The Energy Cost of Tokens (Photons = Tokens)

Every other cost lever in this topic — GPU-hours, HBM bandwidth, memory vintage — sits downstream of one physical input the KB had, until this compile, no source for: electricity. The topic's frontier tracked a named hole — "no energy / power-cost pass-through leg" — because it held web-literature figures (~5×10⁻⁴ Wh/token, reasoning-mode 5–12×, ~$254/mo electricity per H100) but nothing that connected energy to tokens inside a source. Photons = Tokens (Litowitz, Polson & Sokolov, arXiv 2603.06630, 2026-02-23) fills the leg — partly — by treating the token as a physical quantity with a measurable thermodynamic cost and building a supply/demand balance sheet for global token production.

It is filed early stage, and the read-depth is honest: abstract-grade, single preprint, not peer-reviewed, and the figures are explicitly order-of-magnitude policy-framing estimates, not a measured per-SKU cost series. What it changes is that the topic now has an energy→token bridge inside a citable source, and a clear statement of where the physical floor beneath the price sits.

The method — arithmetic, not rhetoric

The paper's stated move is to apply MacKay's (2009) Sustainable Energy — Without the Hot Air method (reframe an energy debate as arithmetic) to AI computation. It defines the token — the elementary unit of LLM input/output — as a physical quantity bounded from two directions:

• A thermodynamic floor via Landauer's principle — irreversible bit operations have a minimum energy cost set by temperature (kT ln 2 per erased bit).
• An information ceiling via Shannon's channel capacity — the maximum information a channel can carry.

Between those bounds, plus current infrastructure data, it constructs a supply-and-demand balance sheet for global token production, and from it derives a "finite question budget": the number of meaningful queries humanity can direct at AI systems under physical, information-theoretic, and economic constraints.

The numbers — the energy → token bridge

All three figures are the paper's own, at current efficiency, order-of-magnitude:

• 326 TWh — the projected 2028 US AI energy allocation — could support
• ≈ 6.5×10¹⁷ tokens per year, or
• ≈ 225,000 tokens per person per day — the per-capita token budget that energy allocation implies —
• > 3 orders of magnitude above estimated mid-2024 utilization.

The moral the paper draws (the contrarian teaching point): at projected 2028 US energy, token volume is abundant, not scarce. Energy is therefore not the near-term binding constraint on how many tokens can be produced. The paper relocates the true scarcity from capacity to direction — "the decisive variable is not how many questions can be answered but which questions are worth asking," a problem of agency that computation alone cannot solve. That is a direct answer to anyone who models the AI economy as energy-gated in the near term: on these numbers, it is demand-worthiness-gated, not supply-gated.

DERIVED (desk, flagged as NOT an independent confirmation). The implied efficiency behind the bridge is 326 TWh ÷ 6.5×10¹⁷ ≈ 5.0×10⁻⁴ Wh/token — which lands exactly on the bottom-up ~5×10⁻⁴ Wh/token web-literature figure the frontier gap already logged. Read this as a consistency check on the units, not as two independent measurements agreeing: the top-down figure was almost certainly built from that per-token efficiency, so the agreement is definitional, not corroborative. The honest statement is that the top-down (TWh → token-count) and bottom-up (Wh/token) framings are the same coin.

What it closes, and what it does not

Closes: the KB now holds an energy source and an energy→token volume bridge — the "no energy leg ingested" half of the frontier gap.

Does not close: this is a top-down TWh → token-count basis, not a bottom-up $/kWh → $/token per-SKU cost pass-through. The paper prices energy against token volume, not token dollars. So it bounds the pass-through leg only loosely — if energy is abundant relative to token demand, the electricity term is unlikely to be the binding variable in near-term $/token — but it does not give a measured $/kWh → $/token conversion, and it does not touch the reasoning-mode 5–12× energy multiplier that the same web literature flags (reasoning workloads are the growing share, and "Photons = Tokens" is a single-rate abstraction that averages over them). That measured $/token energy conversion, and a peer-reviewed energy source (a Joule/Cell paper was 403'd on 2026-07-23 and has not been retried — see frontier.md), remain owed.

