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Koomey's law

The empirical trajectory by which computations delivered per joule dissipated have doubled about every 1.57 years (slowing to ~2.6 after Dennard scaling broke in 2005), tracking the energy cost of a logical operation toward the Landauer floor.

Core Idea

Koomey's law is the empirical observation, first published by Jonathan Koomey in 2010, that the number of computations delivered per joule of energy dissipated has doubled approximately every 1.57 years from the mid-1940s through roughly 2000, slowing to a doubling time of about 2.6 years as Dennard scaling broke down around 2005. Where Moore's law tracks transistor density per unit area, Koomey's law tracks the energy cost of a logical operation, and so describes a distinct axis of semiconductor progress: not how many transistors fit on a chip but how cheaply each switching event can be performed. The mechanism during the Dennard-scaling era was the combination of feature shrinkage (smaller transistors switch at lower voltages and capacitances, reducing energy per operation as roughly the square of the voltage) and architectural improvements (pipelining, caching, and microarchitectural efficiency each extract more useful work per joule). When Dennard scaling ended — supply voltages stopped falling as leakage currents at sub-100nm nodes made further reduction impractical — the primary mechanism shifted to architectural specialization, parallelism, and dark-silicon management rather than per-transistor voltage reduction, lengthening the doubling time. The trend has a hard physical floor: Landauer's principle sets the minimum energy for an irreversible bit erasure at kT ln 2 (approximately 2.8 × 10⁻²¹ joules at room temperature), and the extrapolated trajectory would approach this limit around 2050–2100 depending on which doubling time is assumed. Koomey's law governs the feasibility boundary for battery-limited computing — mobile phones, wearables, embedded sensors, hearing-aid neural networks, edge inference — because in those applications the binding constraint is not transistor count but joules available from the power source: a workload becomes deployable when energy-per-operation falls below the ratio of battery capacity to required operations.

Structural Signature

Sig role-phrases:

  • the efficiency metric — computations delivered per joule dissipated, the energy cost of one logical operation isolated from raw count and speed
  • the exponential trend — that metric doubling on a roughly fixed doubling time across decades of semiconductor progress
  • the supplying mechanism — feature shrinkage plus voltage scaling (Dennard era) then architectural specialization, parallelism, and dark-silicon management (after)
  • the regime break — the ~2005 end of Dennard scaling, where the doubling time lengthens (~1.57 → ~2.6 years) and a projection must select the live slope
  • the thermodynamic floor — Landauer's kT ln 2 per irreversible bit erasure, the hard bound at which the trend must asymptote rather than continue
  • the feasibility envelope — the product categories (mobile, wearable, sensor-scale, edge inference) that open as the metric crosses each one's battery-capacity-over-required-operations threshold
  • the workload coupling — the demand trend whose race against the efficiency curve sets whether aggregate computing energy consumption rises or falls

What It Is Not

  • Not Moore's law restated. Moore's law tracks transistors per unit area; Koomey's law tracks joules per logical operation. The two ran together for decades because the same feature shrinkage fed both, but they are distinct axes — density can stall while energy-per-operation keeps falling, and reading one off the other conflates how many switches a chip holds with how cheaply each one fires.
  • Not a law of physics. It is a fitted exponential to six decades of measured data, not a derived necessity. Nothing in nature requires efficiency to double on any schedule; the regularity held because particular mechanisms (Dennard voltage scaling, then architectural specialization) happened to supply the gains, and it visibly bent when one of them quit around 2005. The only genuinely physical element is the Landauer floor, not the slope above it.
  • Not an exact forecast. The doubling time is a smoothed average over a noisy historical series, so projecting it forward yields a range, not a date — which is why the Landauer-limit crossing is quoted loosely as ~2050 versus ~2080–2100 depending on which slope is assumed. The curve says roughly when a product class becomes feasible, not the precise year any chip will hit a given joules-per-operation figure.
  • Not a causal mechanism. The trend describes that efficiency improved; it does not explain why, and it supplies no engineering recipe. The causes are the underlying mechanisms (feature shrinkage, voltage scaling, pipelining, dark-silicon management); Koomey's law is the aggregate fingerprint they leave, and treating the trend itself as the cause inverts the relationship.
  • Not a sign that today's chips are near the thermodynamic floor. Current CMOS operates orders of magnitude above Landauer's kT ln 2; the floor bounds the eventual asymptote, decades out, not present-day designs. The headroom between today's energy-per-operation and the floor is precisely the total gain still available — large, not nearly exhausted.
  • Not "computers getting faster." Speed and throughput live on the count-and-speed axis (clocks, FLOPS). Koomey's law is silent on them: a chip can deliver the same operations per second while drawing far less power, which is improvement on the energy axis with no change in speed at all.

