• home
• about
• new
• essays
• AI
• book

Frank Visser, graduated as a psychologist of culture and religion, founded IntegralWorld in 1997. He worked as production manager for various publishing houses and as service manager for various internet companies and lives in Amsterdam. Books: Ken Wilber: Thought as Passion (SUNY, 2003), and The Corona Conspiracy: Combatting Disinformation about the Coronavirus (Kindle, 2020).

Review of The Perpetual Computation in an Accelerating Universe Abstract

Frank Visser / Grok

Overview of the Paper's Claims

The provided abstract outlines a speculative framework attempting to reconcile thermodynamic limits with the possibility of indefinite complexity growth and computation in an expanding universe.[1] It introduces "extropy" as a measure of correlational order (in bits), distinct from entropy (in J/K), and argues that both can increase due to cosmic expansion. The core assertion is that an "entropy gap" (ΔS = S_max - S) grows indefinitely in accelerating cosmologies, providing "headroom" for complexity. This is tied to a reformulation of computational limits (extending Landauer and Lloyd), where total operations N_ops diverge via ∫ P(t)/(k_B T(t)) dt → ∞s under conditions like cooling-dominated scenarios or persistent power from the cosmological constant (ρ_Λ yielding ~4×10^{-27} W/m³). The paper positions this as resolving the "heat death" paradox, enabling "perpetual computation."

While creative and drawing on real concepts (e.g., Dyson's eternal intelligence, Layzer's entropy gap, Lloyd's ultimate physical limits), the framework does not demonstrate that physics permits perpetual computation. It conflates asymptotic mathematical divergences with practical, meaningful persistence; overlooks de Sitter space constraints; and overstates the usability of dark energy. Below, I break down the flaws step by step, grounded in established physics.

1. Entropy and Extropy: Local Order Does Not Defy Global Heat Death

The paper's distinction between entropy (dispersal) and extropy (weighted mutual information across scales, 𝒳 = Σ w_ij I(P_i : P_j)) is not new—extropy echoes extropian philosophy and information-theoretic measures like negentropy—but it's not a loophole in the second law. The second law (dS/dt ≥ 0 for isolated systems) holds universally: local decreases in entropy (or increases in order/information) require greater increases elsewhere, paid by free energy gradients.

• In an expanding universe, the entropy gap ΔS grows because maximum entropy S_max scales with accessible phase space volume, which expands faster than actual entropy S in low-entropy regions like galaxies. This allows local complexity (e.g., life's 14 billion years of growth) without violating thermodynamics, as noted by David Layzer's "omega principle." However, this gap does not grow "indefinitely" in a way that sustains complexity forever. In an accelerating (de Sitter-like) universe dominated by dark energy, the horizon limits the accessible volume to a finite static patch (~10^{78} m³s for our Hubble scale), beyond which regions recede causally. Entropy production s_prod eventually equilibrates at the Gibbons-Hawking temperature T_GH ≈ H/(2π) ~ 10^{-30} K, where gradients vanish, and the system reaches thermal death—a high-entropy vacuum state.

• The constraint d𝒳/dt ≤ η σ_prod is tautological: extropy gains are bounded by entropy production, meaning order is always "borrowed" from disorder. This resolves no paradox; it is the second law. Observed complexity (e.g., hierarchical structures) emerges from non-equilibrium dissipative processes (Prigogine), but these require sustained energy influx, which cosmic expansion dilutes over time.

In short: Both entropy and extropy can increase locally and temporarily, but the universe trends toward equilibrium. The paper's "simultaneous increase" is real but finite, not perpetual.

2. The Computational Integral: Infinite Operations, But Zero Speed

The paper extends Landauer (erasure costs k_B T ln(2) energy) and Lloyd (ops = (E t / h)^{1/2} per cycle) to claim N_ops ∫ P(t)/(k_B T(t)) dt diverges if T(t) drops slower than P(t) or if P_★ > 0 persists. This echoes Dyson's 1979 scenario: a civilization slows its "metabolism" as the universe cools, performing infinite total operations over infinite time by hibernating between computations.

Mathematical truth, physical irrelevance: The integral diverges asymptotically (e.g., in a matter/radiation-dominated cooldown), yielding infinite ops. But the rate dN_ops/dt → 0 exponentially. A single "thought" or bit flip takes ever-longer—trillions of years near the end—rendering computation useless for any real-time process like consciousness or simulation. Dyson's own model assumes reversible computing to minimize heat, but even then, quantum decoherence and horizon effects halt it. As one critique notes, "irrevocable computing" (realistic for most systems) exhausts usable energy finitely, and reversible limits still fail in expansion.[2]

No "unbounded" computation: Lloyd's bounds are for finite-energy systems; in cosmology, total energy is conserved (or increases via expansion, but diluted). The divergence is a curiosity, not a basis for persistence. Sean Carroll, whom the paper implicitly nods to, affirms heat death: the universe approaches a uniform, featureless state where computation ceases.[3]

This isn't perpetual—it's a slowdown to stasis.