Where it sits against the rest of the topic

• It is the energy analog of Matsuoka's $/PB unit (the cost-measurement problem). Matsuoka reframes decode cost in bandwidth delivered; Photons = Tokens reframes it in power delivered. Both are attempts to price the token in a model-agnostic physical unit rather than a billing convention. The value chain the paper maps — photon → atom → chip → power → token → question — is the same stack the depreciation/memory story runs on, read from the energy end.
• It puts a physical floor under the price series. The price-decline distribution measures how fast the price of a token falls; this page says the thermodynamic cost has a Landauer floor and the volume has an energy ceiling — the price can keep falling toward, but not below, the physical floor.
• It is a volume/abundance claim, which is the mirror image of the depreciation conveyor's cost-structure claim: one says tokens are physically cheap and abundant, the other says incumbents stay structurally cheaper than entrants. Both can hold at once — abundant tokens with a durable incumbent cost edge.
• It applies Coase's theory of the firm and the durable-goods-monopoly problem to locate where economic rent concentrates in that chain, and connects measurement limits to a Goodhart's-law / Heisenberg parallel and to Arrow's impossibility result for efficient information pricing — theory-driven, not empirical, and recorded as such.

See also — sibling rungs (context, not this rung's evidence)

Added 2026-09-24. The energy rung has taken in three sources since this page was written, and they sharpen a tension this page should state out loud rather than leave for a reader to find.

The tension: energy is abundant in total, but power is scarce at the plug. Photons = Tokens says the quantity of electricity is not the near-term limit on how many tokens can be made. The energy rung's evidence is about something different — getting power delivered to a specific site on time — and there the constraint is real and dated:

• EIA, September 2026 outlook (2026-09-09): record US generation of 4,368 billion kWh in 2026 (+2.2%) and a further +1.7% in 2027, with data-centre build the largest regional driver — raw. Supply of energy is growing.
• ERCOT market notice (2026-08-03): Texas paused the processing of large data-centre loads, missing its own interconnection deadline — raw. Delivery of power to new sites is being rationed politically.
• A 7 GW US gap between announced and under-construction AI data-centre capacity (Q1 2026, analysis-grade) — raw.
• The rung's concept page: Power: the binding constraint.

Both can be true at once: plenty of kilowatt-hours nationally, too few energised megawatts where the GPUs are. For the price of a token, that means the electricity bill is probably not the binding term, but the delay in getting power connected feeds the capacity shortage that keeps list prices sticky (see the serving rung's Epoch capacity model). None of these sources gives a $/kWh-to-$/token conversion either; that gap is unchanged.

Key Claims

• The token is a physical quantity with a measurable thermodynamic cost — a Landauer floor (min energy per irreversible bit op) and a Shannon information ceiling. Evidence: strong as a framework (first-principles physics); its application to real serving is the modelled part (Photons = Tokens)
• The projected 2028 US AI energy allocation of 326 TWh could support ≈ 6.5×10¹⁷ tokens/year ≈ 225,000 tokens/person/day at current efficiency — > 3 orders of magnitude above mid-2024 utilization. Evidence: moderate — the paper's own order-of-magnitude estimate, abstract-grade, single preprint; "at current efficiency" is load-bearing and unstated in the abstract beyond the ~5×10⁻⁴ Wh/token implied rate (Photons = Tokens)
• On these numbers, energy is NOT the near-term binding constraint on token volume; the binding constraint is which questions are worth asking (direction, not capacity). Evidence: moderate as a framing conclusion (follows from the balance sheet; a policy argument, not a measurement) (Photons = Tokens)
• The paper supplies a top-down TWh → token-count basis, NOT a bottom-up $/kWh → $/token per-SKU cost pass-through. Evidence: strong (directly observable in what was read — the estimates are token-volume, not token-dollars) (Photons = Tokens)
• "Photons = tokens" is a single-rate modelling abstraction; real serving efficiency varies by model/hardware/workload, with reasoning-mode drawing 5–12× more. Evidence: the abstraction is stated by the paper; the 5–12× multiplier is web-literature the frontier gap logs, not a Photons = Tokens measurement (Photons = Tokens)
• DERIVED (desk, not independent): 326 TWh ÷ 6.5×10¹⁷ ≈ 5.0×10⁻⁴ Wh/token, matching the bottom-up web-literature per-token energy figure — a units consistency check, not two measurements agreeing. Evidence: derived arithmetic over the paper's own figures; the agreement is definitional, likely because the per-token rate is the paper's input

Benchmarks & Data

All figures are the paper's own order-of-magnitude estimates at "current efficiency," as of the 2026-02-23 preprint. None is a measured per-SKU cost.