Scope of Application

Koomey's law lives entirely within computing — across the hardware, infrastructure, and systems subfields where the energy cost of a logical operation is the design variable — and its reach is bounded there; the loose "a Koomey's law for X" invocations elsewhere are analogy carried by exponential_growth and learning_curve_effects, not the law itself.

  • Semiconductor roadmapping — the curve is read forward to set per-generation efficiency targets; the ITRS, and the post-2017 IRDS that elevated energy-per-operation to a headline metric, treat the trend line as a planning constraint.
  • Data-center and IT-infrastructure planning — the efficiency trend, coupled to a workload-growth trend, underwrites the historical near-constancy of aggregate IT electricity demand and flags when workload growth outruns the slower post-Dennard slope so total demand must climb.
  • Mobile, wearable, and embedded design — the feasibility-threshold move applies directly: a product class ships once energy-per-operation drops below the ratio of battery capacity to required operations, only the battery and operation count changing across phones, watches, hearing-aid neural nets, and sensors.
  • AI cost-of-training and edge-inference projection — the applicable doubling time bounds how cheap a given FLOP can become and dates when a model class becomes deployable at watt-scale power.
  • Computer-architecture analysis — supplies the orthogonal energy-per-operation axis on which a stalled-clock or flattening-density era can still be improving by orders of magnitude, separating "stopped getting faster" from "stopped getting more efficient."
  • ICT environmental policy — frames arguments over whether computing's energy footprint saturates or explodes, by racing the efficiency curve against compute-demand growth toward the thermodynamic floor (Landauer's kT ln 2).

Clarity

Naming Koomey's law separates a quantity that raw benchmark numbers keep fused: how much computing a chip delivers versus how cheaply per joule it delivers it. Performance figures — clock speed, FLOPS, transistor count — all sit on the count-and-speed axis, and against them an era of stalled clocks or flattening Moore's-law density looks like progress grinding to a halt. Koomey's law gives the analyst the orthogonal axis, energy per useful operation, on which that same era can still be improving by orders of magnitude. The sharp question it licenses is no longer "are computers getting faster?" but "are they doing more work per joule, and on what doubling time?" — which is the question that actually decides whether a battery-limited product class is buildable.

That second axis carries its own structure once it is named. It makes the regime break of 2005 legible as a slope change in efficiency specifically — the moment Dennard scaling stopped supplying per-transistor voltage reduction and the doubling time lengthened — rather than as undifferentiated "Moore's-law slowdown," and it locates the trajectory against a thermodynamic floor (Landauer's kT ln 2) rather than the lithographic and economic ceilings Moore's law runs into. The practitioner can thus reason about a feasibility envelope the count metric cannot express: a workload becomes deployable precisely when energy-per-operation drops below the ratio of available battery capacity to required operations, so a falling efficiency curve and a known floor together say when edge inference, wearables, or sensor-scale neural nets cross from impossible to shippable.

Manages Complexity

The thing a hardware analyst would otherwise have to reason through, case by case, is the full stack of what makes a battery-powered computing product feasible: the process node and its leakage behavior, the supply-voltage schedule, the microarchitecture's pipelining and caching, the packaging and cooling, the workload's instruction mix, and the battery chemistry — a sprawl of interacting variables across six decades of semiconductor history, each generation re-tuning the trade-offs. Koomey's law collapses the energy-relevant portion of that sprawl into a single exponential regularity in one observable, computations per joule, summarized by just two scalars: the current energy-per-operation and the current doubling time. Instead of re-deriving, for each prospective device, whether the silicon can do the required work inside the available power budget, the analyst tracks those two numbers, projects the efficiency curve forward, and reads off the qualitative answer — feasible now, feasible in N doubling-times, or never — directly from where the curve crosses the threshold set by the ratio of battery capacity to required operations.

