Physical Transformation AtlasPTA
Disequilibrium · disequilibrium:temperature-gradient

Temperature gradient

Two regions at different temperatures. Heat flows down the gradient, and a fraction bounded by Carnot can be diverted into work.

symbol ∇TThermodynamicsenergy form thermalexergy positivealso: temperature difference, thermal gradient, ΔT, waste heat, body heat, hot and cold

Atlas record: 36 claims reference this disequilibrium — 26 established, 5 demonstrated, 3 replicated, 1 reported and 1 theoretically predicted.

Explorerelations · matrix context · routes · sources · cite

conditions: temperature gradient required
36claims542enumerated routes33routes with complete-composition evidence122candidate routes not searched57cited sources

Relations

drives · 27
Temperature gradient—drives→Alkali-metal thermal-to-electric conversiondemonstrated
  • sodium at 900–1300 K on the hot side of a β″-alumina electrolyte and a condenser at 400–700 K
Temperature gradient—drives→Ionic thermoelectric effectestablished
  • an electrolyte (liquid, gel or polymer) under a temperature difference; ionic Seebeck coefficients of 1–10 mV/K arise from differential thermodiffusion of cations and anions, without electrode redox entropy
Temperature gradient—drives→Marangoni effectestablished
  • thermocapillary case: surface tension falls with temperature, so a temperature gradient along the interface drives flow toward the cold side
Temperature gradient—drives→Spin Nernst effectestablished
  • a heavy metal with strong spin–orbit coupling (Pt, W) under a longitudinal temperature gradient; detected through the magnetoresistance of an adjacent magnetic insulator
Temperature gradient—drives→Thermo-osmosisestablished
  • a membrane separating two reservoirs of the same liquid at different temperatures; the flow direction depends on the membrane–liquid interaction
Temperature gradient—drives→Thermomagnetic convectionestablished
  • a ferrofluid whose magnetisation decreases with temperature, in a non-uniform magnetic field aligned with the temperature gradient
Temperature gradient—drives→Thermal shape-memory effectestablished
  • a shape-memory alloy (NiTi) cycled between a hot reservoir above its austenite finish temperature and a cold one below its martensite finish temperature, under load
Temperature gradient—drives→Thermochemical redox cycleestablished
  • a redox-active metal oxide (ceria, ferrites) reduced at 1400–1800 K, typically in a solar receiver, and re-oxidised by H₂O or CO₂ at 800–1200 K
Temperature gradient—drives→Thermopolarization effectreported
  • a spatial temperature gradient is applied across an insulating solid dielectric
  • this claim represents the direct thermopolarization contribution; a signal established to arise through thermal expansion → strain gradient → flexoelectricity belongs to that longer pathway instead
  • the solid spelling; the polar-liquid spelling is claim:temperature-drives-liquid-thermopolarization, with its own (simulation) evidence
P_i = γ_ij ∇_j T · thermopolarization coefficient γ [C/(m K)]
Temperature gradient—drives→Thermopolarization effecttheoretically predicted
  • a polar molecular liquid is maintained under a spatial temperature gradient
  • the response is the non-equilibrium polarization / electrostatic field of the liquid itself, not ionic thermodiffusion and not the pyroelectric response of an already ordered ferroelectric fluid (Máthé et al. 2022's ferroelectric-nematic thermomotor is that other coupling)
  • simulation only: no experiment has measured the polarization of an ordinary polar liquid under a temperature gradient (pass 32 web search, not a route-search-v1 negative)
E_∥ = S_TP ∇T · liquid thermopolarization coefficient S_TP [V/K]
Temperature gradient—drives→Spin Seebeck effectreplicated
  • a magnetised ferromagnet, metallic or insulating (YIG), under a temperature gradient
  • an adjacent spin sink (heavy-metal layer) is needed for the usual electrical detection through inverse spin Hall conversion, not for the spin-Seebeck response itself
Temperature gradient—drives→Seebeck effectestablished
  • a spatial temperature difference across a conductor or semiconductor
  • a closed circuit of dissimilar materials, or a single material with ends at different temperatures
ΔV = S · ΔT · Seebeck coefficient S [V/K]
Temperature gradient—drives→Thomson effectestablished
  • a current flowing along a temperature gradient in a single conductor
Temperature gradient—drives→Heat conductionestablished
q = −κ · ∇T · thermal conductivity κ [W/(m K)]
Temperature gradient—drives→Thermionic emissionestablished
  • cathode hot enough that kT is a useful fraction of the work function (typically > 1500 K for metals, lower for low-work-function coatings)
  • a cooler anode across a vacuum or caesium-vapour gap
Temperature gradient—drives→Thermoacoustic effectestablished
  • temperature gradient along the stack steeper than the critical gradient set by the acoustic pressure and displacement amplitudes
  • a resonant gas column
|∇T_crit| = β T_m ω |p₁| / (ρ_m c_p |u₁|); prime-mover onset requires |∇T| > |∇T_crit| · critical-gradient factor β T_m ω/(ρ_m c_p u₁) [K/(Pa·m)]
Temperature gradient—drives→Thermogalvanic effectestablished
  • two identical electrodes in one redox electrolyte held at different temperatures
  • a redox couple with large reaction entropy (ferri/ferrocyanide gives ≈ −1.4 mV/K)
ΔE = (ΔS_rxn / nF) · ΔT · thermogalvanic Seebeck coefficient [V/K]
Temperature gradient—drives→Thermally regenerative electrochemical cycledemonstrated
  • a battery chemistry whose open-circuit voltage changes with temperature by ≈ 1 mV/K
  • charge at one temperature, discharge at the other, with heat recuperation between the two
Temperature gradient—drives→Soret effectestablished
  • a liquid mixture or solution under a steady temperature gradient
Temperature gradient—drives→Nernst effectestablished
  • a magnetic field perpendicular to the temperature gradient; the transverse field is proportional to B and ∇T
E_y = N · B_z · ∇T_x · N·B (Nernst coefficient × field), in V/K [V/K]
Temperature gradient—drives→Anomalous Nernst effectreplicated
  • a magnetised ferromagnet or topological semimetal; no external field needed once magnetised
Temperature gradient—drives→Thermomagnetic (Curie-point) transitiondemonstrated
  • a soft ferromagnet with its Curie temperature between the hot and cold reservoir temperatures (Gd ≈ 293 K)
  • the element must be cycled between the reservoirs, so a heat-switch or motion is needed
Temperature gradient—drives→Working-fluid expansion (heat-engine cycle)established
  • a hot reservoir to heat the working fluid and a cold reservoir to condense or cool it
Temperature gradient—drives→Ocean thermal energy conversiondemonstrated
  • a ≈ 20 K difference between warm surface water and cold water from ~1000 m depth
Temperature gradient—drives→Thermal emissionestablished
  • an emitter hotter than the surface it faces
Temperature gradient—drives→Thermal expansionestablished
Temperature gradient—drives→Advective heat transportestablished
  • a bulk fluid flow connects the hotter and colder regions
  • for forced circulation the flow may be supplied by an external pump rather than generated by buoyancy
produces · 8
Combustion—produces→Temperature gradientestablished
Radioisotope heating—produces→Temperature gradientestablished
Nuclear fission—produces→Temperature gradientestablished
  • fragment and neutron kinetic energy thermalised in the fuel; the fuel runs hotter than the coolant
Nuclear fusion—produces→Temperature gradientdemonstrated
  • energetic products (neutrons, alphas) deposit their kinetic energy in a blanket or the plasma, which then runs hotter than its surroundings
Photothermal absorption—produces→Temperature gradientestablished
Peltier effect—produces→Temperature gradientestablished
Ettingshausen effect—produces→Temperature gradientestablished
Radiative sky cooling—produces→Temperature gradientreplicated
  • the cooled surface sits a few kelvin below ambient air
bounded by · 1
Temperature gradient—bounded by→Carnot limitestablished
  • conversion of a heat flow between reservoirs at T_h and T_c into work or a non-thermal free energy; the bound is evaluated against a datum that records both temperatures