Quantity	Value	As of	Nature	Source
Projected 2028 US AI energy allocation	326 TWh	2028 (projected)	projection (paper input)	Photons = Tokens
Tokens/year that supports (current efficiency)	≈ 6.5×10¹⁷	2026-02-23	modelled (order-of-magnitude)	Photons = Tokens
Per-capita token budget	≈ 225,000 tokens/person/day	2026-02-23	modelled (order-of-magnitude)	Photons = Tokens
Headroom vs mid-2024 utilization	> 3 orders of magnitude	2026-02-23	modelled comparison	Photons = Tokens
Implied per-token energy (DERIVED)	≈ 5.0×10⁻⁴ Wh/token	2026-02-23	derived (= paper input; not independent)	desk, over Photons = Tokens
$/kWh → $/token pass-through	[GAP — still none in KB]	—	—	—

Open Questions

• What is the bottom-up $/kWh → $/token conversion for a real 2026 SKU? This page gives energy→token volume; the topic still has no measured dollar energy cost per token. The web literature has the pieces (~5×10⁻⁴ Wh/token × a $/kWh datacenter power price) but no ingested source does the multiply.
• How does the reasoning-mode 5–12× energy multiplier change the budget? The 225k/person/day figure is a single-rate average; if the token mix shifts to reasoning-heavy workloads (the growing share), the effective per-capita budget shrinks materially, and the "energy is abundant" conclusion weakens.
• Is the 326 TWh → 6.5×10¹⁷ chain robust to its efficiency assumption? The whole bridge rests on ~5×10⁻⁴ Wh/token; a 2–3× shift in serving efficiency (either direction) moves the token budget proportionally. The abstract does not disclose the efficiency-improvement path assumed to 2028.
• Does the "direction, not capacity" conclusion survive a peer-reviewed energy source? The one directly on-thesis peer-reviewed paper (Joule/Cell) was blocked on 2026-07-23 and has not been retried; until it is read, the abundance claim rests on a single preprint.

Related Concepts

• The Cost-Measurement Problem — this page is the energy physical unit (power → token); that page holds Matsuoka's bandwidth physical unit ($/PB, bandwidth → token). Both reject the per-token billing convention as the true cost unit.
• The Depreciation Conveyor & Vintage Economics — the value chain "photon → atom → chip → power → token" is the same stack the memory/vintage cost story runs on, read from the energy end; abundant tokens and a durable incumbent cost edge can coexist.
• The Price-Decline Distribution — the price of a token falls fast; this page puts the thermodynamic floor under how far it can fall.
• Inference Cost as a Macro Input — the ICPC prices inference cost into the macro price level via a composite that already includes an electricity term; this page is the physical grounding for that electricity term.

Backlinks

Pages that reference this concept:

• Cost Per Task (Cost-of-Pass)

Changelog

• 2026-09-24 (recompile, no new source) — Added dated energy-rung context: record US generation (EIA, 2026-09-09) against a Texas interconnection pause (ERCOT, 2026-08-03) — energy abundant in total, power scarce at the site — recorded as a tension with this page's "energy is not binding" reading, not a contradiction. Fixed the depreciation-conveyor links (the page lives on capital-structure); set frontier_status to a valid value; dated the Joule retry note.
• 2026-07-24 — Created from the newly compiled Photons = Tokens preprint (arXiv 2603.06630, abstract-grade). Fills the frontier's "no energy pass-through leg" gap partly: supplies a top-down energy→token volume bridge (326 TWh → ≈6.5×10¹⁷ tokens/yr → ≈225,000 tokens/person/day, >3 OOM above mid-2024), and the contrarian moral that energy is not the near-term binding constraint on token volume — direction is. Records what it does NOT close: a bottom-up $/kWh → $/token per-SKU cost, and the reasoning-mode 5–12× multiplier. Single preprint, not peer-reviewed, order-of-magnitude policy-framing figures throughout.