The compression has a branch structure the analyst can read without re-deriving the physics. The trajectory carries a known regime break at roughly 2005, when Dennard scaling ended and the doubling time lengthened from about 1.57 to about 2.6 years, so a projection must select the relevant slope rather than extrapolate one rate across the break — the difference that moves the Landauer-limit crossing from around 2050 to around 2080–2100. And it carries a hard floor: Landauer's kT ln 2, below which irreversible operations cannot go, which tells the analyst when the curve must asymptote rather than continue. The whole question "when does this product class cross from impossible to shippable?" — which on the raw-benchmark axis is buried in undifferentiated talk of Moore's-law slowdown — reduces to locating a workload's threshold between the current efficiency point and the thermodynamic floor, on whichever post-break slope applies. The high-dimensional feasibility problem becomes a one-dimensional reading along a single curve with two slopes and a fixed endpoint.

Abstract Reasoning

Koomey's law licenses a tight family of reasoning moves on the energy axis of computing, all keyed to two numbers — the current energy-per-operation and the applicable doubling time — and a fixed thermodynamic floor.

Feasibility forecasting (predictive): Given a battery capacity and a workload's required operations, the deployability threshold is the energy-per-operation at which battery_joules / required_operations is met; the analyst reads off from the curve how many doubling-times separate today's efficiency point from that threshold, converting "is this product class buildable?" into a date. The move runs FROM a known efficiency point and slope TO a viability year for an entire category — smartphones, smartwatches, hearing-aid neural nets, sensor-scale edge inference each cross from impossible to shippable when the falling curve passes their threshold. The same move runs backward: a device that exists at watt-scale power today implies the efficiency frontier has already crossed its operational threshold, dating when the category became possible.

Slope-selection and regime diagnosis (diagnostic): Because the trajectory carries a regime break at ~2005, any projection must first ask which slope is live — the ~1.57-year Dennard-era doubling or the ~2.6-year post-Dennard one — and choosing wrong moves the Landauer-limit crossing by decades (~2050 versus ~2080–2100). Conversely, observing the realized doubling time of a recent process generation diagnoses which mechanism is supplying the gains: a doubling time near 1.57 years would signal per-transistor voltage reduction is still operating, while the observed lengthening toward 2.6 years is the fingerprint of Dennard scaling's end and the shift to architectural specialization, parallelism, and dark-silicon management. The move reasons FROM an observed slope change TO the underlying physical cause.

Axis-decomposition (diagnostic/boundary-drawing): Confronted with an era of stalled clocks or flattening transistor density, the move is to decline reading stagnation off the count-and-speed axis and instead test the orthogonal energy-per-operation axis, where the same era may still be improving by orders of magnitude. This separates "computers stopped getting faster" (a count-axis claim) from "computers stopped getting more efficient" (a Koomey-axis claim) — two failures with different causes, different floors, and different remedies, that raw benchmarks fuse.

Floor-bounded extrapolation (boundary-drawing): Unlike Moore's law, which runs into lithographic and economic ceilings whose exact location is contestable, Koomey's law has a thermodynamic floor — Landauer's kT ln 2 ≈ 2.8 × 10⁻²¹ J per irreversible bit erasure — that no irreversible operation can cross. The move bounds any forward projection: the curve must asymptote toward the floor rather than continue exponentially, so a forecast that carries the trend past Landauer's bound is invalid on its face, and the only escape route is a substrate change (reversible or quantum computing) that voids the irreversibility premise. The floor also sets the maximum total gain still available — the ratio of today's energy-per-operation to kT ln 2 — capping how much further the entire trajectory can run.

Aggregate-consumption inference (interventionist/predictive): Coupling the efficiency trend to a workload-growth trend predicts whether total computing energy demand rises or falls — the move that underwrites the historical near-constancy of IT electricity demand despite explosive compute growth (efficiency gains roughly offsetting workload growth), and that flags when workload growth outruns the (now slower, post-Dennard) efficiency curve so aggregate demand must climb. The intervention lever is explicit: accelerating energy-per-operation gains (or holding workload growth down) is what keeps the aggregate flat, and the lengthened post-2005 doubling time is precisely why that balance is harder to maintain now than before.

