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.17 · Electric 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
• Onsager–Casimir reciprocity · constitutive-relation · listed, never decisive
  L_ij(B) = ε_i ε_j L_ji(−B): the cross-coefficients of coupled linear transport are equal up to the time-reversal parities ε of the variables and reversal of the magnetic field; L_ij = L_ji is the zero-field, even-parity case

Steps

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

   electrical → thermal · loss to thermal

   • a current through a junction of dissimilar conductors

   solid · conductor required

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

   thermal → thermal

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

   thermal → spin · loss to thermal

   • a heavy metal with strong spin–orbit coupling (Pt, W) under a longitudinal temperature gradient; detected through the magnetoresistance of an adjacent magnetic insulator

   solid · conductor required · temperature gradient required

   refs [3] [4]
4. 04
   Spin Nernst effect —produces→ Spin currentestablishedclaim record

   spin → spin

   refs [3] [4]
5. 05
   Spin current —drives→ Inverse spin Hall effectestablishedclaim record

   spin → electrical · loss to thermal

   • a heavy metal with strong spin–orbit coupling (Pt, Ta, W); works at room temperature

   solid · conductor required · room temperature

   refs [5] [6]
6. 06
   Inverse spin Hall effect —produces→ Charge carriersestablishedclaim record

   electrical → electrical

   refs [5] [6]
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 [7]

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 · 7

1. [1]
   J. C. A. Peltier. Nouvelles expériences sur la caloricité des courants électriques (1834)

   Annales de Chimie et de Physique 56, 371–386 · paper, no DOI · record
2. [2]
   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
3. [3]
   S. Meyer et al.. Observation of the spin Nernst effect (2017)

   Nature Materials 16, 977-981 · doi:10.1038/nmat4964 · crossref ✓ 2026-09-20 · record
4. [4]
   A. Bose, A. A. Tulapurkar. Recent advances in the spin Nernst effect (2019)

   Journal of Magnetism and Magnetic Materials 491, 165526 · doi:10.1016/j.jmmm.2019.165526 · crossref ✓ 2026-09-20 · record
5. [5]
   E. Saitoh et al.. Conversion of spin current into charge current at room temperature: Inverse spin-Hall effect (2006)

   Applied Physics Letters 88, 182509 · doi:10.1063/1.2199473 · crossref ✓ 2026-09-19 · record
6. [6]
   J. Sinova et al.. Spin Hall effects (2015)

   Reviews of Modern Physics 87, 1213 · doi:10.1103/RevModPhys.87.1213 · crossref ✓ 2026-09-19 · record
7. [7]
   N. W. Ashcroft, N. D. Mermin. Solid State Physics (1976)

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