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Hamiltonian switching control of noisy bipartite qubit systems

Abstract We develop a Hamiltonian switching ansatz for bipartite control that is inspired by the quantum approximate optimization algorithm, to mitigate environmental noise on qubits. We demonstrate the control for a central spin coupled to bath spins via isotropic Heisenberg interactions, and then make physical applications to the protection of quantum gates performed on superconducting transmon qubits coupling to environmental two-level-systems (TLSs) through dipole-dipole interactions, as well as on such qubits coupled to both TLSs and a Lindblad bath. The control field is classical and acts only on the system qubits. We use reinforcement learning with policy gradient to optimize the Hamiltonian switching control protocols, using a fidelity objective for specific target quantum gates. We use this approach to demonstrate effective suppression of both coherent and dissipative noise, with numerical studies achieving target gate implementations with fidelities over 0.9999 (four nines) in the majority of our test cases and showing improvement beyond this to values of 0.999 999 999 (nine nines) upon a subsequent optimization by GRadient Ascent Pulse Engineering (GRAPE). We analyze how the control depth, total evolution time, number of environmental TLS, and choice of optimization method affect the fidelity achieved by the optimal protocols and reveal some critical behaviors of bipartite control of quantum gates.

Physics

Ultra-light antennas via charge programmed deposition additive manufacturing

Abstract The demand for lightweight antennas in 5 G/6 G communication, wearables, and aerospace applications is rapidly growing. However, standard manufacturing techniques are limited in structural complexity and easy integration of multiple material classes. Here we introduce charge programmed multi-material additive manufacturing platform, offering unparalleled flexibility in antenna design and the capability for rapid printing of intricate antenna structures that are unprecedented or necessitate a series of fabrication routes. Demonstrating its potential, we present a transmitarray antenna composed of an interconnected, multi-layered array of dielectric/conductive S-ring unit cells, reducing 94% mass of conventional antenna configurations. A fully printed circular polarized transmitarray system fed by a source and a Risley prism antenna system operating at 19 GHz both show close alignment between testing results and numerical simulations. This printing method establishes a universal platform, propelling discovery of new antenna designs and enabling data-driven design and optimizations where rapid production of antenna designs is crucial.

Science & Technology - Other Topics

Thermal Reservoir Networks for Modularly Expandable Thermal Microgrids

The Department of Defense (DoD) faces the substantial challenge of cost-effectively retrofitting one to two installations per month, each comprising approximately 1,000 buildings, to improve resilience, reduce energy consumption, and enhance energy supply security. Achieving these objectives requires optimal system selection and effective risk mitigation during system integration. To address this need, we introduce Platform-Based Design (PBD), a structured, hierarchical methodology adapted from other industrial sectors to the domain of energy system retrofits. We demonstrate the effectiveness of PBD through a techno-economic feasibility study comparing geothermal-coupled thermal energy networks (TENs) with conventional energy systems for heating, cooling, and powering 17 buildings at Joint Base Andrews (JBA) in Maryland. Our analysis illustrates that the PBD approach enables rigorous, data-driven, sequential decision making, resulting in a family of Pareto-optimal systems, among which the TEN emerged as the most promising solution. The selected TEN design integrates geothermal borefields, heat recovery heat pumps, photovoltaic (PV) arrays, and battery storage. Compared to the baseline system – gas heating combined with air-source chillers – the proposed TEN reduces annual imported energy by 74% and peak electricity demand by 45%, achieves a levelized cost of energy of $\$0.210$/kWh, and substantially enhances resilience. Life-cycle costs increase by approximately 6%, and initial investment costs are about 2.5 times higher than the baseline. However, if central plant infrastructure, district loops, and utility-scale PV and battery systems are privately funded and operated, the initial investment would fall below the baseline system cost. Critical to achieving these significant performance improvements were detailed nonlinear dynamic simulations coupling geothermal heat transfer, energy system operation, and realistic feedback control logic. These simulations identified essential design modifications and control strategy refinements that substantially reduced energy use, peak demand, and compressor shortcycling, thereby improving durability and reliability—issues that would have been significantly more expensive to resolve during operation. Additionally, the verification step highlighted sensitivities to key design parameters that could reduce initial investment by approximately $\$2$ million and reduce annual life-cycle costs more than $\$300,000$. We recommend adopting the PBD methodology for future feasibility studies and TEN pilot projects to gain valuable operational experience. Furthermore, we recommend that DoD invest in transferring and scaling the PBD methodology to other installations. This entails developing standardized computational frameworks and component libraries as well as training industry in conducting PBD. Such investments would enable rapid, robust, reliable, and cost-effective retrofits, supporting DoD’s ambitious energy system modernization goals.

