Concentration gradient → Useful heat

Matrix context

D = disequilibrium row · C = coupling family column. A cell reads the state of the atlas for that pair.

D.03 × C.33 · Concentration gradient × Thermodiffusivefamily: Thermodiffusive

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).

• 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
   Concentration gradient —drives→ Dufour effectestablishedclaim record

   chemical → thermal

   • a composition gradient in a liquid or gas mixture; the heat flux is the Onsager-reciprocal partner of Soret thermodiffusion

   refs [1] [2]
2. 02
   Dufour effect —produces→ Heat flowestablishedclaim record

   thermal → thermal

   refs [1] [2]
3. 03
   Heat flow —converts into→ Useful heatestablishedclaim record

   thermal → thermal

   • heat delivered at a temperature above the point of use

   refs [3]

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 · 3

1. [1]
   R. L. Rowley, F. H. Horne. The Dufour effect. II. Experimental confirmation of the Onsager heat–mass reciprocal relation for a binary liquid mixture (1978)

   The Journal of Chemical Physics 68, 325-326 · doi:10.1063/1.435458 · 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. Bejan. Advanced Engineering Thermodynamics (4th ed.) (2016)

   Wiley · doi:10.1002/9781119245964 · crossref ✓ 2026-09-19 · record