Energy budget: locking feasibility into

Energy budget: locking feasibility into numbers — The force, time, and friction checks are only necessary conditions; for rapid plate motion to be feasible the required total energy and dissipation must also be geophysically plausible, or be rejected early. The section decomposes the required work into fracture, sliding, and dissipation terms.

The force/time/friction checks above are only necessary conditions . For rapid plate motion to be feasible, the required total energy and dissipation must be geophysically plausible (or be rejected early if not).

The force/time/friction checks above are only necessary conditions. For rapid plate motion to be feasible, the required total energy and dissipation must be geophysically plausible (or be rejected early if not).

Minimal decomposition of required work

The total work requirement can be decomposed as

W_total ≈ W_fracture + W_slide + W_diss + W_grav,

where

W_fracture: fracture energy for antipodal rupture and formation of a long rupture zone (zipper),
W_slide: mechanical work to produce relative displacement d,
W_diss: dissipation by friction/turbulence/viscosity (mostly heat),
W_grav: gravitational potential-energy change associated with uplift/subsidence and fluid redistribution.

In particular, W_diss is not a single “heat” bucket. With fluids, it can be partitioned as

W_diss ≈ Q_sensible + E_latent + Q_melt + W_hydfrac + ⋯ eq:diss_partition

including latent heat (phase change) and hydrofracturing terms. This partition underlies the P4 branching (melting vs hydrofracturing).

Order comparison: required energy vs representative event scales

The goal here is not to declare “possible,” but to lock the order-of-magnitude first and STOP early if unrealistic.

(i) Sliding work scale.

If suction acts on average as F_suction≈ A_effΔ P and the plate moves distance d, then

For example, with A_eff=10¹² m², Δ P=100 MPa=10⁸ Pa, and d=3× 10⁶ m,

This is not a “correct” number; it is an order-of-magnitude illustration. Because A_eff,Δ P,d can each vary by factors of 10, releases must pre-register input ranges and decide PASS/STOP via sensitivity analysis.

(ii) Upper-bound sketch for gravitational potential energy of the trigger.

If an effective mass M_eff is uplifted by Δ R,

Because M_eff depends on assumed area/thickness, this term can be misestimated. We therefore separate energy sources into competing hypotheses (H-E1–H-E3) and validate by signatures (AR-1, AR-9).

(iii) Comparisons to representative events (order).

The table below is a rough log-order comparison (not a precision table).

Representative event	Energy (order, J)	Note
Very large earthquake (Mw ~ 9.5)	10¹⁸–10¹⁹	reference scale for crustal elastic release
Large impact (Chicxulub class)	~ 10²³	reference global-impact scale
This model (example A_effΔ P d)	10²⁵–10²⁷	varies widely with inputs; sensitivity is mandatory
Planet-scale internal transition/superplume (concept)	≳ 10²⁶	may be required if the model sits at these orders

Decision viewpoint. If, under conservative pre-registered inputs, W_total persistently exceeds physically available energy (or energy supported by independent signatures), the corresponding model version should be STOP.

Work scale of suction driving

With F_suction≈ A_effΔ P,

Thus the core questions reduce to: (i) how large is A_eff, (ii) how long/repeated is Δ P, (iii) how large is d. If all three grow simultaneously, W_slide grows rapidly and itself becomes an Ω-NoGo constraint.

Modularizing candidate energy sources

At present, the most vulnerable point is AR-1 (origin of Δ R). Accordingly, this white paper does not lock a single trigger; it defines competing energy-source modules.

(H-E1) Internal reservoir: supercritical jamming–unjamming (VP/material frame).

Projecting the IR-4 jamming/unjamming frame onto geophysics suggests that deep crust/upper-mantle crack/porosity networks could trap supercritical fluids in a jammed state. If cracks open and unjamming occurs, a pressure deficit (Δ P) and large fluid redistribution can co-occur, strengthening suction and lubrication. This module strongly predicts hydrothermal/hydration signatures in P4.

(H-E2) External/higher-order trigger: geometric friction (“60-degree jamming”) and heat injection.

IR-6's “double lattice” and “60-degree jamming” ideas model energy injection into the planet as a form of geometric friction. In this view, Δ R may reflect heating/expansion of a superplume driven by externally injected energy. This is not a required premise; it is one candidate for AR-1.

(H-E3) Electromagnetic residual energy: using geomagnetic decay as an afterimage.

IR-6 and IR-1 include a frame in which Earth's magnetic field is treated as residual induced currents from a recent catastrophic impulse. Even without adopting that literal claim, geomagnetic data can serve as an independent observable for whether the Earth system experienced a large impulse. One can compare bounds on E_EM with W_total as an auxiliary constraint.