Wetter, Michael [Lawrence Berkeley National Labora

Variational Quantum Circuits to Prepare Low Energy Symmetry States

We explore how to build quantum circuits that compute the lowest energy state corresponding to a given Hamiltonian within a symmetry subspace by explicitly encoding it into the circuit. We create an explicit unitary and a variationally trained unitary that maps any vector output by ansatz A(α → ) from a defined subspace to a vector in the symmetry space. The parameters are trained varitionally to minimize the energy, thus keeping the output within the labelled symmetry value. The method was tested for a spin XXZ Hamiltonian using rotation and reflection symmetry and H 2 Hamiltonian within S z = 0 subspace using S 2 symmetry. We have found the variationally trained unitary gives good results with very low depth circuits and can thus be used to prepare symmetry states within near term quantum computers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Fast Active-Set Thresholding Method for Nonnegative Least Squares

Nonnegative Least Squares (NNLS) is a fundamental constrained optimization problem encountered in many applications such as image deblurring, signal processing, nonnegative matrix factorization, magnetic microscopy, and hyperspectral imaging. Active-set based methods are a common class of algorithms for solving NNLS which identify the optimal variable set of the NNLS solution. They do so by iteratively solving a series of unconstrained least squares problems, identifying which variables violate the nonnegativity constraints, and then swapping variables in/out of consideration until the optimal set of variables is found. Several variations improving upon this method exist in the literature. In this work, we propose an active-set swap heuristic which further improves upon existing active-set based methods for NNLS. Our optimizations are based upon adding multiple variables to the passive set within a threshold of the smallest gradient value and removing variables within a similar threshold of the closest boundary constraint. We leverage these optimizations to yield a Fast Active-Set Thresholding NNLS (FAST-NNLS) algorithm which significantly outperforms the existing state-of-the-art NNLS algorithms for a wide range of problems. Rigorous convergence guarantees are proven for the proposed method. We demonstrate the effectiveness of our proposed method on multiple synthetic datasets and two realworld text analysis applications. In doing so, we present the most comprehensive NNLS solver comparison in the literature to date.

Cobb, Benjamin [Georgia Institute of Technology]

Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum Computers

The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wave functions that are relevant in the behavior of the system under study. Hamiltonian symmetries are important instruments used to classify relevant many-particle wave functions and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions based on the addition theorem of angular momentum, and heuristic approximation of total spin eigenfunctions based on the variational optimization of a suitable cost function. The construction of these quantum circuits is illustrated in detail, and the preparation of total spin eigenfunctions is demonstrated on IBM quantum devices, focusing on three- and five-spin systems on graphs with triangle connectivity.

97 MATHEMATICS AND COMPUTING

Anticipating Optical Availability in Hybrid RF/FSO Links Using RF Beacons and Deep Learning

Radiofrequency (RF) communications offer reliable but low data rates and energy-inefficient satellite links, while free-space optical (FSO) promises high bandwidth but struggles with disturbances imposed by atmospheric effects. A hybrid RF/FSO architecture aims to achieve optimal reliability along with high data rates for space communications. Accurate prediction of dynamic ground-to-satellite FSO link availability is critical for routing decisions in low-earth orbit constellations. In this paper, we propose a system leveraging ubiquitous RF links to proactively forecast FSO link degradation prior to signal drops below threshold levels. This enables pre-calculation of rerouting to maximally maintain high data rate FSO links throughout the duration of weather effects. We implement a supervised learning model to anticipate FSO attenuation based on the analysis of RF patterns. Through the simulation of a dense lower earth orbit (LEO) satellite constellation, we demonstrate the efficacy of our approach in a simulated satellite network, highlighting the balance between predictive accuracy and prediction duration. An emulated cloud attenuation model is proposed to provide insight into the temporal profiles of RF signals and their correlation to FSO channel dynamics. Our investigation sheds light on the trade-offs between prediction horizon and accuracy arising from RF beacon numbers and proximity.

