REVIEW 5 major objections 7 minor 32 references
The Jevons Paradox In Cloud Computing: A Thermodynamics Perspective
T0 review · 5 major / 7 minor · reviewed 2026-08-12 · deepseek-v4-flash
Pith's one-line read The paper claims that cloud energy consumption is proportional to cumulative historical revenue, so efficiency improvements accelerate total energy growth rather than curbing it.
desk verdict A clean, first-of-its-kind application of Garrett's thermodynamic growth model to cloud platforms, but the central validation claim is undercut by the use of total company revenue instead of cloud revenue. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The carrying mechanism is the efficiency-driven growth loop: revenue $W$ is work, work expands the interface $L$, and energy draw $A$ is proportional to $L$. Algebraically, $\varepsilon = W/A = (1/\alpha)\,d\ln L/dt$, so a constant efficiency is a constant exponential growth rate for the system; with $\eta = \alpha\varepsilon$, the energy growth equation $dA/dt = \eta A$ follows directly. The testable identity $A = \alpha C$ (current energy proportional to cumulative revenue) is the model's signature, and the validation section checks it against 2016–2022 data.
What would settle it
Compute, year by year over a decade, the ratio of a hyperscale cloud's total electricity use to its cumulative historical revenue. If that ratio trends away from a constant while revenue grows, the identity $A = \alpha C$ and the implied constant-potential exponential growth are falsified; a second check is whether data-center energy plateaus or declines for several consecutive years while cumulative revenue continues to rise, which would contradict $dA/dt = \eta A$.
Extended reading notes
Core claim
The paper claims that a hyperscale cloud behaves like an open thermodynamic system whose energy consumption is $A = \alpha L \Delta\Phi$, where $L$ is the size of the interface with the energy reservoir and $\Delta\Phi$ is the reservoir potential. Taking cloud revenue as the system's work output, work expands the interface via $W = (dL/dt)\Delta\Phi$, and combining the equations yields $dA/dt = \eta A$ with $\eta = \alpha\varepsilon$, so energy grows exponentially as $A(t) = e^{\eta t}$ and is proportional to cumulative revenue: $A = \alpha C$. The paper validates this proportionality on public energy and financial data from Meta and Google, and shows that capital expenditure and embodied emissions scale with cumulative energy, supporting their role as proxies for interface size.
Load-bearing premise
The argument depends on treating a cloud's revenue as a faithful measure of the useful work it does and assuming that all of that work is reinvested to grow the system against an effectively unlimited energy supply; if revenue includes value unrelated to computation, or if growth is capped by markets or capital, the proportionality between energy and cumulative revenue does not follow.
Editorial extensions
If this is right
- If the model is right, hardware and data-center efficiency improvements raise $\eta$ and therefore steepen the exponential rise in total cloud energy, so point-level metrics like PUE become insufficient for sustainability.
- Energy consumption will keep growing with revenue as long as the reservoir is treated as a constant potential; growth turns sigmoid only if the energy or material reservoir depletes.
- Cumulative historical revenue, capital expenditure, and embodied emissions become usable proxies for system size, enabling energy back-casting from public financial data.
- The system's inertia means today's energy use is set by past growth, so efficiency levers act on a system whose size has already been determined.
- Including clients and the network in the system boundary shows that data-center-only optimizations can push consumption into less efficient parts of the system.
Reading between the lines
- The same $A = \alpha C$ proportionality could be tested on other large cloud platforms and on national data-center aggregates; a clear failure there would delimit the model's domain.
- A saturation test is directly available: if energy growth visibly slows while cumulative revenue keeps rising, then $\Delta\Phi$ is not constant and the constant-potential exponential phase is ending.
- Disaggregating revenue by product line could tighten or break the coupling, since advertising or non-compute income included in total revenue would distort the physical work metric.
- The model implies that the only escape from exponential growth is constraining interface expansion, for example through capacity limits or edge-cloud boundaries, rather than through efficiency alone.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. This paper proposes a coarse-grained thermodynamic model of cloud computing, adapted from Garrett's models of the global economy. The system consumes energy A = αLΔΦ; work (identified with cloud revenue) is W = εA; and the work is assumed to be reinvested in expanding the system's interface, W = (dL/dt)ΔΦ. Combining these equations yields the system-inertia relation A = αC, where C is cumulative revenue, and exponential energy growth dA/dt = ηA. The author claims this explains the Jevons paradox for hyperscale clouds and validates the model using public energy and financial data from Meta and Google (2016–2022): energy versus cumulative revenue (Figure 3), embodied emissions versus cumulative energy (Figure 4), and capital expenditure versus model-back-cast cumulative energy (Figure 5). The paper then draws implications for efficiency metrics, client-side energy, and edge-cloud architectures. The thermodynamic derivation is internally consistent, but the empirical validation uses company-wide rather than cloud revenue, reports no quantitative fit statistics, and includes a circular back-casting step.