Dissipation check: “frictional heat” is not only “melting”

If frictional dissipation is huge, some strong signatures must exist. With average friction force F_fric≈ μ_eff σₙ A_eff,

Thus lubrication (low μ_eff) is not merely convenient; it can be a necessary condition to keep dissipation physically manageable.

However, the common assumption “large Q_fric implies widespread melting/vitrification” may fail in a fluid-involved system because Q_fric can be partitioned into (i) sensible heat of rock/fluid, (ii) melting, (iii) latent heat of phase change, and (iv) work for hydrofracturing/pulverization/brecciation.

Latent-heat cooling.

Energy absorbed by phase change can be written as

with m_v the mass of fluid that undergoes phase change. This shifts the defense from “no heat is produced” to heat can be consumed by phase change (AR-11).

Verification and falsification (critical).

If widespread melting/vitrification signatures are weak, then structural signatures of overpressure + phase change (hydrofractures, injection veins, breccias, porous/vesicular textures, hydrothermal alteration/mineralization) must co-occur (P4-a). If neither melting nor fluid/overpressure signatures exist, physical pathways to “hide” Q_fric are insufficient, and that version of C3 should be FAIL. If strong melting signatures exist, a specific branch (F3 melt lubrication) may be UNLOCKed.

Event-dissipation channel: unjamming latent heat =ε_bind=Θσ{= epsilon_bind}

The dissipation check asks where Q_fric goes if it does not melt rock. WP-T1 (Section §14) gives a specific, quantified answer that closes the budget within one mechanism.

Unjamming costs energy. Driving z→ zᵢₛₒ breaks load-bearing contacts; the energy to break the backbone is a latent heat of unjamming. Per unit fault area, with Δ N_bond broken bonds of binding energy ε_bond,

identified with the foundational continuum's event-dissipation channel (Pillar IV),

where Θ is the per-event dissipation coefficient and σ the relevant stress/areal measure. Re-jamming (State 3 → 4) returns this latent heat, so over a full unjam–rejam cycle this channel is a transient temperature buffer, not a net heat sink: it suppresses the peak shear-zone temperature long enough for friction to collapse, preventing run-away melting during the transition. Net disposal of the cumulative Q_fric is accounted separately (low liquefied friction + advection) in the unified energy ledger, Section §17.

Why Δ T stays low. Because part of Q_fric is consumed as E_unjam (contact breaking / fabric phase change) rather than sensible heat during the transition, the gouge reaches low friction at a transient Δ T≈ 25 K over the friction-collapse interval, instead of the ~1462 K melt-only figure. The defense moves from “no heat is produced” to the peak transition temperature is buffered by the unjamming channel; this specifies the phase change as the jamming transition and supersedes a generic latent-heat-of-vaporization argument. The buffer governs the peak during the transition; the cumulative heat over the full opening is bounded and disposed of in the unified ledger (Section §17), not by this reversible channel.

One mechanism, three ledgers. Friction (WP-T1), heat (Δ T), and the energy budget share a single state variable (z relative to zᵢₛₒ): unjamming lowers friction, the same step absorbs heat as E_unjam, and re-jamming returns friction and releases the latent heat (the brake; Section §16).

Falsifier (WP-T3). If an energy audit of a candidate shear zone cannot balance Q_fric once the unjamming/phase-change channel is included (neither melting, fluid phase change, nor fabric-unjamming textures can absorb the inferred dissipation), the low-μ_eff branch of C3 is FAIL.

Unified energy ledger: one accounting for “input,” “heat,” and “disposal”

The preceding decomposition can be misread, because three physically distinct stresses appear in this paper and a hostile reading collapses them into a single “contradiction” spanning seven orders of magnitude. We therefore make the ledger explicit and chronology-agnostic; the numbers below are reproduced and audited in atl_bundle/engine/c16_energy_ledger.py (checks C16a–c).

Three stresses, three roles (not a contradiction).

Suction deficit Δ P~ 10⁸ Pa: an energy-input term. It sets the driving work Wᵢₙ=Δ P A_eff d.
Liquefied friction τᵣₑₛ=μ_effσₙ ≈ 3×10⁵ Pa (with μ_eff≈2.2×10⁻³, Section §14): the part of the work that is dissipated as heat, Q_fric=τᵣₑₛA_base d.
Mean-rate drive τ_drive~ 3–32 Pa (Section §20, C5): the viscous stress needed merely to hold the slow mean creep rate v=d/t_event against the liquefied viscosity. It is a kinematic book-keeping stress at the mean rate, not the dissipative resistance during a slip burst.

These are different quantities, so Δ P~10⁸ Pa and τ_drive~ 3–32 Pa are not in conflict.