Knowledge Transfer

Within computing, Koomey's law transfers as a working trend-line wherever the energy axis of silicon is the binding constraint, and the transfer is mechanistic in the sense that what carries is a real, measured regularity in one observable — computations per joule — together with the diagnostics built on it. In semiconductor roadmapping (ITRS, and the post-2017 IRDS that elevated energy-per-operation to a headline metric) the curve is read forward to set efficiency targets a process generation must hit. In data-center and IT-infrastructure planning the same efficiency trend, coupled to a workload-growth trend, is what underwrites the historical near-constancy of aggregate IT electricity demand despite explosive compute growth, and flags when workload growth outruns the now-slower post-Dennard slope so total demand must climb. In mobile, wearable, and embedded design the feasibility-threshold move (a product class ships when energy-per-operation drops below battery_joules / required_operations) applies directly, only the battery capacity and operation count changing. In AI cost-of-training and edge-inference projection the applicable doubling time bounds how cheap a given FLOP can become and dates when a model class becomes deployable at watt-scale power. Across all of these the substrate is the same — logical operations on CMOS-and-successor hardware — the floor is the same thermodynamic bound (Landauer's kT ln 2), and the slope-selection discipline around the ~2005 Dennard break carries intact. The vocabulary travels because the referent does not change: energy-per-operation, doubling time, and the Landauer floor mean the same thing in every one of these subfields.

Beyond computing the transfer is of two distinct kinds, and they should be kept apart. The honest case for most cross-domain invocations is analogy: speaking of "a Koomey's law" for the falling cost-per-unit of some non-computing technology renames the components (joules → dollars or watts of some other resource, logical operations → the relevant output unit) and borrows the shape — an exponential efficiency trend bending toward a hard limit — while dropping the specific machinery (Dennard voltage scaling, dark-silicon management, the thermodynamic irreversibility bound) that gives the original its predictive force and its particular floor. That use is illuminating but is pattern-by-resemblance, not the law travelling. The more precise statement is that the genuinely portable content was never Koomey-specific to begin with: the skeleton "an efficiency metric improves exponentially toward a physical floor, on a slope that can break, capping total available gain" is already carried in substrate-neutral form by the primes this law instantiates — exponential_growth for the trend form, learning_curve_effects (Wright's law) for cost-per-unit falling with cumulative production, and physical_limits for the asymptote, with Landauer's bound being merely the computing-specific value of that floor. So when the structural lesson is wanted in another field, it should be drawn from those parents, which transfer as mechanism; "Koomey's law," as named, adds only the computing-specific commitments — the substrate is logical switching events, the floor is thermodynamic, the broken slope is Dennard scaling's end — and those do not and should not travel. (See Structural Core vs. Domain Accent.)

Examples

Canonical

Koomey and colleagues (2010) assembled electrical-efficiency data for computing back to ENIAC (1945) and found that computations per joule doubled roughly every 1.57 years for over half a century — a fixed exponential on the energy axis, distinct from Moore's density curve. The trajectory's hard endpoint is thermodynamic. Landauer's principle sets the minimum energy to erase one bit irreversibly at kT ln 2: with Boltzmann's constant k ≈ 1.38 × 10⁻²³ J/K, room temperature T ≈ 300 K, and ln 2 ≈ 0.693, that is 1.38 × 10⁻²³ × 300 × 0.693 ≈ 2.8 × 10⁻²¹ joules per operation. Today's CMOS runs many orders of magnitude above this floor, so the ratio of current energy-per-operation to 2.8 × 10⁻²¹ J measures the total efficiency gain still physically available before the curve must asymptote.

Mapped back: Computations per joule is the efficiency metric, and the 1.57-year doubling is the exponential trend. The computed 2.8 × 10⁻²¹ J is the thermodynamic floor — Landauer's kT ln 2 worked out — at which the curve must bend, distinct from the lithographic ceilings Moore's law meets. The large gap between present CMOS and that floor is the headroom the trend can still traverse.

Applied / In Practice

Through the early-to-mid 2010s, total U.S. data-center electricity consumption stayed remarkably flat even as the amount of computation, storage, and network traffic they handled grew explosively. Analyses (including Koomey's own and a 2016 Lawrence Berkeley National Laboratory report) attributed this near-constancy to efficiency gains — more computation delivered per joule, together with better power-usage effectiveness — roughly offsetting the growth in workload, so aggregate demand did not balloon as many had feared. This is exactly the workload-coupling inference: aggregate energy tracks the race between the efficiency curve and demand growth. The more recent surge in AI training and inference, arriving after Dennard scaling's end slowed the efficiency doubling, is now widely expected to break that balance and push data-center electricity demand sharply upward.

