The accelerating energy demands from artificial intelligence (AI) deployment introduce systemic challenges for achieving carbon neutrality. Large language models (LLMs) represent a dominant driver of AI energy consumption, with inference operations constituting 80–90% of total energy usage. Current energy benchmarks report aggregate metrics without domain-level breakdowns, preventing accurate carbon footprint estimation for workloadspecific operations. This study addresses this critical gap by introducing a carbon-aware framework centered on the carbon cost of intelligence (CCI), a novel metric enabling workload-specific energy and carbon calculation that balances accuracy and efficiency across heterogeneous domains. This paper presents a comprehensive cross-domain energy benchmark using the massive multitask language understanding (MMLU) dataset, measuring accuracy and energy consumption in five representative domains: clinical knowledge (medicine), professional accounting (finance), professional law (legal), college computer science (technology), and general knowledge. Empirical analysis of GPT-4 across 100 MMLU questions, 20 per domain, reveals substantive variations: legal queries consume 4.3× more energy than general knowledge queries (222 J vs. 52 J per query), while energy consumption varies by domain due to input length differences. Our analysis demonstrates the evolution from simple ratio-based approaches (weighted accuracy divided by weighted energy) to harmonic mean aggregation, showing that the harmonic mean, by preventing bias from extreme values, provides more accurate carbon usage estimates. The CCI metric, calculated using weighted harmonic mean (analogous to P/E ratios in finance, where A/E represents accuracy-to-energy ratio), enables practitioners to accurately estimate energy and carbon emissions for specific workload mixes (e.g., 80% medicine + 15% general + 5% law). Results demonstrate that the domain workload mix significantly impacts carbon footprint: a law firm workload (60% law) consumes 96% more energy per query than a hospital workload (80% medicine), representing 49% potential savings through workload optimization. Carbon footprint analysis using US Northeast grid intensity (320 gCO₂e/kWh) shows domain-specific emissions ranging from 0.0046–0.0197 gCO₂ per query. CCI is validated through comparison with simple weighted average, demonstrating differences up to 12.1%, confirming that the harmonic mean provides more accurate and conservative carbon estimates essential for carbon reporting and neutrality planning. Our findings provide a novel cross-domain energy benchmark for GPT-4 and establish a practical carbon calculator framework for sustainable AI deployment aligned with carbon neutrality goals.

High-stakes logistics, defined as supply chains where delays, quality loss, or noncompliance have serious human, safety, financial, or geopolitical consequences, are a prominent case of a broader reality: global supply chains are safety-, cost-, and time-critical socio-technical systems where forecasting quality, vendor coordination, and operational decisions shape service levels and stakeholder welfare. At the same time, decarbonization pressures and the growing use of AI for planning and control introduce new risks and trade-offs across energy, computation, and physical logistics. We develop a multi-agent framework that models supply chain system-of-systems dynamics drawing on (1) supply chain decision functions (shipment planning, sourcing and vendor management), (2) national energy-transition conditions that determine grid carbon intensity, and (3) carbon-aware computation accounting for AI-enabled decision support. Methodologically, we combine predictive analytics, unsupervised segmentation, and a carbon-cost-of-intelligence layer in a scenario-based assessment of how national energy-transition profiles–from Norway to India–affect the intensity of AI compute carbon, meaning the carbon emissions generated by the hardware and data centers required to train and run AI models. We introduce the carbon-adjusted supply chain performance (CASP) metric that integrates physical transport carbon, cold-chain overhead where applicable, and AI compute carbon into a per-package-type performance measure. Our analysis yields three actionable outputs for systems engineering and environmental management: carbon, service, and cost trade-off frontiers; governance levers (sourcing portfolio rules, buffers, and compute policies); and system-level early-warning indicators for disruption amplification. This study implements a tool-augmented multi-agent system (orchestrator, risk, and sourcing agents) using AWS bedrock and strands agents, where LLM-based agents orchestrate deterministic analytical engines through structured tool interfaces with adaptive query generation. Theoretically, we extend previous systems-of-systems and sustainable supply chain findings by formalizing package-type-specific carbon–service frontiers and by embedding AI compute carbon into a socio-technical resilience framework. Practically, the CASP benchmark, governance lever analysis, and multi-agent implementation provide decision-makers with concrete tools to compare carriers, routes, and compute strategies across countries while making transparent the trade-offs between service reliability and total carbon.