FSO availability

User-Centric Communication With Aerial Network for 6G: A Reinforcement Learning Approach

Meeting the diverse needs of user verticals requires innovative cellular architectures that can offer additional degrees of freedom to provide on-demand services. The terrestrial user-centric radio access network (UC-RAN) stands out as an excellent choice for this purpose. However, a drawback of UC-RAN is its tendency to prioritize high-priority verticals, often resulting in a subpar quality of experience for low-priority verticals. This issue is particularly exacerbated in hotspot areas. Here, to address this problem, we introduce an aerial network integrated with terrestrial UC-RAN to provide coverage to users which are not served by the terrestrial network. Furthermore, we analyze the impact of key configuration and optimization parameters (COPs), such as location, transmit power, altitude, and beamwidth of aerial base stations (ABSs) on system key performance indicators (KPIs), such as coverage, latency satisfaction, average spectral efficiency, and energy efficiency. We formulate a robust multiobjective function to maximize these KPIs without biasing toward any specific KPI(s). Finally, we propose a deep reinforcement learning optimization framework based on the state-of-the-art soft actor-critic algorithm to control ABS COPs and optimize system KPIs. Experimental evaluations demonstrate that the proposed optimization framework can converge to near-optimal solutions derived from the pseudo brute force in a few thousand epochs.

6G

DEPRECATED AI-Batt-OS (Autonomous Identification of Battery Life Models - Open Source) [SWR 21-17]

DEPRECATED. This repository was archived by the owner on Jun 30, 2026. It is now read-only. Open source implementation of some of the methods utilized by AI-Batt, a battery lifetime modeling and analysis toolkit provided by the National Laboratory of the Rockies (NLR). This software demonstrates the use of bi-level optimization and symbolic regression techniques to semi-autonomously identify algebraic models predicting the capacity fade of lithium-ion batteries during calendar aging. Modeling the degradation of batteries is a complex task, due to the difficulty in separating the time-dependent and time-independent factors impacting cell level degradation, across multiple data series with different numbers of measurements and/or data quality. Bi-level optimization enables model parameters to be optimized to either the entire data set or to individual data series, allowing statistical disambiguation of global behaviors (data series independent) and local behaviors (data series dependent). Symbolic regression is used to automatically search for optimal low-dimesional models predicting the variation of locally optimized parameters versus time-independent experimental variables from millions of possible models, resulting in a more accurate and repeatable model identification process than is possible by a manual search. The provided tools also implement cross-validation and bootstrap resampling schemes, empowering statistical model comparison/selection and quantification of model uncertainties. An example script replicates the results from the manuscript "Challenging Practices of Algebraic Battery Life Models through Statistical Validation and Model Identification via Machine-Learning", submitted to ECS. All code is written in MATLAB. Requires the Statistics and Machine Learning Toolbox. Contact Dr. Paul Gasper at Paul.Gasper@nlr.gov for any questions.

Gasper, Paul [National Renewable Energy Lab. (NREL

Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open quantum dynamics in structured thermal environments

In this work, we introduce an efficient method, TTN-HEOM, for exactly calculating the open quantum dynamics for driven quantum systems interacting with highly structured bosonic baths by combining the tree tensor network (TTN) decomposition scheme with the bexcitonic generalization of the numerically exact hierarchical equations of motion (HEOM). The method yields a series of quantum master equations for all core tensors in the TTN that efficiently and accurately capture the open quantum dynamics for non-Markovian environments to all orders in the system–bath interaction. These master equations are constructed based on the time-dependent Dirac–Frenkel variational principle, which isolates the optimal dynamics for the core tensors given the TTN ansatz. The dynamics converges to the HEOM when increasing the rank of the core tensors, a limit in which the TTN ansatz becomes exact. We introduce TENSO, tensor equations for non-Markovian structured open systems, as a general-purpose Python code to propagate the TTN-HEOM dynamics. We implement three general propagators for the coupled master equations: two fixed-rank methods that require a constant memory footprint during the dynamics and one adaptive-rank method with a variable memory footprint controlled by the target level of computational error. We exemplify the utility of these methods by simulating a two-level system coupled to a structured bath containing one Drude–Lorentz component and eight Brownian oscillators, which is beyond what can presently be computed using the standard HEOM. Our results show that the TTN-HEOM is capable of simulating both dephasing and relaxation dynamics of driven quantum systems interacting with structured baths, even those of chemical complexity, with an affordable computational cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Semi-Transparent Perovskite Solar Cells in a Stacked Tandem Module: Cooperative Research and Development Final Report, CRADA Number CRD-19-00810