Mapped back: Computation-per-joule improvement is the efficiency metric on the exponential trend; demand growth is the workload coupling whose race against it sets whether aggregate consumption rises or falls. The flat 2010s reflect efficiency offsetting workload; the projected AI-era climb reflects the regime break — the post-2005 lengthened doubling — letting demand outrun a slower efficiency curve.

Structural Tensions

T1: The orthogonal energy axis clarifies by isolating versus products that need both axes. Koomey's law supplies the energy-per-operation axis orthogonal to speed and count, so a stalled-clock era can still show orders-of-magnitude progress and a battery-limited product class can be dated by when the efficiency curve crosses its threshold. The isolation is the clarity. But real devices must satisfy both axes: a chip efficient enough to fit the energy budget but too slow to meet latency or throughput requirements does not ship, so reasoning purely on the Koomey axis can pronounce a product "feasible" (joules met) while it fails on the count-and-speed axis the law deliberately sets aside. The tension is that the concept's clarifying move — isolate energy from performance — is also what lets it certify feasibility on one axis while the other, jointly necessary, goes unchecked. Diagnostic: Does crossing the energy-per-operation threshold actually make this product shippable, or does it still fail the throughput and latency the Koomey axis abstracts away?

T2: The thermodynamic floor as a principled bound versus its near-term irrelevance. Unlike Moore's contestable lithographic and economic ceilings, Koomey's law terminates at a real physical floor — Landauer's kT ln 2 ≈ 2.8 × 10⁻²¹ J — which makes any forward extrapolation rigorously bounded and invalidates forecasts that carry the trend past it. That principled floor is the law's most distinctive feature. But today's CMOS runs many orders of magnitude above it, so the floor is decades out and does nothing for present-day design decisions, which are governed entirely by the near-term slope. The tension is that the concept's most intellectually satisfying element — a hard thermodynamic bound where Moore's law has only soft ceilings — is also its least practically binding, and foregrounding it can distract from the ordinary slope that actually decides whether this year's product is feasible. Diagnostic: Is the Landauer floor doing real work in this analysis, or is it a decades-out asymptote being invoked where the near-term doubling slope is what governs?

T3: Efficiency races workload versus efficiency drives workload (the rebound). The workload-coupling move treats aggregate energy as a race between the falling efficiency curve and independently-growing demand — the framing that explained the flat 2010s and now predicts an AI-era climb. But efficiency and workload are not independent: cheaper computation per joule induces more computation (Jevons/rebound — AI training scaled precisely because it became cheap), so efficiency gains feed the very workload growth that outruns them. The concept models two trends racing when one causally drives the other. The tension is that the same efficiency improvement the law tracks as the force holding aggregate demand flat is, through rebound, a force expanding the demand it is supposedly offsetting — so "efficiency offsets workload" and "efficiency inflates workload" can both be true of the same gain. Diagnostic: Is the efficiency gain here offsetting a fixed workload, or inducing the additional computation that will more than consume the joules it saved?

T4: The two-slope regime-break model versus the fragility of the post-Dennard slope. The slope-selection discipline — choose the ~1.57-year Dennard slope or the ~2.6-year post-2005 one, and read the 2005 break as Dennard scaling's end — imposes clean structure on the trajectory and prevents extrapolating one rate across the break. But the post-Dennard gains come from a heterogeneous grab-bag (architectural specialization, parallelism, dark-silicon management) with no single mechanism guaranteeing any stable doubling time, so treating the post-break era as a clean new exponential is itself a fit that can break again as specialization hits its own limits. The tension is that the two-slope model's tidiness — one break, two rates — is cleaner than the messy, mechanism-shifting reality of architecture-driven efficiency, so the discipline of picking "the live slope" can impose a stability on the post-2005 curve that its underlying causes do not actually possess. Diagnostic: Is the ~2.6-year post-Dennard slope a durable rate to project, or a provisional fit over architecture tricks that may bend again without notice?