The ledger. At the end of the event the plate is again at rest (Δ KE=0), so

Wᵢₙ = Δ PE_basin + Q_fric + W_fracture. eq:ledger

With Δ P=10⁸ Pa, A_eff=10¹² m², d=3×10⁶ m, Wᵢₙ~3×10²⁶ J (the “headline” number). Fracture energy (G_c~10⁴ J m⁻²) is negligible (~10¹⁵ J). Crucially, for liquefied friction and A_base~10¹²–3×10¹³ m²,

Q_fric ~ 10²⁴--10²⁵ J ≈ (0.3--10)% of Wᵢₙ.

The bulk of Wᵢₙ is therefore the potential-energy work of opening the basin and redistributing mass, not heat. The heat to be disposed of is Q_fric, of order a Chicxulub-class energy (~10²³–10²⁵ J), not a planet-scale (≳10²⁶ J) thermal pulse. (The physical origin of Wᵢₙ itself remains the separate, openly-flagged AR-1 question; this ledger constrains where the through-flowing energy goes, not where it comes from.)

Disposal #1 — conduction alone is insufficient (stated honestly). Treating the basal shear plane as a continuous heat source over the event duration t_event, heat penetrates a layer of thickness δ=√κ t_event, giving a mean rise

Δ T_cond ≈ Q_fric2 ρ c A_base √κ t_event = τᵣₑₛ d2 ρ c √κ t_event,

which (note: independent of A_base) is ~1000 K at t_event=1 kyr and ~330 K at 10 kyr. For the shorter end of the kyr window this reaches the melt threshold: conduction alone cannot be relied upon to keep the décollement sub-solidus. We do not paper over this. An additional physical sink is required — and the mechanism already requires one, namely the over-pressured lubricating fluid. Advection is thus forced by the same fluid the low-μ_eff path already invokes, not an extra assumption.

Disposal #2 — advection, quantified as a falsifiable prediction. If the lubricating fluid carries the heat out, the required cumulative throughput is m_w = Q_fric/(c_w Δ T_w), i.e.

of order 0.1–10% of the Atlantic basin volume. This is a large, regionally pervasive hydrothermal signature, not a hidden one — which is exactly what makes it testable rather than convenient.

FALSIFIER (WP-T4 / P4-thermal; pre-register in config/constraints.yml).

UNLOCK if the Atlantic basal detachment/margins show a regionally extensive, moderate-temperature (sub-solidus) hydrothermal-alteration + over-pressure signature of the predicted magnitude (alteration volume / mineralization budget consistent with ≳10⁴ km³ fluid throughput), and it is not a pervasive melt sheet.
FAIL if either (a) the basal contact is pristine/unheated at the predicted scale (no sink for Q_fric ⇒ the low-μ_eff branch of C3 is rejected), or (b) a pervasive regional melt/vitrification sheet is required (which contradicts the liquefaction-not-melt claim of Section §14 ⇒ the melt-only branch is selected and C3-liquefaction FAILs).

This makes the “heat problem” a two-sided, magnitude-calibrated test. It does not, by itself, establish the absolute timescale; that remains behind the chronology firewall (Section §20).

AR-1 energy-source audit: bounding the load-bearing open link

Section §17 closed the question of where the through-flowing energy goes. It did not answer where it comes from — AR-1, which this paper itself names as its most vulnerable point. We do not claim to solve AR-1; we bound it, exclude the candidates that fail on energy grounds, and convert the residual into a falsifier. The numbers are reproduced in atl_bundle/engine/c17_energy_source.py (checks C17a–c).

First, a category correction. A pressure-deficit void is not a power source: Δ P is a boundary condition that lets pre-existing gravitational, elastic, and thermal potential energy do work. The quantity that must be externally supplied is therefore not Wᵢₙ as a freshly-powered term, but the energy needed to charge the initial out-of-equilibrium configuration (the trigger: Pacific-side uplift Δ R / an over-pressured reservoir), whose relaxation then drives the opening. We require a source able to supply or release ≳ Wᵢₙ~3×10²⁶ J.

Bounding the three candidates against ~10²⁶ J.

H-E1 (internal reservoir; release of stored energy). The stored thermal energy of a deep, hot (Δ T~500 K), Pacific-scale reservoir is ~10²⁷–10²⁸ J — ample; a mechanical-conversion efficiency of only a few percent suffices. Stand-alone PV-work of trapped over-pressured fluid is marginal (~10²⁴–10²⁵ J). H-E1 is the only energetically admissible source class. The genuine open sub-question is the conversion efficiency η_mech and the reservoir's geophysical signature.
H-E2 (heat injection / superplume). As energy generation within a kyr, this needs ~20–200× the entire planet's present heat flow — excluded. As a literal impact, 10²⁶ J implies a ~100 km impactor (~10× Chicxulub linear scale), which would leave an unmistakable global melt/ejecta layer — excluded by its absence in the window. The only surviving reading is release of stored heat, i.e. it collapses into H-E1.
H-E3 (electromagnetic residual). The core field energy is ~10²¹–10²² J, four to six orders short of 10²⁶ J. Decisively excluded as a source; geomagnetic data is an observable only. This makes the paper's existing demotion of H-E3 mandatory, not optional.

