing of achievable thermal performance with optimized system design parameters. The proposed scope of work seeks to systematically address these two critical needs through a highly complementary international collaboration spanning theory, laboratory, and mesoscale field evaluation. The proposed work plan calls for using dimensional analysis and existing state-of-the-art numerical simulators to design carefully scaled laboratory and 10-meter-scale field tests of the thermal efficiency of FTES. The existing advanced laboratory and intermediate-scale field testbeds that will be used for this project will allow for detailed monitoring of the system performance during the test and of how the performance changes across time and length scales. These results will determine the feasibility of full- scale FTES systems. If the thermal performance is consistent with model predictions, the results will provide a strong economic justification for rapid commercialization of FTES technology in a wide range of geographical areas.

25 ENERGY STORAGE↗
DOE OSTI2024

The role of air sealing while ground source heat pump system retrofits in the U.S. single-family houses

Widespread commercial adoption of ground source heat pumps (GSHP) is hindered by the relatively high initial cost associated with drilling boreholes in the ground to deploy ground heat exchangers. Reducing the energy demand of buildings has the potential to reduce the required borehole length and the associated drilling costs. In single-family residential buildings, air sealing can significantly lower heating energy usage, according to recent studies and reports. Thus, air sealing in conjunction with GSHP retrofits can lower the required GSHP system's capacity and borehole length to meet the thermal demands of the buildings. In order to understand the role of combining air sealing with GSHP retrofit quantitatively, the current study employs a whole building energy simulation tool integrated with an advanced design tool for the ground heat exchanger to determine changes in required GSHP capacity, total borehole length, and building energy consumption for with- and without-air sealing in single-family houses in 3 climate zones in the United States. The study considers one representative city for each climate zone, Phoenix, AZ for a hot climate, Seattle, WA for a moderate climate, and Minneapolis, MN for a cold climate. The results from this study show that reducing air infiltration from 0.8 ACH to the minimum ventilation requirement (0.35 ACH) can reduce borehole length requirement by up to 24% in Phoenix, 32% in Seattle, and 70% in Minneapolis. A similar magnitude of reduction can be seen for GSHP capacity and total building energy usage as well.

Prem Anand Jayaprabha, Jyothis Anand↗
DOE OSTI2023

Assessment of exchange-correlation functionals on oxygen vacancy formation energies of metal oxides

Oxygen vacancies are a common defect in oxides and play vital roles in many technological applications such as oxygen separation, catalytic reactors, solid oxide fuel cells, and solar thermochemical water splitting. The oxygen vacancy formation energy is directly related to the oxide reduction enthalpy and the vacancy concentration and, therefore, is a key quantity underlying these applications. The complexity of measuring oxygen vacancy formation energies experimentally suggests the utility of calculations based on density functional theory (DFT). However, the calculated results are strongly dependent on the exchange-correlation functionals and other parameters such as the Hubbard U . In this work, we compare the performance of the meta-GGA strongly constrained and appropriately normed (SCAN) functional and the commonly used semilocal generalized gradient approximation (GGA) functionals with experimental values of structural parameters, band gaps, magnetic structures, and oxygen vacancy formation energies for six representative oxides, i.e., CaMnO 3 , SrMnO 3 , LaMnO 3 , YMnO 3 , LaFeO 3 , and CeO 2 . Further, our results show that SCAN usually has better agreement with the experimental lattice constants and band gaps and larger magnetic moments than the commonly used GGA functionals. Although SCAN overestimates the oxygen vacancy formation energies of transition metal oxides and therefore requires unusually large Hubbard U values to reproduce the experimental reduction enthalpies, it does predict the correct oxygen vacancy formation energy of CeO 2 , which challenges the commonly used GGA and hybrid functionals. Our results underscore the challenges that exist in describing these complex oxides by DFT and may shed light on developing more accurate exchange-correlation functionals for oxygen vacancy formation energy calculations.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Ionic functionalization of aromatic polymers for ion exchange membranes