Matrix context

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

C.01 ThermoelectricC.02 ThermionicC.03 ThermoacousticC.04 PyroelectricC.05 ThermogalvanicC.06 ThermomagneticC.07 ThermophotovoltaicC.08 Heat engine (thermomechanical)C.09 Caloric (magneto/electro/elasto)C.10 PiezoelectricC.11 FlexoelectricC.12 TriboelectricC.13 Electrostatic (variable capacitance)C.14 Electromagnetic inductionC.15 MagnetostrictiveC.16 MagnetoelectricC.17 Spin caloritronicC.18 PhotovoltaicC.19 PhotoelectrochemicalC.20 PhotothermalC.21 ElectrochemicalC.22 Osmotic / salinity-gradientC.23 ElectrokineticC.24 TurbomachineryC.25 MagnetohydrodynamicC.26 RadiovoltaicC.27 Nuclear heatC.28 RectennaC.29 ThermochemicalC.30 BiologicalC.31 Fluctuation / information-drivenC.32 Photon momentumC.33 ThermodiffusiveC.34 MarangoniC.35 AcoustoelectricC.36 PhotodiffusiveC.37 Thermo-osmoticC.38 ElectrohydrodynamicC.39 RadioluminescentC.40 Thermopolarization

Enumerated routes through this · 542 (showing 24)

