Pathway · p-b820ec885f · weakly supported

Temperature gradient → Electrical work

Temperature gradientThermopolarization effectSeparated surface chargeElectrical work

Epistemic state of the route

known constituent relations: 1 / 3 established or replicated · weakest constituent reported
constituent maturity floor: K4 · experimentally observed
search for this exact route: Exact composition search: reviewed 2026-09-21 — partial; None found in the runs made (a partial, never a protocol-complete negative): nothing OpenAlex returns puts a load on a thermopolarised dielectric or reports output power from the direct effect. The literature that names the composition is the 1982–1994 measurement lineage (currents, no load), its theory (Marvan 1969, Tagantsev 1987 and 1991, Marvan & Fähnrich 1997, Nasu 2022, Onishi 2025), its converse (1995), and a separate simulation literature on the thermal polarization of polar liquids (Bresme and co-workers, 2008–2025), spelled since pass 32 as a second, theoretically-predicted claim into the same phenomenon. Inconclusive as a route search until the Scholar and Semantic Scholar runs exist.
recorded-pathway overlap: none recorded
route-level evidence: 0 sources for the complete composition · 7 cited by the constituent steps
boundaries and interfaces: BOUNDARY compatible · no region transition

Explorematrix context · physics checks · steps · route evidence · constituent evidence · cite

Matrix context

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

D.01 × C.40 · Temperature gradient × Thermopolarization family: Thermopolarization

Literature search for this exact composition

Reviewed search · 2026-09-21OpenAlexpartial

None found in the runs made (a partial, never a protocol-complete negative): nothing OpenAlex returns puts a load on a thermopolarised dielectric or reports output power from the direct effect. The literature that names the composition is the 1982–1994 measurement lineage (currents, no load), its theory (Marvan 1969, Tagantsev 1987 and 1991, Marvan & Fähnrich 1997, Nasu 2022, Onishi 2025), its converse (1995), and a separate simulation literature on the thermal polarization of polar liquids (Bresme and co-workers, 2008–2025), spelled since pass 32 as a second, theoretically-predicted claim into the same phenomenon. Inconclusive as a route search until the Scholar and Semantic Scholar runs exist.

6 runs · 48 unique records · 0 read in full · reviewed by Ava Kim's loop-3 lane · protocol route-search-v1

Analysis of Vibration Energy Harvesting Performance of Thermo-Electro-Elastic Microscale Devices Based on Generalized Thermoelasticity (2024) · simulation only · He et al. 2024 (Actuators 13, 533): a generalized-thermoelastic model of a piezoelectric microbeam vibration harvester that includes a thermopolarization term — the reviewer's precision query's only relevant hit, a model of a vibration-driven piezoelectric device, not a thermopolarization generator.
Effects of thermally induced birefringence in high-output-power electro-optically Q-switched Nd:YAG lasers and their compensation (1993) · wrong coupling · Applied Optics 1993: a laser paper matched on 'output power' and 'thermally induced'; not the composition.
Laser Intensity Modulation Method and Thermal Gradient Induced Polarization (1997) · theory only · Marvan & Fähnrich 1997 (phys. stat. sol. (a) 163, 263–270; abstract read on OpenAlex in the pass-32 review): the contribution of the thermopolarization effect (P ∝ ∇T) to the laser-intensity-modulation-method signal studied theoretically, shown large enough to observe, and compared with the pyroelectric signal — a prediction of a measurement method, not an experiment in polymer films; ruled insufficient-information on the title alone before the abstract was found.
The rich phase behavior of the thermopolarization of water: from a reversal in the polarization, to enhancement near criticality conditions (2016) · simulation only · Iriarte-Carretero et al. 2016 (PCCP 18, 19894): non-equilibrium molecular dynamics of water polarised by a thermal gradient, strongly dependent on the thermodynamic state with an enhancement near the critical point — a sibling in polar liquids (with the 2013 water, 2020 acetonitrile, 2024 supercooled-water and 2025 ethanol simulations on the same list), all simulation, no experiment, no load.
Thermo-electro-elastic analysis of piezoelectric hollow cylinder with thermopolarization effect (2024) · theory only · Journal of Thermal Stresses 2024 (with the 2024 flexoelectric hollow-cylinder analysis on the same list): continuum analyses that include the thermopolarization coefficient, by title — theory.
Reverse thermopolarization effects in dielectrics (1995) · wrong coupling · Trepakov et al. 1995: the converse effect (a ≈ 10⁻⁴ K temperature difference across a PMN capacitor charged at 10⁶ V/m), recorded under p-a093d7ecc5 as well.
Theory of Thermopolarization Effect (2025) · theory only · Onishi, Isobe, Shitade & Nagaosa 2025 (Nano Letters 25, 2763): the modern linear-response theory of the direct effect; no experiment.
Antisymmetric thermopolarization by electric toroidicity (2022) · theory only · Nasu & Hayami 2022 (Phys. Rev. B 105, 245125): theory of the tensor's antisymmetric part.