In both experimental and theoretical analyses of data, we often look to select a set of simple components that can be combined to create an appropriate model for the data. A convenient way to do this is to use quantile functions that can be added or transformed to obtain new distributions. In this work, we connect quantile statistics and mean absolute deviations (MADs) by deriving a general class of MAD-based shape metrics expressed as integrals of the quantile function, with a direct geometric interpretation. Our approach is applicable to distributions with finite mean that include many of the commonly used distributions, including those without a variance, such as the Pareto. When simple midpoint quadrature is used, the proposed metrics recover widely used quantile-shape metrics, including the interquartile range, Galton skewness, and Moore’s octile kurtosis as special cases. We further propose a C-Trapezoid quadrature approximation that combines cubic polynomial endpoint extrapolation with trapezoidal integration, achieving approximation errors that are significantly lower than those of the midpoint approximation for many common distributions. The proposed approximation provides simple-to-compute formulas for shape analysis and yields closed-form, non-iterative parameter-estimation formulas. These formulas are easy to compute and interpret, and they are applicable to a wide class of distributions, including those without an explicit cumulative distribution function or some with heavy tails. Unlike maximum likelihood estimation, the proposed method is more robust and has simple geometric interpretation. We illustrate the methodology with two detailed case studies. The proposed approach gives a simple way to quickly assess distributional shape without any specialized tools.

Grid carbon intensity varies hour to hour, so a load that must finish by a deadline but not at a specific hour, such as electric-vehicle charging, heat-pump operation, or batch computation, can be shifted to a cleaner time at no cost to delivered energy. We present a transparent, fully reproducible pipeline that derives hourly, lifecycle-based grid carbon intensity for ISO New England from public fuel-mix data and documented emission factors, and that computes the exact minimum-carbon schedule for real deferrable loads: mixed-integer optimization is used where a shared per-hour allocation budget binds, and a provably optimal greedy placement where it does not. Over the full 2019 ISO New England year, hourly carbon intensity ranges from 116.7 to 389.4 gCO₂/kWh; in an idealized re-timing benchmark that holds delivered electrical energy fixed and does not model building thermal dynamics or comfort bounds, carbon-aware shifting of a residential heat-pump load avoids 8.29% of its average-basis emissions under a shifted-load allocation budget of three times its median active load (12.70% without one; 12.19% when, instead, total hourly draw is held within the building’s observed peak). The attainable saving is set primarily by two operational quantities we characterize, deadline slack and the shared allocation budget, and it is strongly seasonal, ranging from roughly 10% in the milder shoulder seasons to about 3.1% in January, where the limit is the allocation budget rather than a shortage of clean hours: January’s ceiling without an allocation budget is the highest of any month. It is robust across buildings and to the least certain emission factor (between 5.57% and 7.70%). In our experiments, a weather-blind climatology forecast retains about 88% of the savings without an allocation budget and 91.5% of the savings under the allocation budget.

Large-scale artificial intelligence systems increasingly disclose energy and carbon metrics, but their freshwater costs remain less consistently measured. This paper introduces the Water Cost of Intelligence (WCI), a per-query metric combining direct water consumed for on-site data-center cooling with indirect water consumed during electricity generation, weighted by local scarcity using Aqueduct 4.0 Baseline Water Stress (BWS) scores. We first reconstruct Google’s disclosed Gemini direct-water figure from Google’s own reported parameters, an internal consistency check on the implementation rather than an independent validation. Expanding the accounting boundary to include electricity-generation water raises the estimate for a median large language model (LLM) prompt by 179% under a uniform national water-intensity value. Parameterizing that intensity by the regional generation mix instead changes the estimate substantially and reverses the regional ordering, depending on whether hydroelectric reservoir evaporation is allocated to generation: the same grid is the least water-intensive of those studied under one convention and the most water-intensive under the other. A region cannot be characterized as water-efficient in terms of electricity without first establishing that convention. Direct-only reporting can be internally accurate yet boundary-incomplete, and regional scarcity can change the interpretation of identical physical water use by an order of magnitude.