This project seeks to develop device design, materials composition, and processing tools and parameters to fabricate semi-transparent perovskite solar cells and modules for application in stand-alone products or added to other solar cells in a mechanically stacked tandem configuration. This technology presents significant advanced manufacturing challenges and opportunities in getting to scale, including development of perovskite inks, scalable perovskite and heterojunction deposition and annealing processes, heterojunction composition, transparent electrode composition and deposition process, anti-reflection layer composition and deposition process, and cell to module integration processes. Modification 5: The proposed project seeks to develop device design, materials composition, and processing tools and parameters to fabricate semi-transparent perovskite solar cells and modules for application in stand-alone products or added to other solar cells in a mechanically-stacked tandem configuration. This technology presents significant advanced manufacturing challenges and opportunities in getting to scale, including development of perovskite inks, scalable perovskite and heterojunction deposition and annealing processes, heterojunction composition, transparent electrode composition and deposition process, passivation layers including in module scribes, anti-reflection layer composition and deposition process, and cell to module integration processes. Advanced metrology and characterization will be performed on perovskite films, cells and module. Furthermore, we will examine module or materials recycling for circular economy considerations. Modifcation 6: Gigahertz frequency microwave pump-probe spectroscopies are highly sensitive to thin film semiconductor photoconductivity of individual and stacks of layers that comprise perovskite solar cells. As such, these techniques will be used to qualify reproducibility and quality correlations during the manufacturing process. Modification 7: Mechanical adhesion of top contacts within perovskite modules significantly impacts the durability of the module when exposed to accelerated degradation testing. The adhesion between the perovskite/transport layer interface and the transport layer/top contact interface are both very sensitive small changes in processing. ALD processing conditions of the transport layer will be tuned to optimize the mechanical adhesion within the perovskite module stack.

14 SOLAR ENERGY

SENTRA: A Modular Computational Graph Framework for Critical Mineral and Materials Supply Chains: Part I: Network Construction Latent-Quantity Estimation, and Temporal Graph Forecasting

Global supply chains for critical minerals and materials are complex, evolving networks of countries, products, production stages, and trade relationships. Existing analytical approaches are limited by fragmented data and static network representations that do not capture the dynamic production dependencies linking raw materials, intermediate products, and final goods across multiple countries. Trade and production statistics provide only a partial view of domestic production, inventories, and material flows, making it difficult to identify indirect sourcing pathways, hidden dependencies, and embedded foreign exposures. This paper introduces the Supply Chain Exposure Network Tracking and Risk Assessment (SENTRA) framework, a modular graph-based computational framework for constructing, analyzing, and forecasting dynamic supply chain networks. As the first paper in a three-part methodological series, it establishes the computational foundation of SENTRA by constructing a temporal attributed multi-relational graph whose nodes represent product–country pairs and whose edges encode observed trade and within-country value-chain relationships. Statistical estimation and constrained optimization recover latent production, final demand, and product input dependency coefficients while enforcing economic accounting constraints. Graph-derived exposure measures quantify direct, transshipment, value-chain, and multi-hop supply chain dependencies independently of the forecasting model. A temporal graph forecasting architecture based on a relational graph neural network then forecasts the evolution of the graph under mass-balance constraints with distribution-free conformal uncertainty quantification. Validation on the global aluminum supply chain shows that the learned graph representations recover economically meaningful supply chain structure, accurately forecast out-of-sample trade relationships, and produce well-calibrated prediction intervals. Subsequent papers apply this computational foundation to exposure assessment, disruption analysis, and scenario-based policy analysis, and extend the framework to multimaterial supply chain modeling and decision support.

36 MATERIALS SCIENCE

Integrated Neutronics Modeling for Inertial Fusion Energy Systems: Development and Application to LD-FIRST

