Temperature gradient → Electrical work

Matrix context

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

D.01 × C.09 · Temperature gradient × Caloric (magneto/electro/elasto)family: Caloric (magneto/electro/elasto)D.01 × C.14 · Temperature gradient × 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
   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 [1] [2]
2. 02
   Thermal shape-memory effect —produces→ Mechanical motionestablishedclaim record

   mechanical → mechanical

   refs [2] [1]
3. 03
   Mechanical motion —drives→ Electromagnetic inductionestablishedclaim record

   mechanical → electrical · loss to thermal

   • a magnet moving relative to a coil

   conductor required · magnetic field required

   refs [3] [4]
4. 04
   Electromagnetic induction —produces→ Charge carriersestablishedclaim record

   electrical → electrical · loss to thermal

   refs [3] [5]
5. 05
   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 [6]

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 · 6

1. [1]
   K. Otsuka (ed.), C. M. Wayman (ed.). Shape Memory Materials (1998)

   Cambridge University Press · book, no DOI · record
2. [2]
   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
3. [3]
   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
4. [4]
   S. P. Beeby, et al.. A micro electromagnetic generator for vibration energy harvesting (2007)

   Journal of Micromechanics and Microengineering 17, 1257 · doi:10.1088/0960-1317/17/7/007 · crossref ✓ 2026-09-19 · record
5. [5]
   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
6. [6]
   N. W. Ashcroft, N. D. Mermin. Solid State Physics (1976)

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