Verdict — AR-1 source = HOLD (honest), narrowed to one class. H-E2-generation and H-E3 are excluded by 1–6 order energy gaps; H-E2-impact by signature. The open problem is now narrow and specific: (1) does a ≳10²⁶ J stored-energy reservoir exist in the trigger region, and (2) is η_mech≳ a few percent achievable? AR-1 is not solved here — but it is bounded, its under-determination is localized to a single admissible mechanism, and it is made testable.

FALSIFIER (AR-1-source; pre-register in config/constraints.yml).

UNLOCK only if an independent geophysical or fossil reservoir of the required magnitude (≳10²⁶ J stored — e.g. a deep low-velocity / high-conductivity / over-pressured anomaly, or its fossil remnant, beneath the trigger region) is identified, and a conversion path with η_mech≳ few % is demonstrated.
FAIL if no sufficient stored-energy reservoir can be identified at the required magnitude: the rapid trigger is then energetically unsourced, the rapid-trigger branch (AR-1) is rejected, and the slow-spreading default is not displaced.

This is a necessary-condition gate on the trigger; like the chronology firewall (Section §20), it does not by itself decide the absolute timescale.

Master-scale extrapolation: bounding the lab→Earth leap

The mechanism's quantitative core (jamming fraction, friction collapse) is established at laboratory / simulation scale (mm–cm grains, idealized disks). Whether that physics governs a continental (~10⁶ m) shear zone — a ~8–10 order-of-magnitude leap — is the master-scale extrapolation, held open as HOLD (Section §16). As with AR-1 (Section §17) we do not claim to close it; we bound it, separating what transfers from what does not. Reproduced in atl_bundle/engine/c19_master_scale.py (checks C19a–c).

What transfers.

Regime (dimensionless): the inertial number I=γ d√(ρ/σₙ) is ≪1 at both lab and lithospheric conditions (I_Earth~10⁻⁴), so both sit in the dense / quasi-static granular regime where jamming physics applies.
Continuum limit: finite-size corrections to φ_jam scale as 1/N; with a total grain count N~10²¹ the correction vanishes, so the large scale is the clean (N→∞) limit for the jamming fraction. Statistics is not the obstacle. (A genuinely separate caveat is shear-zone thinness, h/d~30 grains, a localization question, not a φ_jam question.)
The load-bearing phenomenon: dramatic dynamic weakening at seismic slip rates is experimentally established at lithospheric normal stress. High-velocity rotary-shear experiments show μ dropping from Byerlee (~0.6) to ~0.1 at V~1 m s⁻¹ (Di Toro et al. 2011); the Tohoku/Japan-Trench fault is measured <0.2, and catastrophic landslide surfaces reach 0.05–0.2 [R12]. A ~6× weakening is thus confirmed at the relevant conditions — the existence of the collapse is not in doubt.

What does not (yet) transfer — and the honest gap.

Exact φ_jam: the value is dimension/regime-specific (2D bidisperse ≈0.842, used here; 3D random close packing ≈0.64), and at σₙ~150 MPa the ratio σₙ/σ_crush~0.5 means grains crush — driving toward fractal gouge whose packing differs from the idealized value. The exact φ_jam is therefore not directly transferable.
The magnitude μ_eff≈0.002: this is a ~270× weakening, at or beyond the experimental tail. It is reachable only in the near-complete liquefaction limit: with μ_eff=μ(1-P_pore/σₙ) and μ≈0.6, it requires pore pressure within ~0.4% of lithostatic (λ≈0.996). This is extreme but well-defined — and is the same σ'→0 endpoint that mainstream thermal-pressurization models reach. So the jamming–liquefaction picture and the standard thermal-pressurization picture converge on the same load-bearing condition.

Verdict — master-scale = HOLD, separated. The qualitative mechanism, the dense-granular regime, the continuum limit, and the existence of dynamic weakening all transfer; the exact φ_jam and the extreme magnitude μ_eff≈0.002 (near-complete liquefaction) do not, and remain the load-bearing HOLD.

FALSIFIER (master-scale; pre-register in config/constraints.yml).

UNLOCK if high-σₙ (~100 MPa), high-V (~1 m s⁻¹) gouge experiments or natural fault fabrics demonstrate sustained μ_eff≲0.01 (λ≳0.98) over the required displacement, and the comminution / fractal-gouge evolution matches prediction.
FAIL if the lowest sustained μ_eff achievable at lithospheric conditions is ≳0.1: the suction work then cannot close (the Section §17–§17 budgets fail) and the rapid branch is rejected.

This gates the magnitude, not the existence, of weakening; like the chronology firewall it does not by itself establish the timescale. [R12] is added to Section §8.