T5: An empirical fit as feasibility forecast versus range-not-date false precision. Projecting the curve to date when a product class crosses from impossible to shippable is the law's most valued use. But it is a smoothed average over a noisy six-decade series with no physical necessity behind the slope, so it yields a range, not a date — the Landauer crossing itself is quoted as ~2050 versus ~2080–2100 depending on slope assumed — and the 2005 break shows the fit bends without warning. Using it to pin a feasibility year imports a precision the fitted exponential cannot supply. The tension is that the concept's forecasting utility depends on treating a noisy, atheoretical average as a planning constant, while its own history (a mid-trajectory slope change) demonstrates that the constant is neither constant nor guaranteed. Diagnostic: Is this feasibility projection presented as a bounded range acknowledging the fit's noise and break-risk, or as a date that treats a smoothed empirical average as a physical certainty?

T6: Autonomy versus reduction (a computing trajectory or the exponential-growth/learning-curve/physical-limits parents). Koomey's law is an empirically fitted exponential specific to computing, with home-bound cargo — the substrate of logical switching events, the Dennard-scaling regime break, dark-silicon management, and the thermodynamic Landauer floor — and within computing it transfers intact across roadmapping, data-center planning, embedded design, and AI-cost projection because the referent (energy per logical operation) never changes. But its portable skeleton, "an efficiency metric improves exponentially toward a physical floor on a slope that can break," was never Koomey-specific: it is carried by exponential_growth (the trend form), learning_curve_effects/Wright's law (cost-per-unit falling with cumulative production), and physical_limits (the asymptote, of which Landauer's bound is merely the computing-specific value). "A Koomey's law for X" elsewhere renames the components and borrows the shape. The tension is that the cross-domain lesson belongs to those parents while the Dennard/thermodynamic machinery stays home. Diagnostic: Resolve toward exponential-growth/learning-curve/physical-limits when carrying the efficiency-toward-a-floor shape to another field; toward Koomey's law when the metric is energy per logical operation on CMOS-and-successor hardware in situ.

Structural–Framed Character

Koomey's law sits at mixed on the structural–framed spectrum — a genuine, evaluatively neutral trend measured in the world, but one whose subject and framing are so bound to human-engineered silicon that its distinctive vocabulary cannot leave the domain. The five criteria pull in both directions.

Evaluative weight is low and points structural: computations-per-joule doubling is a measured regularity, neither praised nor condemned; the law renders no verdict, only a slope and a floor. Even the connotation of "progress" is descriptive here — the metric is whatever the silicon delivers, and the concept is silent on whether more efficiency is desirable.

Human-practice-bound pulls hardest toward framed, but with a wrinkle. The phenomenon runs observer-free in the narrow sense that a fabricated chip dissipates a definite number of joules per operation whether or not anyone measures it — no judging agent is needed for the physics of switching. But there is no computing in nature: the entire subject matter — logical operations, CMOS transistors, Dennard voltage scaling, dark-silicon management — is an artifact of an ongoing human engineering enterprise, and the six-decade doubling exists only because that enterprise kept supplying the gains. Strip the practice of chip-building and there is nothing left for the law to track. So the mechanism is not constituted by an act of judgment (as ad hominem is), but its referent is wholly constituted by a human techno-practice — mixed, tilting framed.

Institutional origin is likewise split. The law — a fitted exponential named after Koomey, extracted from a 2010 survey of efficiency data back to ENIAC — is an artifact of measurement and naming, exactly the kind of survey-born, curve-fitted regularity that reads framed; the doubling time is a smoothed average over a noisy series, not a rate nature enforces (the entry's own "Not a law of physics"). Yet the floor the trajectory asymptotes to is pure nature: Landauer's kT ln 2 is a thermodynamic bound that owes nothing to any tradition. So the trend is an institutional artifact strung between two genuinely physical anchors — the observer-free energy-per-operation below it and the Landauer limit beneath — which is what makes the criterion read mixed rather than cleanly framed.

Vocab-travels points framed: the operative vocabulary is irreducibly computing-bound — energy-per-operation, doubling time, the Dennard break, the Landauer floor — and none of it floats free of silicon substrates the way "growing quantity" or "ceiling" does in a pure structural prime. Import-vs-recognize is bimodal exactly as the entry documents. Within computing — roadmapping, data-center planning, embedded design, AI-cost projection — the transfer is recognition of the same measured regularity, because the referent (joules per logical operation) never changes. Beyond computing it is import-by-analogy: "a Koomey's law for X" borrows the exponential-toward-a-floor picture while renaming every component and dropping the Dennard/thermodynamic machinery.

