Physical Transformation AtlasPTA
Constraint · constraint:onsager-reciprocity

Onsager–Casimir reciprocity

Every direct effect has a converse of fixed magnitude. A relation between coefficients, not an efficiency ceiling: it is recorded with governed_by and is never an applicable bound.

Atlas record: 6 claims reference this constraint — 6 established.

Explorerelations · sources · cite

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

6claims0enumerated routes0routes with complete-composition evidence0candidate routes not searched8cited sources

Relations

governed by · 6
Villari effect—governed by→Onsager–Casimir reciprocityestablished
  • Villari and Joule magnetostriction are converse effects with equal coefficients
Streaming potential—governed by→Onsager–Casimir reciprocityestablished
  • streaming current and electro-osmosis are reciprocal
Dufour effect—governed by→Onsager–Casimir reciprocityestablished
  • near equilibrium the properly defined heat–mass Onsager cross-coefficients are reciprocal when fluxes and conjugate forces use the same convention; this does not imply numerical equality of the convention-dependent Soret and Dufour coefficients
Inverse spin Hall effect—governed by→Onsager–Casimir reciprocityestablished
  • the spin Hall and inverse spin Hall angles are equal
Seebeck effect—governed by→Onsager–Casimir reciprocityestablished
  • Seebeck and Peltier coefficients are linked by Π = S·T
Soret effect—governed by→Onsager–Casimir reciprocityestablished
  • the Soret and Dufour coefficients are Onsager-reciprocal

Cited sources · 8

  1. [1]
    J. P. Joule. On the effects of magnetism upon the dimensions of iron and steel bars (1847)
    Philosophical Magazine 30, 76–87 · doi:10.1080/14786444708645656 · crossref ✓ 2026-09-19 · record
  2. [2]
    E. Villari. Ueber die Aenderungen des magnetischen Moments, welche der Zug und das Hindurchleiten eines galvanischen Stroms in einem Stabe von Stahl oder Eisen hervorbringen (1865)
    Annalen der Physik 202, 87–122 · doi:10.1002/andp.18652020906 · crossref ✓ 2026-09-19 · record
  3. [3]
    S. R. de Groot, P. Mazur. Non-Equilibrium Thermodynamics (1962)
    North-Holland · book, no DOI · record
  4. [4]
    L. Onsager. Reciprocal relations in irreversible processes. I. (1931)
    Physical Review 37, 405 · doi:10.1103/PhysRev.37.405 · crossref ✓ 2026-09-19 · record
  5. [5]
    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
  6. [6]
    A. Würger. Do thermal diffusion and Dufour coefficients satisfy Onsager's reciprocity relation? (2014)
    The European Physical Journal E 37, 96 · doi:10.1140/epje/i2014-14096-y · crossref ✓ 2026-09-20 · record
  7. [7]
    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
  8. [8]
    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

Cite this entity

Physical Transformation Atlas (2026). entity constraint:onsager-reciprocity: Onsager–Casimir reciprocity. Dataset revision rbfbfcbb70e57 (hash of the canonical data). https://physical-transformation-atlas.wldud5192.workers.dev/e/constraint/onsager-reciprocity

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