{
  "id": "oai:papers.qnfo.org:jpcub-llm-energy",
  "slug": "jpcub-llm-energy",
  "title": "Joules-per-Solution for Stochastic and Agentic Inference: Benchmarking Frontier and Agentic LLMs Against the Human Brain",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "The joules-per-solution (J/S) metric, introduced in JPCUB P0 as a universal, physics-grounded measure of computational efficiency, assumed deterministic solvers: one run yields one solution. Large language models (LLMs) violate that assumption twice over: they are stochastic samplers whose outputs must be verified, and agentic systems execute graphs of sub-queries whose total token budget dwarfs a single inference. This paper extends J/S to stochastic and agentic inference. We define the closed-form stochastic correction J/S_τ(n) = n E_q / (1-(1-p_q(τ))^n), prove that — at fixed per-query energy — it is monotonically increasing in the sampling regime n (so single-shot sampling is the joules-per-solution-efficient operating point, and sampling buys accuracy at strictly increasing energy per correct solution), show that interior minima arise only through batching efficiency, and show that the J/S of agentic tasks must charge the full orchestration graph, including failed attempts. Using published measurement data (TokenPowerBench; Where Do the Joules Go?), we derive order-of-magnitude task-stratified estimates and compare them to the human brain baseline (≈ 20 W resting brain power). Result: on cheap single-shot tasks a frontier LLM is roughly one order of magnitude more energy-efficient than a human expert; on graduate-level reasoning the two substrates meet at parity (∼ 10⁴ J per correct solution); and under self-consistency sampling or agentic orchestration the LLM is frequently less efficient. We argue the efficiency crossover is governed by task verifiability, accuracy, and token budget — not by intrinsic substrate advantage — and pre-register falsification conditions and a calibration register for independent measurement.",
  "abstract_markdown": "The joules-per-solution (J/S) metric, introduced in JPCUB P0 as a universal, physics-grounded measure of computational efficiency, assumed deterministic solvers: one run yields one solution. Large language models (LLMs) violate that assumption twice over: they are stochastic samplers whose outputs must be verified, and agentic systems execute graphs of sub-queries whose total token budget dwarfs a single inference. This paper extends J/S to stochastic and agentic inference. We define the closed-form stochastic correction $J/S_{\\tau}(n) = n\\,E_{q}\\,/\\,(1-(1-p_{q}(\\tau))^{n})$, prove that — at fixed per-query energy — it is monotonically increasing in the sampling regime $n$ (so single-shot sampling is the joules-per-solution-efficient operating point, and sampling buys accuracy at strictly increasing energy per correct solution), show that interior minima arise only through batching efficiency, and show that the J/S of agentic tasks must charge the full orchestration graph, including failed attempts. Using published measurement data (TokenPowerBench; Where Do the Joules Go?), we derive order-of-magnitude task-stratified estimates and compare them to the human brain baseline ($\\approx 20$ W resting brain power). Result: on cheap single-shot tasks a frontier LLM is roughly one order of magnitude more energy-efficient than a human expert; on graduate-level reasoning the two substrates meet at parity ($\\sim 10^{4}$ J per correct solution); and under self-consistency sampling or agentic orchestration the LLM is frequently less efficient. We argue the efficiency crossover is governed by task verifiability, accuracy, and token budget — not by intrinsic substrate advantage — and pre-register falsification conditions and a calibration register for independent measurement.",
  "date": "2026-08-15",
  "first_published": "2026-08-15",
  "last_revised": "2026-08-15T00:00:00Z",
  "modified": "2026-08-15T00:00:00Z",
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  "url": "https://papers.qnfo.org/papers/jpcub-llm-energy",
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    "creators": [
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Joules-per-Solution for Stochastic and Agentic Inference: Benchmarking Frontier and Agentic LLMs Against the Human Brain"
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    "publicationYear": "2026",
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        "description": "The joules-per-solution (J/S) metric, introduced in JPCUB P0 as a universal, physics-grounded measure of computational efficiency, assumed deterministic solvers: one run yields one solution. Large language models (LLMs) violate that assumption twice over: they are stochastic samplers whose outputs must be verified, and agentic systems execute graphs of sub-queries whose total token budget dwarfs a single inference. This paper extends J/S to stochastic and agentic inference. We define the closed-form stochastic correction J/S_τ(n) = n E_q / (1-(1-p_q(τ))^n), prove that — at fixed per-query energy — it is monotonically increasing in the sampling regime n (so single-shot sampling is the joules-per-solution-efficient operating point, and sampling buys accuracy at strictly increasing energy per correct solution), show that interior minima arise only through batching efficiency, and show that the J/S of agentic tasks must charge the full orchestration graph, including failed attempts. Using published measurement data (TokenPowerBench; Where Do the Joules Go?), we derive order-of-magnitude task-stratified estimates and compare them to the human brain baseline (≈ 20 W resting brain power). Result: on cheap single-shot tasks a frontier LLM is roughly one order of magnitude more energy-efficient than a human expert; on graduate-level reasoning the two substrates meet at parity (∼ 10⁴ J per correct solution); and under self-consistency sampling or agentic orchestration the LLM is frequently less efficient. We argue the efficiency crossover is governed by task verifiability, accuracy, and token budget — not by intrinsic substrate advantage — and pre-register falsification conditions and a calibration register for independent measurement.",
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