Chemical 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.05 × C.29 · Chemical potential difference × Thermochemicalfamily: ThermochemicalD.05 × C.17 · Chemical potential difference × Spin caloritronicfamily: Spin caloritronic

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
   Chemical potential difference —drives→ Combustionestablishedclaim record

   chemical → thermal · loss to radiative

   • fuel, oxidiser and an ignition source; flame temperature 1500–2500 K

   gas · above ~700 K

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

   thermal → thermal

   refs [1]
3. 03
   Temperature gradient —drives→ Anomalous Nernst effectreplicatedclaim record

   thermal → electrical · loss to thermal

   • a magnetised ferromagnet or topological semimetal; no external field needed once magnetised

   solid · ferromagnet required · temperature gradient required

   refs [2] [3]
4. 04
   Anomalous Nernst effect —produces→ Charge carriersreplicatedclaim record

   electrical → electrical

   refs [2] [3]
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 [4]

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 · 4

1. [1]
   A. Bejan. Advanced Engineering Thermodynamics (4th ed.) (2016)

   Wiley · doi:10.1002/9781119245964 · crossref ✓ 2026-09-19 · record
2. [2]
   A. Sakai, et al.. Giant anomalous Nernst effect and quantum-critical scaling in a ferromagnetic semimetal (2018)

   Nature Physics 14, 1119–1124 · doi:10.1038/s41567-018-0225-6 · crossref ✓ 2026-09-19 · record
3. [3]
   G. E. W. Bauer, E. Saitoh, B. J. van Wees. Spin caloritronics (2012)

   Nature Materials 11, 391–399 · doi:10.1038/nmat3301 · crossref ✓ 2026-09-19 · record
4. [4]
   N. W. Ashcroft, N. D. Mermin. Solid State Physics (1976)

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