Lawrence Livermore National Laboratory (LLNL) is proposing a new Laser Driven Fusion Integration Research and Science Test Facility (LD-FIRST) with the goal of providing an experimental testbed for future Inertial Fusion Energy (IFE) systems. However, IFE systems require detailed and accurate multiphysics modeling to quantify material damage, thermal loading, and tritium breeding within complex chamber environments. This article presents the first step in an integrated multiphysics framework that couples meshed CAD-based geometry within Monte Carlo neutronic simulations to enable high-fidelity analysis of IFE chamber concepts, with future coupling to external codes. The neutronics workflow utilizes OpenMC and its third-party capability to use CAD-based geometries through DAGMC and tally on unstructured meshes with Libmesh to evaluate neutron transport behavior, geometric fidelity, and material performance under reactor-relevant conditions. The use of tailored tallies on unstructured meshes in this framework allows direct transfer without interpolating to CFD simulation tools. Two IFE chambers were evaluated, both conceived by LLNL: HYLIFE-II and Laser IFE (LIFE). This work produced high-fidelity conformal surface and volumetric meshes of the HYLIFE-II and LIFE chambers with mapped spatial insight into material damage, thermal loading, and tritium breeding. The HYLIFE-II model was built utilizing available resources and used as a test case to verify that the neutronics framework can handle complex geometries. The LIFE chamber CAD was provided by LLNL and was the main focus of this work. This work analyzes multiple ternary alloy breeding materials for the LIFE chamber, across different 6 Li enrichments to produce data relevant to the LD-FIRST project. This work also investigates the level of model fidelity for the LIFE chamber, and results show that inclusion of detailed first wall and coolant structures increased the predicted tritium breeding ratio (TBR) by ~30%, highlighting the sensitivity of tritium breeding and the need for a high-fidelity simulation framework for IFE chambers. These developments provide a scalable toolset for the design and optimization of next-generation IFE chambers, forming a solid foundation for future coupled multiphysics analysis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Theoretical design and performance of three-dimensional, pillared FeS 2 cathodes

Three-dimensional (3D) electrode design can provide improved capacities and rate capabilities over conventional two-dimensional electrodes by enhancing electrical and ionic transport. Here, expanding upon our previous modeling efforts for conversion chemistry lithium-ion batteries, we develop a pseudo-four-dimensional (P4D) approach that is subsequently used to investigate the design of a pillared FeS 2 electrode. The model considers transport in three dimensions with an additional “fourth” dimension corresponding to the solid-state lithium transport within the active material particles. Additionally, we allow for expansion of the active material during the conversion reaction to understand how internal stresses impact the electrochemical performance of the cell. By optimizing the model with respect to areal capacity, we are able to predict areal capacities up to 16.8 mAh/cm 2 for an areal current density of 1.78 mA/cm 2 and a 103% improvement for the three-dimensional electrodes over planar electrodes of equal volume. Despite the promising results, our simulations suggest that 3D design may be difficult for conversion cathode materials due to the large internal stresses that arise during conversion. Nevertheless, the model is robust and adaptable to other materials that may be more suitable for 3D electrodes due to a lesser change in volume during discharge.

Conversion cathode materials

Challenges in Continuous In-Field Critical Current Testing of High-Temperature Superconducting Tapes: Thermal and Mechanical Perspectives

High-temperature superconductors (HTS) are essential for ultra-high-field applications requiring exceptional current-carrying capacity under extreme conditions. However, systematic characterization of critical current in long-length conductors remains challenging due to complex thermal, electromag netic, and mechanical interactions during continuous testing. This study reports the development of a continuous in-field magnetization testing system for position-dependent critical current measurement in HTS tapes at 20 K under 7.5 T fields applied normal to the tape plane, enabling identification of performance-limiting regions that could compromise magnet stability. Here, the system addresses two fundamental challenges inherent to cryogenic reel to-reel testing. First, thermal management requires continuous cooling of a moving conductor to 20 K, achieved through liquid nitrogen precooling combined with a 100 W@20 K Gifford McMahon cryocooler. Second, screening currents in high fields generate Lorentz forces that induce twisting, bowing, and potential delamination. To mitigate these risks, we propose mechanical reinforcement and active current density suppression strategies. Numerical simulations using the stream function formulation reveal four primary failure modes: frictional heating at guide interfaces, unstable equilibria causing deformation, transverse current-induced stresses at guide transitions, and unsupported forces in vertical spans. Our mitigation strategies include PTFE coated guides to minimize friction, spring-loaded stabilization mechanisms to maintain tape alignment, controlled pre-heating using the liquid nitrogen thermal jacket to suppress critical current at stress points, and optimized guide positioning to minimize force accumulation. The experimental system is nearing completion, with testing planned to commence within two months. Preliminary validation at 65 K under 0.5 T demonstrates strong correlation between simulation-predicted mechanical instabilities and observed critical current variations during conductor tran sitions through the measurement region. These findings establish a robust foundation for quality assurance protocols essential to next-generation superconducting magnet applications.