Cited sources · 57

  1. [1]
    T. Cole. Thermoelectric energy conversion with solid electrolytes (1983)
    Science 221, 915–920 · doi:10.1126/science.221.4614.915 · crossref ✓ 2026-09-19 · record
  2. [2]
    M. Bonetti et al.. Huge Seebeck coefficients in nonaqueous electrolytes (2011)
    The Journal of Chemical Physics 134, 114513 · doi:10.1063/1.3561735 · crossref ✓ 2026-09-20 · record
  3. [3]
    D. Zhao, A. Würger, X. Crispin. Ionic thermoelectric materials and devices (2021)
    Journal of Energy Chemistry 61, 88-103 · doi:10.1016/j.jechem.2021.02.022 · crossref ✓ 2026-09-20 · record
  4. [4]
    L. E. Scriven, C. V. Sternling. The Marangoni Effects (1960)
    Nature 187, 186-188 · doi:10.1038/187186a0 · crossref ✓ 2026-09-20 · record
  5. [5]
    Q. Dai et al.. Directional interfacial motion of liquids: Fundamentals, evaluations, and manipulation strategies (2021)
    Tribology International 154, 106749 · doi:10.1016/j.triboint.2020.106749 · crossref ✓ 2026-09-20 · record
  6. [6]
    S. Meyer et al.. Observation of the spin Nernst effect (2017)
    Nature Materials 16, 977-981 · doi:10.1038/nmat4964 · crossref ✓ 2026-09-20 · record
  7. [7]
    A. Bose, A. A. Tulapurkar. Recent advances in the spin Nernst effect (2019)
    Journal of Magnetism and Magnetic Materials 491, 165526 · doi:10.1016/j.jmmm.2019.165526 · crossref ✓ 2026-09-20 · record
  8. [8]
    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
  9. [9]
    S. R. de Groot, P. Mazur. Non-Equilibrium Thermodynamics (1962)
    North-Holland · book, no DOI · record
  10. [10]
    R. E. Rosensweig. Ferrohydrodynamics (1985)
    Cambridge University Press · book, no DOI · record
  11. [11]
    S. A. Suslov. Peculiarities of Convective Heat and Mass Transfer in Magnetic Nanofluids (2023)
    ASME Journal of Heat and Mass Transfer 145(3), 030801 (online December 2022) · doi:10.1115/1.4055343 · crossref ✓ 2026-09-20 · record
  12. [12]
    K. Otsuka (ed.), C. M. Wayman (ed.). Shape Memory Materials (1998)
    Cambridge University Press · book, no DOI · record
  13. [13]
    P. Kumar et al.. Shape memory alloy engine for high efficiency low-temperature gradient thermal to electrical conversion (2019)
    Applied Energy 251, 113277 · doi:10.1016/j.apenergy.2019.05.080 · crossref ✓ 2026-09-20 · record
  14. [14]
    A. Steinfeld. Solar thermochemical production of hydrogen––a review (2005)
    Solar Energy 78, 603-615 · doi:10.1016/j.solener.2003.12.012 · crossref ✓ 2026-09-20 · record
  15. [15]
    S. Abanades. Redox Cycles, Active Materials, and Reactors Applied to Water and Carbon Dioxide Splitting for Solar Thermochemical Fuel Production: A Review (2022)
    Energies 15, 7061 · doi:10.3390/en15197061 · crossref ✓ 2026-09-20 · record
  16. [16]
    M. Marvan. The electric polarization induced by temperature gradient and associated thermoelectric effects (1969)
    Czechoslovak Journal of Physics B 19, 1240–1245 · doi:10.1007/bf01690309 · record
  17. [17]
    A. K. Tagantsev. Pyroelectric, piezoelectric, flexoelectric, and thermal polarization effects in ionic crystals (1987)
    Soviet Physics Uspekhi 30, 588–603 · doi:10.1070/PU1987v030n07ABEH002926 · record
  18. [18]
    V. A. Trepakov, K. M. Nurieva, A. K. Tagantsev. Recent developments of the thermopolarization effect investigation (1989)
    Ferroelectrics 94, 377–381 · doi:10.1080/00150198908014283 · record
  19. [19]
    Y. Onishi et al.. Theory of Thermopolarization Effect (2025)
    Nano Letters 25, 2763–2768 · doi:10.1021/acs.nanolett.4c05870 · record
  20. [20]
    A. L. Kholkin, V. A. Trepakov, G. A. Smolenskii. Thermopolarization currents in dielectrics (1982)
