Nuclear binding-energy difference → Electrical work

Matrix context

D = disequilibrium row · C = coupling family column. A cell reads the state of the atlas for that pair.

D.20 × C.27 · Nuclear binding-energy difference × Nuclear heatfamily: Nuclear heatD.20 × C.03 · Nuclear binding-energy difference × Thermoacousticfamily: ThermoacousticD.20 × C.10 · Nuclear binding-energy difference × Piezoelectricfamily: Piezoelectric

Typed bounds on this route

Every limit the atlas holds for this route, as constraint records: reached through bounded_by claims on the route's own entities. Hard bounds (an upper bound or a formula) decide the thermodynamic-bound check above; benchmarks, constitutive relations and resource limits are listed and never decisive. No prose limit exists anywhere (pass 42).

• Carnot limit · formula-bound · hard, applies to this route
  η ≤ 1 − T_c/T_h for any heat engine between reservoirs at T_h and T_c
• Electromechanical coupling factor · formula-bound · hard, applies to this route
  converted fraction per cycle ≤ k² = d²/(s·ε)

Steps

1. 01
   Nuclear binding-energy difference —drives→ Nuclear fusiondemonstratedclaim record

   nuclear → kinetic · loss to radiative

   • for a power-producing D–T thermonuclear plasma: ion temperatures of order 10 keV and a sufficient density–confinement product (Lawson); these are power-balance conditions, not prerequisites for an individual fusion reaction

   plasma · above ~700 K

   Fusion reactions and target-level fusion energy release are experimentally demonstrated (target gain > 1 at NIF, 2022–2024); net electrical output from a fusion power plant is not.

   refs [1] [2] [3]
2. 02
   Nuclear fusion —produces→ Temperature gradientdemonstratedclaim record

   kinetic → thermal · loss to radiative

   • energetic products (neutrons, alphas) deposit their kinetic energy in a blanket or the plasma, which then runs hotter than its surroundings

   refs [2] [3]
3. 03
   Temperature gradient —drives→ Thermoacoustic effectestablishedclaim record

   thermal → acoustic · loss to thermal

   |∇T_crit| = β T_m ω |p₁| / (ρ_m c_p |u₁|); prime-mover onset requires |∇T| > |∇T_crit| · critical-gradient factor β T_m ω/(ρ_m c_p u₁) [K/(Pa·m)]

   p₁ and u₁ are the local first-order acoustic pressure and particle-velocity amplitudes; β is the volumetric thermal expansion coefficient (β T_m ≈ 1 for an ideal gas); this is the linear short-stack / standing-wave criterion of Swift 1988 — above the critical gradient the stack amplifies the wave, below it the same interaction pumps heat — not a closed-form performance law for every travelling-wave regenerator.

   • temperature gradient along the stack steeper than the critical gradient set by the acoustic pressure and displacement amplitudes
   • a resonant gas column

   gas · temperature gradient required

   refs [4]
4. 04
   Thermoacoustic effect —produces→ Acoustic waveestablishedclaim record

   acoustic → acoustic

   • travelling-wave thermoacoustic regime with a non-zero time-averaged acoustic power flux; pressure and particle velocity have the phase relation required for directed acoustic power (a looped tube or a travelling-wave regenerator), unlike the standing wave of a straight resonator

   gas

   refs [5] [6]
5. 05
   Acoustic wave —drives→ Direct piezoelectric effectdemonstratedclaim record

   acoustic → electrical · loss to thermal

   • sound pressure strains a compliant piezoelectric membrane or plate; standing and travelling waves both serve, the response following the pressure oscillation

   solid

   refs [7] [8]
6. 06
   Direct piezoelectric effect —produces→ Separated surface chargeestablishedclaim record

   electrical → electrical

   refs [9]
7. 07
   Separated surface charge —converts into→ Electrical workestablishedclaim record

   electrical → electrical · loss to thermal

   • electrodes on the charged surfaces connected through a load

   refs [10]

Evidence for the complete composition · 0

No source on record for this exact composition. The sources below support the individual steps, not the route as a whole.

Evidence for the constituent relations · 10

1. [1]
   H. A. Bethe. Energy production in stars (1939)

   Physical Review 55, 434 · doi:10.1103/PhysRev.55.434 · crossref ✓ 2026-09-19 · record
2. [2]
   J. D. Lawson. Some criteria for a power producing thermonuclear reactor (1957)

   Proceedings of the Physical Society B 70, 6–10 · doi:10.1088/0370-1301/70/1/303 · crossref ✓ 2026-09-19 · record
3. [3]
   H. Abu-Shawareb, et al. (Indirect Drive ICF Collaboration). Achievement of target gain larger than unity in an inertial fusion experiment (2024)

   Physical Review Letters 132, 065102 · doi:10.1103/PhysRevLett.132.065102 · crossref ✓ 2026-09-19 · record
4. [4]
   G. W. Swift. Thermoacoustic engines (1988)

   Journal of the Acoustical Society of America 84, 1145–1180 · doi:10.1121/1.396617 · crossref ✓ 2026-09-19 · record
5. [5]
   T. Yazaki et al.. Traveling Wave Thermoacoustic Engine in a Looped Tube (1998)

   Physical Review Letters 81, 3128–3131 · doi:10.1103/PhysRevLett.81.3128 · record
6. [6]
   S. Backhaus, G. W. Swift. A thermoacoustic-Stirling heat engine: Detailed study (2000)

   Journal of the Acoustical Society of America 107, 3148–3166 · doi:10.1121/1.429343 · record
7. [7]
   Y. Zheng et al.. Thermoacoustic energy harvesting using thermally-stabilized polyacrylonitrile nanofibers (2022)

   Nano Energy 95, 106995 · doi:10.1016/j.nanoen.2022.106995 · record
8. [8]
   J. Smoker et al.. Energy harvesting from a standing wave thermoacoustic-piezoelectric resonator (2012)

   Journal of Applied Physics 111, 104901 · doi:10.1063/1.4712630 · record
9. [9]
   J. F. Nye. Physical Properties of Crystals: Their Representation by Tensors and Matrices (1985)

   Oxford University Press · book, no DOI · record
10. [10]
    H. B. Radousky, H. Liang. Energy harvesting: an integrated view of materials, devices and applications (2012)

    Nanotechnology 23, 502001 · doi:10.1088/0957-4484/23/50/502001 · crossref ✓ 2026-09-19 · record