Significance. If the central proportionality A = αC could be established with cloud-segment data, the paper would offer a useful quantitative regularity linking an easily measured financial variable to cloud energy use, and a mechanism-based account of the Jevons paradox that goes beyond the standard elasticity story. The strengths of the manuscript are real: the derivation from Eqs. (1)–(6) is transparent and internally consistent; the model makes explicitly falsifiable predictions (A ∝ C with stable α; embodied emissions ∝ cumulative energy; CapEx ∝ cumulative energy); the empirical work uses publicly available data; and the paper candidly discloses the Google emissions failure and the back-casting step. These strengths, however, do not compensate for the validation gap: the headline empirical claim is tested with total-company revenue for two firms, with no fit statistics or baseline comparisons, and with a system boundary that shifts between model and data. The significance for a journal readership is therefore conditional on a substantially strengthened evaluation, in particular a test using actual cloud-platform revenue and quantitative goodness-of-fit measures.
major comments (5)
- [§4 (Model Evaluation), Fig. 3; §3 (work metric)] The validation in Fig. 3 does not test the model's work metric. Section 3 defines work as 'cloud revenue' ('we claim that cloud revenue is a suitable work metric'), but the evaluation uses total company revenues from SEC filings: Meta's consolidated revenue is almost entirely advertising (Meta sells no public cloud service), and Alphabet's figure is dominated by Google Services and advertising rather than the Google Cloud segment. This contradicts the system boundary stated at the start of Section 4 ('We only consider the cloud provider as part of the system, and not the users'). Total revenue is generated by users and advertisers outside that boundary, so the fitted proportionality A = αC is a statement about company-wide revenue, not about cloud-platform revenue, and the central claim is not actually tested on cloud revenue. The derivation also assumes that all work (revenue) is reinvested in interface growth, Eq. (3), whereas both companies paid substantial dividends and conducted share repurchases during 2016–2022; the paper should at least quantify how much of the revenue is excluded by that assumption.
- [§4 (Model-based back-casting), Fig. 5] The CapEx analysis in Fig. 5 is not independent confirmation of the model. As the text discloses, 'To estimate the cumulative historical (pre-2016) energy usage, we use our model's linear relation from Figure 3.' The cumulative-energy series used to compute the ratio CapEx/cumulative energy is therefore generated from the very A = αC relation that the paper is validating, so the agreement in Fig. 5 is partly built in. The disclosure is commendable, but the section should be reframed: Fig. 5 illustrates a back-casting application of the model; it does not provide independent evidence for the size-proxy claim or for the proportionality.
- [§4 (Model Evaluation), Fig. 3] No goodness-of-fit or baseline comparison is reported for the central relation. Figure 3 shows the declared linearity visually, but the paper gives no R², no residuals, no error bars, and no uncertainty on the fitted slope α; nor is α derived independently, so the dashed lines are a functional-form consistency check rather than a parameter-free prediction. Because both revenue and energy grew roughly monotonically over 2016–2022 for both companies, visual proportionality between two growing series is a weak test: an alternative such as A proportional to contemporaneous revenue, or two unrelated exponential trends, would be hard to distinguish by eye. With two firms and seven annual points, this is the main empirical support for A = αC, and quantitative measures of fit plus at least one null model are needed before the statement 'the model prediction holds true' is warranted.
- [§3 vs. §4 (system boundary for A)] The system boundary is inconsistent between the model and the data. Section 3 defines A as 'the electricity consumption of the cloud data centers and the client-side consumption' and states that the system includes users, whereas Section 4 restricts the system to the provider-only boundary and uses data-center electricity from sustainability reports only. The relation A = αC is thus fitted to a different quantity than the A in Eqs. (1)–(6). The author should either re-derive the model for the provider-only boundary or validate the full-boundary model with the client-side and internet-energy estimates that Section 5.2 shows to be significant; as it stands, the data and the model do not refer to the same system.
- [§4 (Model Evaluation), Fig. 4] The embodied-emissions size proxy is confirmed for only one of the two companies: the text reports that the Google analysis 'fails to show the proportional relation between Scope 3 emissions and cumulative energy.' The paper explains this by the non-standard nature of emissions accounting, but the consequence is that the interface-size branch of the validation rests on a single company. The finding should be stated accordingly (for example, 'consistent for Meta only'), rather than as a general confirmation that emissions are a usable proxy for system size.
minor comments (7)
- [§3, Eq. (7)] Equation (7), A(t) = e^{ηt}, omits the prefactor A(0); as written it is dimensionally inconsistent and would imply A(0) = 1 in whatever units are used. It should read A(t) = A(0)e^{ηt}.