    JETP Letters 35 (3), 124–127 (Pis'ma Zh. Eksp. Teor. Fiz. 35, 103–106) · www.jetpletters.ru/ps/1313/article_19837.shtml · record
  21. [21]
    F. Bresme et al.. Water Polarization under Thermal Gradients (2008)
    Physical Review Letters 101, 020602 · doi:10.1103/PhysRevLett.101.020602 · record
  22. [22]
    J. Armstrong, F. Bresme. Temperature inversion of the thermal polarization of water (2015)
    Physical Review E 92, 060103 · doi:10.1103/PhysRevE.92.060103 · record
  23. [23]
    O. R. Gittus, P. Albella, F. Bresme. Polarization of acetonitrile under thermal fields via non-equilibrium molecular dynamics simulations (2020)
    The Journal of Chemical Physics 153, 204503 · doi:10.1063/5.0025148 · record
  24. [24]
    K. Uchida, et al.. Observation of the spin Seebeck effect (2008)
    Nature 455, 778–781 · doi:10.1038/nature07321 · crossref ✓ 2026-09-19 · record
  25. [25]
    K. Uchida, et al.. Spin Seebeck insulator (2010)
    Nature Materials 9, 894–897 · doi:10.1038/nmat2856 · crossref ✓ 2026-09-19 · record
  26. [26]
    G. E. W. Bauer, E. Saitoh, B. J. van Wees. Spin caloritronics (2012)
    Nature Materials 11, 391–399 · doi:10.1038/nmat3301 · crossref ✓ 2026-09-19 · record
  27. [27]
    M. Weiler et al.. Experimental test of the spin mixing interface conductivity concept (2013)
    Physical Review Letters 111, 176601 · doi:10.1103/PhysRevLett.111.176601 · crossref ✓ 2026-09-19 · record
  28. [28]
    T. J. Seebeck. Ueber die magnetische Polarisation der Metalle und Erze durch Temperatur-Differenz (1826)
    Annalen der Physik 82(2), 133–160 · doi:10.1002/andp.18260820202 · crossref ✓ 2026-09-19 · record
  29. [29]
    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
  30. [30]
    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
  31. [31]
    W. Thomson. On a mechanical theory of thermo-electric currents (1851)
    Proceedings of the Royal Society of Edinburgh 3, 91–98 · doi:10.1017/S0370164600027310 · crossref ✓ 2026-09-19 · record
  32. [32]
    A. Bejan. Advanced Engineering Thermodynamics (4th ed.) (2016)
    Wiley · doi:10.1002/9781119245964 · crossref ✓ 2026-09-19 · record
  33. [33]
    O. W. Richardson. On the negative radiation from hot platinum (1901)
    Proceedings of the Cambridge Philosophical Society 11, 286–295 · paper, no DOI · record
  34. [34]
    G. N. Hatsopoulos, E. P. Gyftopoulos. Thermionic Energy Conversion, Vol. 1: Processes and Devices (1973)
    MIT Press · book, no DOI · record
  35. [35]
    G. W. Swift. Thermoacoustic engines (1988)
    Journal of the Acoustical Society of America 84, 1145–1180 · doi:10.1121/1.396617 · crossref ✓ 2026-09-19 · record
  36. [36]
    T. I. Quickenden, Y. Mua. A review of power generation in aqueous thermogalvanic cells (1995)
    Journal of the Electrochemical Society 142, 3985 · doi:10.1149/1.2048446 · crossref ✓ 2026-09-19 · record
  37. [37]
    M. F. Dupont, D. R. MacFarlane, J. M. Pringle. Thermo-electrochemical cells for waste heat harvesting – progress and perspectives (2017)
    Chemical Communications 53, 6288–6302 · doi:10.1039/C7CC02160G · crossref ✓ 2026-09-19 · record
  38. [38]
    S. W. Lee et al.. An electrochemical system for efficiently harvesting low-grade heat energy (2014)
    Nature Communications 5, 3942 · doi:10.1038/ncomms4942 · crossref ✓ 2026-09-19 · record
  39. [39]
    C. Soret. Sur l'état d'équilibre que prend au point de vue de sa concentration une dissolution saline primitivement homogène dont deux parties sont portées à des températures différentes (1879)
    Archives des Sciences Physiques et Naturelles 2, 48–61 · paper, no DOI · record
  40. [40]
    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
  41. [41]