The electrochemical energy conversion system of the present disclosure includes an anode, a cathode, and an ion exchange membrane including a polymer having an aromatic polymer chain and an alkylated substrate including an alkyl chain, and at least one ionic group. The alkylated substrate is bound to at least one aromatic group in the polymer chain via Friedel-Crafts alkylation of the at least one aromatic group. The alkylation reaction utilizes a haloalkylated tertiary alcohol or a haloalkylated alkene as a precursor. In the presence of an acid catalyst, a carbocation is generated in the precursor which reacts with the aromatic rings of the polymer chain. The at least one ionic group is then replaced with a desired cationic or anionic group using a substitution reaction. The membranes exhibit advantageous stability achieved through a simplified and scalable reaction scheme.

Bae, Chulsung↗
DOE OSTI2022

Domain state exchange bias in a single layer FeRh thin film formed via low energy ion implantation

Modern spintronics relies heavily on the exchange bias effect to pin the orientation of ferromagnetic layers in magnetic tunnel junctions. The current implementations of exchange bias in magnetic tunnel junctions employ pristine interfaces between antiferromagnetic and ferromagnetic layers. Here we reveal an interfacial exchange bias introduced by a single-step, low-energy ion implantation process in a single layer FeRh thin film. Both 1 keV He + ions and 5 keV Fe + were investigated, their energy selected to ensure the ions would stop within the FeRh film. The ions reduce the metamagnetic transition temperature through defect generation to form a surface layer with ferromagnetic ordering. Temperature dependent magnetism measurements reveal a room temperature exchange bias between the ferromagnetic surface and the antiferromagnetic bulk of ~41 Oe in 5 keV Fe + implanted samples and ~36 Oe for 1 keV He + implanted samples. We directly scrutinize this exchange bias effect in magnetic depth profiles obtained by polarized neutron reflectometry which clearly show a pinned ferromagnetic layer adjacent to the disordered layer created by low energy Fe + ion implantation. These results reveal a novel method to implement exchange bias in an antiferromagnetic layer that can have direct application in the field of spintronics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Radiative Electronic Bound States in the Continuum from Defects in Semiconductors

Continuum-buried defect states in semiconductors are generally expected to be optically inactive because of their strong coupling to continuum bands. Here, we show that such defects can instead host radiative electronic bound states in the continuum (BICs) using the silicon G center as a prototypical example. Hybrid functional first-principles calculations with a Hubbard U correction reveal that a localized defect state, initially buried below the valence band maximum (VBM) in the ground state, undergoes exchange-driven energy-level reordering under optical excitation and shifts above the VBM. This exchange-induced transition suppresses nonradiative decay and enables a robust radiative emission. By computing temperature-dependent nonradiative lifetimes and comparing them to experimental photoluminescence (PL) lifetimes, we quantitatively reproduce the observed temperature dependence of the emission. These results uncover a stabilization mechanism for continuum-embedded defect states and establish electronic BICs as a general paradigm for designing defect-based optical systems, including quantum emitters and qubits.

Hong, SeongYun↗
DOE OSTI2020

Recovering Gardner restacking with purely diffusive operations

The maximum particle kinetic energy that can be extracted from an initial six-dimensional phase space distribution motivates the concept of free or available energy. The free energy depends on the allowed operations that can be performed. A key concept underlying the theoretical treatment of plasmas is the Gardner free energy, where the exchange of the contents of equal phase volumes is allowed. Further, a second free energy concept is the diffusive free energy, in which the contents of volumes are instead averaged. For any finite discretization of phase space, the diffusive free energy is known to be less than the Gardner free energy. However, despite the apparent fundamental differences between these free energies, it is demonstrated here that the Gardner free energy may be recovered from the continuous limit of the diffusive free energy, leading to the surprise that macroscopic phase-space conservation can be achieved by ostensibly entropy-producing microscopic operations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