- [Throughout] Please correct the typos and garbled sentences: 'phenomonological' → 'phenomenological' (§3), 'minitua' → 'minutiae' (§1), 'inspite' → 'in spite' (§§1, 4), 'reason-detrie' → 'raison d'être' (§3), and 'conventional PUE-improving have data center optimizations' in §5.3, which is not a grammatical sentence.
- [Fig. 3 caption] The caption 'Cumulative Revenue/Energy' is ambiguous: it does not state that the two series are normalized for comparison, nor how the slope of the dashed model line was determined (fitted to the same data? derived from an independent constant?). Both points should be stated explicitly.
- [§5.2, Fig. 6] The assumptions are stated inconsistently: 'We assume 2 hours a day of usage, with 1 Watt energy usage' gives 2 Wh/day only if the 1 W is the average draw over the 2 hours, and the later sentence states 'we assume 2 Watt-Hours per day.' The client-usage (2 h/day) and internet-attribution (10%) parameters are free choices; since the figure's purpose is to show that client energy can be significant, a brief sensitivity discussion would strengthen it.
- [§3, references] The statement that the model is 'adapted from prior work in [10]' under-specifies the provenance: Eqs. (1)–(3) and the L = N_S^{1/3}·N_R remark appear to come from Garrett's series [8, 9, 11, 12] and the bio-economics literature [14, 15]. Please cite each equation to its source.
- [Manuscript formatting] The ACM template placeholders ('Conference'17, July 2017', '7 pages', 'ACM ISBN 978-x-xxxx-xxxx-x/YY/MM', 'https://doi.org/10.1145/nnnnnnn.nnnnnnn') remain in the manuscript and should be removed.
- [Reproducibility] No scripts or data repository are provided for reproducing Figures 3–5. Given that the empirical claims are the load-bearing part of the paper, a small release of the extracted time series and fitting code would materially help reviewers and readers.
Circularity Check
Central A=αC relation is definitional; validation fits the same data and back-casts using the model itself.
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self definitional
[Section 3, Equations (1)-(3) and the cumulative-revenue paragraph]
"Based on these requirements, we claim that cloud revenue is a suitable work metric. ... Work thus captures how a system grows: W = dL/dt · ΔΦ. (3) ... In our cloud system model, the cumulative revenue is: C(t) = ∫ W(x) dx. Using Equation 3, we get: A = αC, which indicates that the current energy consumption is proportional to the cumulative revenue of the cloud platform."
The relation is not an independent prediction: 'cloud revenue' is stipulated to be the thermodynamic work W, Eq. (3) defines W as (dL/dt)ΔΦ, and Eq. (1) defines A as αLΔΦ. With constant ΔΦ, integrating Eq. (3) gives C = ΔΦ(L−L0), so A = αC (up to the initial term) follows algebraically from the definitions. Any system for which these constitutive definitions are accepted will exhibit A proportional to cumulative revenue; no additional physical constraint is derived. The paper supplies no independent measurement of L or ΔΦ for this relation, so the 'derivation' reduces to the meaning assigned to revenue and work.
-
fitted input called prediction
[Section 4, 'Energy and Cumulative Revenue', Figure 3]
"As derived in the previous section, the energy consumption is proportional to the cumulative work (i.e., A = αC). This is shown for Meta and Google in Figure 3, and we see that the model prediction holds true in both the cases. We have used the historical revenue of both these companies (going past 2016), since it is crucial in determining the system inertia."
No independent value of α is derived from the model or measured separately; the dashed lines in Figure 3 are proportionality curves fitted to the same A and C series that are then said to validate the prediction. A single fitted constant can always make two roughly growing series coincide, so the 'confirmation' is a fit rather than a test. The paper gives no error bars, R², null model, or out-of-sample check, so the data do not discriminate the mechanism from the trivial observation that both quantities increased over 2016–2022.
2 more flagged steps
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other
[Section 4, 'Model-based back-casting']
"For the analysis presented in Figure 5, historical energy use was difficult to obtain with public data sources, since the sustainability reports only go as far back as 2016. To estimate the cumulative historical (pre-2016) energy usage, we use our model’s linear relation from Figure 3. Since energy is proportional to cumulative revenue even for Google, we used the historical revenue data and obtained the energy estimates."
The CapEx proxy in Figure 5 is presented as 'further confirms the model predictions', but part of the cumulative-energy series used in that figure is itself generated from the very A = αC relation being validated. The model's assumption is inserted into the input data and then observed to hold, making the CapEx confirmation partly circular. The 2016–2022 reported energy data remain independent, but the historical extension cannot count as an independent validation of the model.