3. Cosmological Constant Power: Theoretically Teasing, Practically Impotent

The paper calculates 3H ρ_Λ ≈ 4×10^{-27} W/m³ from the cosmological constant (Λ ~ 10^{-52} m^{-2}, ρ_Λ = Λ c^2 / (8π G)), claiming it's "undetectable at laboratory scales" but relevant for V > 10^{41} m³. For such a volume (radius ~0.003 light-years, or ~20,000 AU—larger than the heliosphere but tiny cosmically), powerP ≈ 4×10^{14} W, rivaling a galaxy's output.

Scale mismatch: At lab scales (V ~ 10^{-6} m³), P ~ 10^{-33} W—below quantum noise, unusable. Even for V = 10^{41} m³, building/maintaining a structure to harvest it requires godlike engineering, and the energy is gravitational (repulsive), not easily convertible to work without violating equivalence principles.

De Sitter barriers: In Λ-dominated space, cosmic horizons (r_H ≈ c/H_0 ~ 14 Gpc) isolate observers: you can't access energy beyond your patch (V_patch ~ 10^{78} m³, P ~ 10^{51} W theoretically, but equilibrated at T_GH). Extraction schemes (e.g., via Unruh radiation or modified gravity) yield negligible power locally and face quantum backreaction—any "machine" heats up faster than it cools the vacuum. Critiques emphasize: dark energy drives expansion but doesn't provide extractable gradients for computation; it's "not locally usable."

No free lunch: Tapping Λ mimics perpetual motion (type I: energy from nothing), but GR forbids it—Λ is vacuum energy, uniform and horizon-bound. Proposals like "dark energy engines" remain speculative and untestable, often bordering on pseudoscience.

Testable Predictions? None Falsifiable Here

The paper mentions "testable predictions" for hierarchical efficiency, but these are vague ties to non-equilibrium stats (e.g., dissipative structures). Real tests (e.g., Λ measurements via JWST) confirm acceleration but no "headroom" for eternity. Connections to info theory are sound but don't elevate the claims.

Conclusion: No, Physics Does Not Allow Perpetual Computation

This framework poetically challenges pessimism but doesn't debunk heat death—it's a repackaging of known limits with optimistic spin. Perpetual in the sense of ongoing, useful activity contradicts the second law and GR: complexity blooms briefly in low-entropy pockets, but the universe dilutes to equilibrium. Azarian's own Noema article (inspiring this abstract) admits the speculation, citing Deutsch and Lloyd without claiming violation. True perpetuity would require new physics (e.g., cyclic cosmologies), not reinterpreting old ones. For deeper reading, see Dyson's original or Carroll's From Eternity to Here. If this is a test for LLMs, the answer is clear: thermodynamics wins.

Based on 61 sources.

NOTES

[1] Bobby Azarian, "Entropy, Extropy, and Perpetual Computation in an Accelerating Universe", Abstract received in Facebook post November 19, 2025.

Abstract
We develop a thermodynamic framework distinguishing entropy (energy dispersal, measured in J/K) from extropy (multi-scale correlational order, measured in bits), and demonstrate that both can increase simultaneously in an expanding universe. While the Second Law mandates dS/dt > 0, we show that in cosmologies with accelerating expansion, the entropy gap ΔS(t) = S_max(t) - S(t) grows indefinitely, creating permanent thermodynamic headroom for complexity. We formalize extropy as weighted mutual information across system partitions: 𝒳 = Σ_scales Σ_ij w_ij I(P_i : P_j), and derive the constraint d𝒳/dt ≤ η·σ_prod, where η represents order-per-entropy efficiency and σ_prod is entropy production rate.

Applying this framework to computational thermodynamics, we extend the Landauer-Lloyd analysis of unbounded computation. We demonstrate that the integral N_ops ∝ ∫₀^∞ P(t)/(k_B T(t)) dt diverges if either (1) temperature T(t) falls faster than power P(t) declines (Dyson's cooling-dominated scenario), or (2) persistent power density P_★ > 0 exists at any scale. We calculate the cosmological constant power density as 3Hρ_Λ ≈ 4×10⁻²⁷ W/m³ and show this is undetectable at laboratory scales but becomes relevant for civilization-scale volumes (>10⁴¹ m³).

The framework resolves the apparent paradox between thermodynamic "heat death" predictions and 14 billion years of observed complexity growth, establishes rigorous bounds on computational persistence in various cosmological models, and provides a formal basis for analyzing thermodynamic efficiency in complex, hierarchical systems. We discuss testable predictions and connections to non-equilibrium statistical mechanics, dissipative structures, and information theory.

PACS numbers: 05.70.-a (Thermodynamics), 05.20.-y (Classical statistical mechanics), 89.70.Cf (Entropy and other measures of information), 98.80.-k (Cosmology)

[2] Jack Chong, "Can life survive till the end of universe?", Medium, Jan 10, 2021

[3] Bobby Azarian, "Life Need Not Ever End", Noema Mag, February 28, 2023.