Chen, Siwei [Princeton Plasma Physics Laboratory (

Investigating the Combustion Performance of Dual Fuel Combustion with Diesel and Port Injected Hydrogen in a Large Bore Locomotive Engine

The heavy-duty transportation sector has primarily relied on conventional diesel combustion engines given their reliability and high thermal efficiency relative to spark ignition engines, but increased focus on reducing greenhouse gas emissions has led to investigation into alternative fuels. Gaseous hydrogen fuel has garnered a great deal of recent interest in the engine community given it has zero carbon, but hydrogen is not available at the scale and cost that petroleum fuels are currently available, and this is a barrier to adoption for industries that are looking to decarbonize their operations. Because of the fuel flexibility provided, dual fuel technology offers a pathway for some industries to adopt hydrogen as a fuel source while maintaining sufficient flexibility in times and locations where the new fuel is not yet available. This computational study investigates dual fuel combustion in a large bore locomotive engine architecture using direct injected diesel and port injected gaseous hydrogen fuel. With an optimal port fuel injection configuration from previous work, simulations of varying substitution ratio, compression ratio, manifold air temperature, diesel injection timing, and diesel injection pressure were performed to understand their effect on combustion performance. Results indicated that both increased substitution ratio and higher intake air temperature accelerates hydrogen flame propagation and can result in high peak cylinder pressures. Additionally, diesel injection timing and injection pressure were demonstrated as effective methods for controlling dual fuel combustion heat release rates.

ODonnell, Patrick Christopher

Order–Disorder Phase Stabilization by Pressure‐Induced Charge Transfer Enhances the Ferroelectric Photovoltaic Effect in Multiferroic BaFe 4 O 7

Abstract Multiferroic ferroelectric photovoltaic (FPV) materials, combining magnetic and ferroelectric properties, are of paramount importance for optoelectronic and photovoltaic applications. However, optimizing both the remanent polarization and the optical bandgap—key factors for enhanced FPV performance—presents a significant challenge due to their trade‐off. This work shows that pressure‐induced charge transfer between different metal sites can break this trade‐off. Above ≈20 GPa, charge transfer between different trivalent iron (Fe) sites in the multiferroic material BaFe 4 O 7 leads to Fe valence disproportionation, FeO 4 tetrahedra disorder, and Jahn–Teller distortion of FeO 6 octahedra. These changes reduce the bandgap, lower resistivity, and enhance ferroelectric polarization, resulting in a 2.5‐fold increase in photocurrent. Upon decompression, BaFe 4 O 7 retains an order–disorder structure, optimal ferroelectric and optical properties at ambient conditions. This work provides a novel pathway to simultaneously optimizing ferroelectricity and bandgap via pressure‐induced charge transfer, overcoming the traditional trade‐off in FPV materials, and offers a promising approach for developing high polarization performance, narrow‐bandgap FPV materials.

Chemistry

Photon–photon chemical thermodynamics of frequency conversion processes in highly multimode systems

Abstract Frequency generation in highly multimode nonlinear optical systems is inherently a complex process, giving rise to an exceedingly convoluted landscape of evolution dynamics. While predicting and controlling the global conversion efficiencies in such nonlinear environments has long been considered impossible, here, we formally address this challenge even in scenarios involving a very large number of spatial modes. By utilizing fundamental notions from optical statistical mechanics, we develop a universal theoretical framework that effectively treats all frequency components as chemical reactants/products, capable of undergoing optical thermodynamic reactions facilitated by a variety of multi-wave mixing effects. These photon–photon reactions are governed by conservation laws that directly determine the optical temperatures and chemical potentials of the ensued chemical equilibria for each frequency species. In this context, we develop a comprehensive stoichiometric model and formally derive an expression that relates the chemical potentials to the optical stoichiometric coefficients, in a manner akin to atomic/molecular chemical reactions. This advancement unlocks new predictive capabilities that can facilitate the optimization of frequency generation in highly multimode photonic arrangements, surpassing the limitations of conventional schemes that rely exclusively on nonlinear optical dynamics. Notably, we identify a universal regime of Rayleigh–Jeans thermalization where an optical reaction at near-zero optical temperatures can promote the complete and entropically irreversible conversion of light to the fundamental mode at a target frequency. Our theoretical results are corroborated by numerical simulations in settings where second-harmonic generation, sum-frequency generation and four-wave mixing processes can manifest.

Optics