Electric potential difference → Electrical work

Matrix context

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

D.06 × C.01 · Electric potential difference × Thermoelectricfamily: ThermoelectricD.06 × C.06 · Electric potential difference × Thermomagneticfamily: ThermomagneticD.06 × C.14 · Electric potential difference × Electromagnetic inductionfamily: Electromagnetic induction

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

Steps

1. 01
   Electric potential difference —drives→ Ettingshausen effectestablishedclaim record

   electrical → thermal

   • a current in a conductor with a perpendicular magnetic field

   solid · conductor required · magnetic field required

   refs [1] [2]
2. 02
   Ettingshausen effect —produces→ Temperature gradientestablishedclaim record

   thermal → thermal

   refs [2] [3]
3. 03
   Temperature gradient —drives→ Thermomagnetic (Curie-point) transitiondemonstratedclaim record

   thermal → magnetic · loss to thermal

   • a soft ferromagnet with its Curie temperature between the hot and cold reservoir temperatures (Gd ≈ 293 K)
   • the element must be cycled between the reservoirs, so a heat-switch or motion is needed

   solid · ferromagnet required · temperature gradient required

   refs [4] [5] [6]
4. 04
   Thermomagnetic (Curie-point) transition —produces→ Changing magnetic fluxestablishedclaim record

   magnetic → magnetic

   refs [5]
5. 05
   Changing magnetic flux —drives→ Electromagnetic inductionestablishedclaim record

   magnetic → electrical · loss to thermal

   ℰ = −dΦ/dt · rate of change [1/s]

   • the changing flux threads a conducting loop

   conductor required

   refs [7] [8]
6. 06
   Electromagnetic induction —produces→ Charge carriersestablishedclaim record

   electrical → electrical · loss to thermal

   refs [7] [8]
7. 07
   Charge carriers —converts into→ Electrical workestablishedclaim record

   electrical → electrical · loss to thermal

   • carriers driven through an external load at the potential difference the source maintains

   refs [9]

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 · 9

1. [1]
   A. von Ettingshausen, W. Nernst. Ueber das Auftreten electromotorischer Kräfte in Metallplatten, welche von einem Wärmestrome durchflossen werden und sich im magnetischen Felde befinden (1886)

   Annalen der Physik 265, 343–347 · doi:10.1002/andp.18862651010 · crossref ✓ 2026-09-19 · record
2. [2]
   H. B. Callen. The application of Onsager's reciprocal relations to thermoelectric, thermomagnetic, and galvanomagnetic effects (1948)

   Physical Review 73, 1349 · doi:10.1103/PhysRev.73.1349 · crossref ✓ 2026-09-19 · record
3. [3]
   H. J. Goldsmid. Introduction to Thermoelectricity (2nd ed.) (2016)

   Springer Series in Materials Science 121 · doi:10.1007/978-3-662-49256-7 · crossref ✓ 2026-09-19 · record
4. [4]
   N. Tesla. Pyromagneto-electric generator (US Patent 428,057) (1890)

   United States Patent Office · patents.google.com/patent/US428057A · record
5. [5]
   R. A. Kishore, S. Priya. A review on design and performance of thermomagnetic devices (2018)

   Renewable and Sustainable Energy Reviews 81, 33–44 · doi:10.1016/j.rser.2017.07.035 · crossref ✓ 2026-09-19 · record
6. [6]
   A. Waske, et al.. Energy harvesting near room temperature using a thermomagnetic generator with a pretzel-like magnetic flux topology (2019)

   Nature Energy 4, 68–74 · doi:10.1038/s41560-018-0306-x · crossref ✓ 2026-09-19 · record
7. [7]
   M. Faraday. Experimental researches in electricity (1832)

   Philosophical Transactions of the Royal Society 122, 125–162 · doi:10.1098/rstl.1832.0006 · crossref ✓ 2026-09-19 · record
8. [8]
   L. D. Landau, E. M. Lifshitz, L. P. Pitaevskii. Electrodynamics of Continuous Media (Course of Theoretical Physics, Vol. 8, 2nd ed.) (1984)

   Pergamon · book, no DOI · record
9. [9]
   N. W. Ashcroft, N. D. Mermin. Solid State Physics (1976)

   Holt, Rinehart and Winston · book, no DOI · record