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.37 · Electric potential difference × Thermo-osmoticfamily: Thermo-osmoticD.06 × C.23 · Electric potential difference × Electrokineticfamily: Electrokinetic

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→ 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→ Thermo-osmosisestablishedclaim record

   thermal → kinetic · loss to thermal

   • a membrane separating two reservoirs of the same liquid at different temperatures; the flow direction depends on the membrane–liquid interaction

   selective membrane required · temperature gradient required · liquid

   refs [4] [5]
4. 04
   Thermo-osmosis —produces→ Fluid flowestablishedclaim record

   kinetic → kinetic

   Confined in a nanochannel (Zhao 2020) or collected as a pressurised bulk flow: Straub et al. 2016 measured 3.53 W/m² of hydraulic power from the thermo-osmotic flux, so the produced flow can load a turbine.

   refs [4] [6]
5. 05
   Fluid flow —drives→ Streaming potentialreplicatedclaim record

   kinetic → electrical · loss to thermal

   • the produced liquid flow passes a charged surface or through a charged channel; the charged boundary is a condition of the step
   • not something the upstream flow provides

   aqueous medium required · bulk flow required · charged surface required

   refs [7] [8]
6. 06
   Streaming potential —produces→ Ionic currentestablishedclaim record

   electrical → electrical

   refs [8] [9]
7. 07
   Ionic current —converts into→ Electrical workestablishedclaim record

   electrical → electrical · loss to thermal

   • electrodes exchange the ionic current for an electronic current through the external load

   refs [10]

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 · 10

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]
   V. M. Barragán, S. Kjelstrup. Thermo-osmosis in Membrane Systems: A Review (2017)

   Journal of Non-Equilibrium Thermodynamics, 42 · doi:10.1515/jnet-2016-0088 · crossref ✓ 2026-09-20 · record
5. [5]
   S. R. de Groot, P. Mazur. Non-Equilibrium Thermodynamics (1962)

   North-Holland · book, no DOI · record
6. [6]
   A. P. Straub et al.. Harvesting low-grade heat energy using thermo-osmotic vapour transport through nanoporous membranes (2016)

   Nature Energy 1, 16090 · doi:10.1038/nenergy.2016.90 · crossref ✓ 2026-09-20 · record
7. [7]
   J. Yin, et al.. Generating electricity by moving a droplet of ionic liquid along graphene (2014)

   Nature Nanotechnology 9, 378–383 · doi:10.1038/nnano.2014.56 · crossref ✓ 2026-09-19 · record
8. [8]
   J. Yang et al.. Electrokinetic microchannel battery by means of electrokinetic and microfluidic phenomena (2003)

   Journal of Micromechanics and Microengineering 13, 963 · doi:10.1088/0960-1317/13/6/320 · crossref ✓ 2026-09-19 · record
9. [9]
   R. J. Hunter. Zeta Potential in Colloid Science: Principles and Applications (1981)

   Academic Press · doi:10.1016/C2013-0-07389-6 · crossref ✓ 2026-09-19 · record
10. [10]
    A. J. Bard, L. R. Faulkner. Electrochemical Methods: Fundamentals and Applications (2nd ed.) (2001)

    Wiley · book, no DOI · record