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.09 · Electric potential difference × Caloric (magneto/electro/elasto)family: Caloric (magneto/electro/elasto)D.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→ Thermal shape-memory effectestablishedclaim record

   thermal → mechanical · loss to thermal

   • a shape-memory alloy (NiTi) cycled between a hot reservoir above its austenite finish temperature and a cold one below its martensite finish temperature, under load

   solid · temperature gradient required

   refs [4] [5]
4. 04
   Thermal shape-memory effect —produces→ Mechanical motionestablishedclaim record

   mechanical → mechanical

   refs [5] [4]
5. 05
   Mechanical motion —drives→ Rotating-machine generator actionestablishedclaim record

   mechanical → electrical · loss to thermal

   • a shaft turning a rotor inside a stator, or a magnet moved past a coil

   conductor required · magnetic field required

   refs [6] [7]
6. 06
   Rotating-machine generator action —produces→ Charge carriersestablishedclaim record

   electrical → electrical · loss to thermal

   refs [6] [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]
   K. Otsuka (ed.), C. M. Wayman (ed.). Shape Memory Materials (1998)

   Cambridge University Press · book, no DOI · record
5. [5]
   P. Kumar et al.. Shape memory alloy engine for high efficiency low-temperature gradient thermal to electrical conversion (2019)

   Applied Energy 251, 113277 · doi:10.1016/j.apenergy.2019.05.080 · crossref ✓ 2026-09-20 · record
6. [6]
   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
7. [7]
   S. L. Dixon, C. A. Hall. Fluid Mechanics and Thermodynamics of Turbomachinery (7th ed.) (2014)

   Butterworth-Heinemann · doi:10.1016/C2011-0-05059-7 · 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