The portable structural skeleton is an efficiency metric improving exponentially toward a hard physical floor, on a slope that can break — and, as the entry is careful to establish, that skeleton is exactly what Koomey's law instantiates from its umbrella primes (exponential_growth for the trend form, learning_curve_effects for cost-per-unit falling with cumulative output, physical_limits for the asymptote), not what makes "Koomey's law" itself travel. The cross-domain reach belongs to those parents; the domain-accented specifics — logical switching events, the thermodynamic floor's particular value, Dennard scaling's end — stay home. Its character: an evaluatively neutral empirical trend with genuine physical anchors at both ends, but a survey-fitted, silicon-bound expression that keeps it mixed rather than a free-floating prime.

Structural Core vs. Domain Accent

This is the section that decides why Koomey's law is a domain-specific abstraction and not a prime, and it carries the case for its domain-specificity — so it pays to be exact about which layer travels and which stays home.

What is skeletal (could lift toward a cross-domain prime). Strip the silicon and a thin relational structure survives: an efficiency metric improves exponentially toward a hard physical floor, on a slope that can break, with the ratio of the current value to the floor capping the total gain still available. The portable pieces are abstract — a ratio of useful output to resource consumed, a doubling-time regularity in that ratio, a fixed lower bound the trajectory must asymptote to rather than cross, and a regime break where the supplying mechanism changes and the slope resets. That skeleton is genuinely substrate-portable, which is exactly why it recurs in the catalog as the general primes Koomey's law instantiates: exponential_growth supplies the trend form, learning_curve_effects (Wright's law) supplies cost-per-unit falling with cumulative production, and physical_limits supplies the asymptote. But this is the core Koomey's law shares with every other efficiency-toward-a-floor trend, not what makes it distinctive.

What is domain-bound. Almost everything that makes the concept Koomey's law in particular is computing-hardware furniture, and none of it survives extraction. The metric is not any efficiency ratio but computations delivered per joule dissipated — the energy cost of a single logical switching event on CMOS-and-successor silicon. The supplying mechanism is specific: Dennard voltage scaling (energy falling as roughly the square of supply voltage as features shrink), then, past the ~2005 regime break, architectural specialization, parallelism, and dark-silicon management. The floor is not a generic bound but Landauer's kT ln 2 ≈ 2.8 × 10⁻²¹ J per irreversible bit erasure — a thermodynamic limit tied to the irreversibility of the operation, escapable only by a substrate change (reversible or quantum computing) that voids the premise. The empirical cases — the ENIAC-to-2000 series, the flat-2010s data-center demand, the mobile/wearable/edge-inference feasibility envelope — are all worked in joules, doubling times, and battery-capacity-over-required-operations thresholds. The decisive test: remove the logical-switching substrate and its thermodynamic floor, and "an efficiency trend bending toward a limit" is no longer Koomey's law but the looser, substrate-neutral shape that any falling-cost technology shares.

Why this does not clear the prime bar. A prime is a relational structure whose vocabulary travels and whose cross-domain transfer is recognition of the same mechanism, not analogy. Koomey's law's transfer is bimodal. Within computing — semiconductor roadmapping, data-center planning, embedded and wearable design, AI cost-of-training projection — it travels intact as recognition, because the referent never changes: energy-per-operation, doubling time, the Dennard break, and the Landauer floor mean the same thing in every subfield, and the slope-selection discipline carries with them. Beyond computing it travels only by analogy: "a Koomey's law for X" renames the components (joules → dollars or some other resource, logical operations → the relevant output unit) and borrows the exponential-toward-a-floor shape while dropping the Dennard and thermodynamic machinery that gives the original its predictive force and its particular floor — illuminating resemblance, not the law itself moving. And crucially, when the bare structural lesson is wanted in another field, it is already carried in more general form by the parents Koomey's law instantiates: the trend form by exponential_growth, cost-per-unit falling with cumulative production by learning_curve_effects, the asymptote by physical_limits, with Landauer's bound being merely the computing-specific value of that floor. The cross-domain reach belongs to those parents; "Koomey's law," as named, adds only the domain-specific commitments — a logical-switching substrate, a thermodynamic floor, a broken Dennard slope — and those stay home.