Limitations: OpenAlex only (21/09, 12:53 pm Sydney): driver-mechanism 17 works (all screened, the thermopolarization theory and the thermally polarised-liquid simulations); whole-chain 0; demonstration-precision 0; the reviewer's precision query 2 (both false positives); the composite-name form 43 works, every one already in the flexoelectric route's composite-name bundle (screened there in pass 27 and here again at title level); Semantic Scholar answers 429 keyless (owner exception e953) and Google Scholar a captcha — both mandatory for a negative, neither run the constituent observations (Kholkin 1982, read in full; Trepakov 1989 and Rafikov 1994 at abstract level) are sink-variant by construction — a polarization current with no load — and are not repeated as hits here; the claims stay reported until Trepakov 1989 is read (owner exception e9d8) Marvan & Fähnrich 1997, the one title that might have reported an experiment, is theory by its abstract (found after the record was first written); no hit on the list is an experiment

Index query only · 2026-09-21OpenAlex · 6 queriesnot reviewed

79 indexed works reported across the queries, 48 unique retrieved; nobody has read them for a qualifying demonstration. A person can screen this frozen list and promote it to a reviewed record without re-running the query.

OAdriver-mechanism:117 reported · 17 retrieved
OAdriver-mechanism:117 reported · 17 retrieved
OAwhole-chain0 reported · 0 retrieved
OAdemonstration-precision0 reported · 0 retrieved
OAdemonstration-precision2 reported · 2 retrieved
OAcomposite-name43 reported · 43 retrieved

Planned runs NOT run in this bundle (engine unavailable): search:2026-09-21-p-b820ec885f/s2-dm1 (semantic-scholar); search:2026-09-21-p-b820ec885f/s2-wc (semantic-scholar); search:2026-09-21-p-b820ec885f/s2-dp (semantic-scholar); search:2026-09-21-p-b820ec885f/s2-cn (semantic-scholar).

Protocol route-search-v1: a frozen index run changes only the search state; only a reviewed record can say that a demonstration was or was not found.

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

01
Temperature gradient —drives→ Thermopolarization effectreportedclaim record
thermal → electrical
P_i = γ_ij ∇_j T · thermopolarization coefficient γ [C/(m K)]
phenomenological tensor form; in Onishi et al.'s linear-response notation γ corresponds to −L̃₁₂/T for the relevant component; Kholkin 1982 report B₁₁ ≈ 3 × 10⁻¹² C/(cm·K) (≈ 3 × 10⁻¹⁰ C/(m·K)) for PMN at 310 K
- 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
refs [1] [2] [3] [4] [5]
02
Thermopolarization effect —produces→ Separated surface chargereportedclaim record
electrical → electrical
- the induced bulk polarization terminates at a surface or electrode as bound / screening charge; modulating the gradient produces a displacement / polarization current
- the solid, electroded dielectric of the 1982–1994 measurements; the polar-liquid spelling has no charge-collection evidence (the simulations report bulk polarization and electrostatic potential) and does not inherit this sink
refs [5] [3] [6]
03
Separated surface charge —converts into→ Electrical workestablishedclaim record
electrical → electrical · loss to thermal
- electrodes on the charged surfaces connected through a load
refs [7]

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]
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
[2]
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
[3]
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
[4]
Y. Onishi et al.. Theory of Thermopolarization Effect (2025)
Nano Letters 25, 2763–2768 · doi:10.1021/acs.nanolett.4c05870 · record
[5]
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
[6]
E. Rafikov et al.. Frequency and temperature dependence of the thermopolarization response in dynamic investigations (1994)
physica status solidi (a) 144, 471–477 · doi:10.1002/pssa.2211440228 · record
[7]
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

Cite this route

Physical Transformation Atlas (2026). route p-b820ec885f: Temperature gradient → Thermopolarization effect → Separated surface charge → Electrical work. Dataset revision rbfbfcbb70e57 (hash of the canonical data). https://physical-transformation-atlas.wldud5192.workers.dev/path/b820ec885f

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.