    A. Sakai, et al.. Giant anomalous Nernst effect and quantum-critical scaling in a ferromagnetic semimetal (2018)
    Nature Physics 14, 1119–1124 · doi:10.1038/s41567-018-0225-6 · crossref ✓ 2026-09-19 · record
  42. [42]
    N. Tesla. Pyromagneto-electric generator (US Patent 428,057) (1890)
    United States Patent Office · patents.google.com/patent/US428057A · record
  43. [43]
    R. A. Kishore, S. Priya. A review on design and performance of thermomagnetic devices (2018)
    Renewable and Sustainable Energy Reviews 81, 33–44 · doi:10.1016/j.rser.2017.07.035 · crossref ✓ 2026-09-19 · record
  44. [44]
    A. Waske, et al.. Energy harvesting near room temperature using a thermomagnetic generator with a pretzel-like magnetic flux topology (2019)
    Nature Energy 4, 68–74 · doi:10.1038/s41560-018-0306-x · crossref ✓ 2026-09-19 · record
  45. [45]
    G. Walker. Stirling Engines (1980)
    Oxford University Press · book, no DOI · record
  46. [46]
    G. Claude. Power from the tropical seas (1930)
    Mechanical Engineering 52, 1039–1044 · paper, no DOI · record
  47. [47]
    P. T. Landsberg, G. Tonge. Thermodynamic energy conversion efficiencies (1980)
    Journal of Applied Physics 51, R1–R20 · doi:10.1063/1.328187 · crossref ✓ 2026-09-19 · record
  48. [48]
    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
  49. [49]
    U.S. Nuclear Regulatory Commission. Pressurized Water Reactors — how a typical commercial PWR works (2025)
    nrc.gov · www.nrc.gov/reactors/power/pwrs · record
  50. [50]
    U.S. Department of Energy. DOE Fundamentals Handbook: Thermodynamics, Heat Transfer, and Fluid Flow, Volume 2 of 3 (DOE-HDBK-1012/2-92) (1992)
    DOE-HDBK-1012/2-92, June 1992 · www.energy.gov/sites/default/files/2026-04/DOE-HDBK-1012-92_VOL2.pdf · record
  51. [51]
    M. A. Prelas, et al.. A review of nuclear batteries (2014)
    Progress in Nuclear Energy 75, 117–148 · doi:10.1016/j.pnucene.2014.04.007 · crossref ✓ 2026-09-19 · record
  52. [52]
    O. R. Frisch. Physical evidence for the division of heavy nuclei under neutron bombardment (1939)
    Nature 143, 276 · doi:10.1038/143276a0 · crossref ✓ 2026-09-19 · record
  53. [53]
    J. D. Lawson. Some criteria for a power producing thermonuclear reactor (1957)
    Proceedings of the Physical Society B 70, 6–10 · doi:10.1088/0370-1301/70/1/303 · crossref ✓ 2026-09-19 · record
  54. [54]
    H. Abu-Shawareb, et al. (Indirect Drive ICF Collaboration). Achievement of target gain larger than unity in an inertial fusion experiment (2024)
    Physical Review Letters 132, 065102 · doi:10.1103/PhysRevLett.132.065102 · crossref ✓ 2026-09-19 · record
  55. [55]
    A. P. Raman et al.. Passive radiative cooling below ambient air temperature under direct sunlight (2014)
    Nature 515, 540–544 · doi:10.1038/nature13883 · crossref ✓ 2026-09-19 · record
  56. [56]
    A. P. Raman, W. Li, S. Fan. Generating light from darkness (2019)
    Joule 3, 2679–2686 · doi:10.1016/j.joule.2019.08.009 · crossref ✓ 2026-09-19 · record
  57. [57]
    J.-l. Kou et al.. Daytime radiative cooling using near-black infrared emitters (2017)
    ACS Photonics 4, 626–630 · doi:10.1021/acsphotonics.6b00991 · crossref ✓ 2026-09-19 · record

Cite this entity

Physical Transformation Atlas (2026). entity disequilibrium:temperature-gradient: Temperature gradient. Dataset revision rbfbfcbb70e57 (hash of the canonical data). https://physical-transformation-atlas.wldud5192.workers.dev/e/disequilibrium/temperature-gradient

Ids and matrix addresses are stable across revisions; the revision hash identifies the exact canonical files the record was compiled from and is meta.data_hash in every /api export. Reuse terms: see the license field in any export.