Found first: a primary source the press has not covered yet.
Researchers at the University of Bologna and CINECA have derived a four-parameter analytical model for LLM inference energy, finding a 13.0× energy overhead for agentic serving over standard serving and a decline of up to 3.14× in Intelligence per Joule as reasoning budget grows 4×. The paper is The SIMPLE Law for Energy Cost of LLM Inference, posted to arXiv on November 2, 2026.
What the source says
The SIMPLE law separates prefill energy from decode energy and splits decode into KV-cache cost and next-token computation. Hiari Pizzini Cavagna, Andrea Proia, Daniele Cesarini, Zeynep Kiziltan, and Andrea Bartolini validated it across 13 dense LLMs from six model families on NVIDIA H100 GPUs with no per-model calibration, achieving R2=0.969, an MAPE of 11.97%, and 3.1 to 3.5× lower error than prior state-of-the-art. Prefix caching cuts prefill energy by 93% but leaves the KV-cache term unaffected, so cached agentic requests still cost 4.8× more than non-agentic ones. Intelligence per Joule peaks at an intermediate reasoning budget and declines by up to 3.14× as that budget is scaled 4×.
Why it matters
A closed-form formula lets infrastructure teams estimate inference energy from workload parameters without per-model benchmarking. The 13.0× agentic overhead, which falls only to 4.8× with prefix caching applied, sets a concrete floor for the energy cost of multi-turn and tool-calling workloads. The Intelligence per Joule curve shows that extending a model's reasoning budget past a moderate level costs progressively more energy for smaller accuracy gains.