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.37 · Temperature gradient × Thermo-osmoticfamily: Thermo-osmoticD.01 × C.12 · Temperature gradient × Triboelectricfamily: Triboelectric

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→ 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 [1] [2]
2. 02
   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 [1] [3]
3. 03
   Fluid flow —drives→ Flow-induced vibrationestablishedclaim record

   kinetic → mechanical · loss to thermal

   • a bluff or flexible body in the produced stream at a Reynolds number where vortex shedding locks to a structural mode

   bulk flow required

   refs [4]
4. 04
   Flow-induced vibration —produces→ Mechanical vibrationestablishedclaim record

   mechanical → mechanical

   refs [4]
5. 05
   Mechanical vibration —drives→ Triboelectric effectestablishedclaim record

   mechanical → electrical · loss to thermal

   • vibration or motion that repeatedly contacts and separates two dissimilar surfaces

   solid · dielectric required

   refs [5] [6]
6. 06
   Triboelectric effect —produces→ Separated surface chargeestablishedclaim record

   electrical → electrical

   refs [5] [7]
7. 07
   Separated surface charge —converts into→ Electrical workestablishedclaim record

   electrical → electrical · loss to thermal

   • electrodes on the charged surfaces connected through a load

   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 · 7

1. [1]
   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
2. [2]
   S. R. de Groot, P. Mazur. Non-Equilibrium Thermodynamics (1962)

   North-Holland · book, no DOI · record
3. [3]
   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
4. [4]
   H. B. Radousky, H. Liang. Energy harvesting: an integrated view of materials, devices and applications (2012)

   Nanotechnology 23, 502001 · doi:10.1088/0957-4484/23/50/502001 · crossref ✓ 2026-09-19 · record
5. [5]
   F.-R. Fan, Z.-Q. Tian, Z. L. Wang. Flexible triboelectric generator (2012)

   Nano Energy 1, 328–334 · doi:10.1016/j.nanoen.2012.01.004 · crossref ✓ 2026-09-19 · record
6. [6]
   C. Wu et al.. Triboelectric nanogenerator: a foundation of the energy for the new era (2019)

   Advanced Energy Materials 9, 1802906 · doi:10.1002/aenm.201802906 · crossref ✓ 2026-09-19 · record
7. [7]
   D. J. Lacks, T. Shinbrot. Long-standing and unresolved issues in triboelectric charging (2019)

   Nature Reviews Chemistry 3, 465–476 · doi:10.1038/s41570-019-0115-1 · crossref ✓ 2026-09-19 · record