Relationships to Other Abstractions

Local relationship map for Koomey's lawParents appear above the current abstraction, mutual partners to the right, and children below. Node labels state whether each abstraction is prime or domain-specific; colors identify relation types.Koomey's lawDOMAINPrime abstraction: Irreducible Floor — is part ofIrreducibleFloorPRIMEPrime abstraction: Exponentiation — is a decomposition ofExponentiationPRIME

Current abstraction Koomey's law Domain-specific

Parents (2) — more general patterns this builds on

  • Koomey's law is part of Irreducible Floor Prime

    Koomey's Law contains an Irreducible Floor because Landauer's thermodynamic cost per irreversible bit erasure bounds the total efficiency gain remaining under the law's computational premise.

  • Koomey's law is a decomposition of Exponentiation Prime

    Koomey's Law extracts Exponentiation because computations delivered per joule follow an empirical doubling-time trajectory whose slope can be measured separately before and after a regime break.

Hierarchy paths (3) — routes to 3 parentless roots

Not to Be Confused With

  • Moore's law. The empirical trend that transistors per unit area (or per chip at fixed cost) doubles on a roughly fixed schedule — the density axis of semiconductor progress. Koomey's law tracks a distinct observable, joules per logical operation, so the two can diverge: density can stall while energy-per-operation keeps falling, and Moore's law runs into lithographic and economic ceilings whereas Koomey's law asymptotes to a thermodynamic floor. Tell: is the metric how many switches fit on the chip (Moore) or how cheaply each switch fires (Koomey)?

  • Dennard scaling. Not a rival trend but the supplying mechanism behind Koomey's law's fast pre-2005 slope — the MOSFET rule that as features shrink, voltage and current scale down together so power density stays constant and energy-per-switch falls with the square of supply voltage. Koomey's law is the aggregate efficiency fingerprint; Dennard scaling is one of the underlying causes that produced it, and its ~2005 breakdown is exactly what lengthened Koomey's doubling time. Tell: Dennard scaling is a device-physics scaling rule with a specific end date; Koomey's law is the decades-long efficiency curve whose slope that rule (while it lasted) helped set.

  • Landauer's principle. The thermodynamic result that erasing one bit irreversibly costs at least kT ln 2 (~2.8 × 10⁻²¹ J at room temperature) — a fixed physical bound, derived, not fitted. Koomey's law is the empirical trajectory approaching that bound; Landauer's principle is the endpoint the trajectory must asymptote to, decades out. Tell: is the claim a hard lower limit that no irreversible operation can cross (Landauer) or a historical doubling trend with a contestable slope (Koomey)?

  • Wright's law / learning-curve effects. The regularity that unit cost falls by a fixed percentage with each doubling of cumulative production — progress indexed to accumulated experience, not to calendar time. Koomey's law is indexed to time (a ~1.57- then ~2.6-year doubling) and to a specific physical metric (energy per operation), and it has a hard thermodynamic floor that a generic learning curve lacks. Tell: does the improvement track cumulative units built (Wright) or elapsed years toward a physical limit (Koomey)?

  • Jevons paradox / rebound effect. The economic pattern in which efficiency gains lower the effective cost of a resource and thereby induce more consumption of it, so total use can rise despite rising efficiency. Koomey's law is the efficiency trend itself; the rebound is a consequence that couples that trend back to workload growth (the entry's T3), not a property of the curve. Tell: are you describing the falling energy-per-operation (Koomey) or the induced demand that eats the joules it saved (Jevons/rebound)?

  • The umbrella primes it instances (exponential growth, learning-curve effects, physical limits). The substrate-neutral skeleton — an efficiency metric improving exponentially toward a hard floor on a slope that can break — that Koomey's law instantiates with computing-specific content (joules per CMOS switch, the Dennard break, the Landauer floor). Koomey's law is the silicon instance; outside computing, the portable lesson is carried by these parents, not by the named law. Tell: strip away logical switching events and the thermodynamic floor and what remains is bare "efficiency trend bending toward a limit" — at which point you are using the general primes, not Koomey's law. (Treated fully in an earlier section.)

Neighborhood in Abstraction Space

Koomey's law sits in a sparse region of the domain-specific corpus (91st percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Unclustered & Miscellaneous (309 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-07-12