-
self definitional
[Section 3, embodied-emissions paragraph, and Section 4, 'System Expansion']
"By definition, the emissions embodied in computing hardware are a result of the cumulative energy and material flows. If the system is expanded to include hardware manufacturing and distribution entities, then the total embodied emissions is proportional to the historical cumulative energy usage. That is, Embodied(t) = ∫ A(x) dx. ... Thus, we use the Scope 3 emissions as one of the interface size metrics. Based on our model, we should expect that interface size (i.e., emissions) are proportional to the cumulative energy usage."
The 'prediction' that embodied emissions scale with cumulative energy is an identity in the model: the paper defines embodied emissions as proportional to ∫ A. Using Meta's Scope 3 data to confirm this relation is therefore not an independent test of the model, even though the emissions data themselves are empirical. The authors acknowledge that Google's Scope 3 data fail this relation and then switch to the CapEx proxy, which in turn depends on the back-casting step above.
full rationale
The paper is self-contained in one respect: the thermodynamic formalism is adapted from Garrett's published models and from Georgescu-Roegen, not from the author's own prior work, so there is no load-bearing self-citation chain. The circularity is internal to the construction and validation. The central headline result A = αC is obtained by stipulating that cloud revenue is thermodynamic work W, writing W = (dL/dt)ΔΦ in Eq. (3), and combining it with A = αLΔΦ in Eq. (1); with constant ΔΦ, cumulative revenue is ΔΦ times the change in L, so A = αC is a definitional identity up to initial conditions. The validation in Section 4 then fits the proportionality constant to the same data and calls the resulting fit a 'model prediction', which provides no independent support. The CapEx validation is further weakened because the model's own A = αC relation is used to synthesize pre-2016 energy data, which are then fed into the CapEx comparison; the embodied-emissions 'prediction' is also definitional since the model defines embodied emissions as proportional to ∫A. There is some residual empirical content: Google's Scope 3 emissions fail the predicted relation, the 2016–2022 A-versus-C plots are not random, and the exponential-growth dynamics (Eqs. 5–7) are illustrative. Still, the paper's central claimed prediction reduces by construction rather than by independent measurement. One stated boundary limitation should also be weighed, though it is a correctness issue rather than a circularity: Section 4 says 'We only consider the cloud provider as part of the system, and not the users', while the validation uses company-wide revenue from Meta and Alphabet, which includes advertising and user-driven revenue; that mismatch threatens whether the work metric matches the stated system boundary.
Assumptions & free parameters
free parameters (3)
- alpha (conductivity or energy-revenue proportionality) =
Not reported; fitted to Meta and Google cumulative-revenue vs energy data
- client phone usage per day =
2 hours/day at 1 W
- internet traffic attribution fraction =
10% of internet traffic attributed to app usage
assumptions (5)
- domain assumption The cloud plus users ensemble is large enough to be modeled thermodynamically.
- ad hoc to paper Cloud revenue is a suitable work metric, with efficiency in dollars per Joule.
- ad hoc to paper All work (revenue) is reinvested into expanding the system boundary, so W = (dL/dt) Delta-Phi.
- domain assumption The reservoir potential Delta-Phi (and hence the growth rate eta) is constant over the observed period.
- domain assumption The integration constant in A = alpha C is zero, so the system starts with zero cumulative revenue and zero energy.
invented entities (2)
-
System interface length L
-
Reservoir potential difference Delta-Phi
Cite this review
Pith. "Pith review of The Jevons Paradox In Cloud Computing: A Thermodynamics Perspective." pith.science (2026). https://pith.science/paper/IIOPLNO5
@misc{pith2026241111540,
author = {Pith},
title = {Pith review of: The Jevons Paradox In Cloud Computing: A Thermodynamics Perspective},
year = {2026},
howpublished = {\url{https://pith.science/paper/IIOPLNO5}},
note = {Machine review of arXiv:2411.11540}
}
read the original abstract
How do we explain the simultaneous growth in energy efficiency of cloud computing and its energy consumption? The Jevons paradox provides one perspective of this phenomenon. However, it is not clear or obvious \emph{why} the Jevons paradox exists, and \emph{when} is it applicable. To answer these questions, we seek inspiration from thermodynamics, and model the cloud as a thermodynamic system. We find that system growth, due to the revenue generation of cloud platforms, is a key driver behind energy consumption. This thermodynamic model provides energy consumption insights into modern hyperscale clouds, and we validate it using data from Meta and Google. Our investigation points to the necessity of future work in new and meaningful efficiency metrics, implications for future applications and edge clouds, and the need for studying system-wide energy and sustainability.
Figures
Figures from the paper (3 more)
Reference graph
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Reviewed August 12, 2026 · model on record in the stance chip above.
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