Electric potential difference → Useful heat

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.08 · Electric potential difference × Heat engine (thermomechanical)family: Heat engine (thermomechanical)D.06 × C.09 · Electric potential difference × Caloric (magneto/electro/elasto)family: Caloric (magneto/electro/elasto)

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, filtered out by its applicability
  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→ 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→ Thermal expansionestablishedclaim record

   thermal → mechanical

   refs [3] [4]
4. 04
   Thermal expansion —produces→ Mechanical stress or strainestablishedclaim record

   mechanical → mechanical

   • non-uniform thermal expansion is mechanically incompatible across adjacent regions of a solid, or is constrained by an adjoining material or structure, producing a strain or stress gradient; the constraining region may be the cooler part of the same continuous specimen rather than a separate stiffer body

   solid

   refs [5] [4]
5. 05
   Mechanical stress or strain —drives→ Elastocaloric effectreplicatedclaim record

   mechanical → thermal

   • stress large enough to drive the martensitic transformation of a shape-memory alloy

   solid

   refs [6] [7]
6. 06
   Elastocaloric effect —converts into→ Useful heatdemonstratedclaim record

   thermal → thermal · loss to thermal

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

   Wiley · doi:10.1002/9781119245964 · crossref ✓ 2026-09-19 · record
4. [4]
   S. Iwakiri, Y. Miyata, T. Mori. Observation of universal thermopolarization effect in insulators (2026)

   arXiv:2605.17224 (17 May 2026), National Institute for Materials Science, Tsukuba · arxiv.org/abs/2605.17224 · record
5. [5]
   J. F. Nye. Physical Properties of Crystals: Their Representation by Tensors and Matrices (1985)

   Oxford University Press · book, no DOI · record
6. [6]
   J. Tušek et al.. A regenerative elastocaloric heat pump (2016)

   Nature Energy 1, 16134 · doi:10.1038/nenergy.2016.134 · crossref ✓ 2026-09-19 · record
7. [7]
   X. Moya, S. Kar-Narayan, N. D. Mathur. Caloric materials near ferroic phase transitions (2014)

   Nature Materials 13, 439–450 · doi:10.1038/nmat3951 · crossref ✓ 2026-09-19 · record