An analytic study of the Wiedemann–Franz law and the thermoelectric figure of merit
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Bibliographic record
Abstract
Abstract Advances in optimizing thermoelectric material efficiency have seen parallel activities in theoretical and computational studies. In the current work, we calculate the exact Fermi–Dirac integrals to enable the generalization of the Wiedemann–Franz law (WF) in order to enhance the dimensionless thermoelectric figure of merit <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="italic">ZT</mml:mi> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mi>σ</mml:mi> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mi>κ</mml:mi> </mml:math> . This is done by optimizing the Seebeck coefficient α , the electrical conductivity σ , and the thermal conductivity κ in terms of the Lambert W, and the generalized Lambert W functions (offset log). In the calculation of the thermal conductivity κ , we include both electronic and phononic contributions. The solutions provide insight into the relevant parameter space including the physical significance of complex solutions and their dependance on the scattering parameter r and the reduced chemical potential μ *.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it