Bibliographic record
Abstract
Axel Lorke’s Quick Study (Physics Today, May 2021, page 66) discusses underlying connections between seemingly unrelated phenomena. His brief reminder of Svante Arrhenius’s major contributions to science—and in particular, his now-famous empirical relation describing the rate of thermally activated processes—is thought-provoking.There is, however, a minor point appearing in the caption of figure 2, showing electron density versus inverse temperature, that needs clarification. If we concentrate on the high-temperature (left) portion of the graph, the “reaction” involved is the generation of an electron–hole pair (analogous to electron–positron pair production in particle physics), for which the Gibbs free-energy change is what is known as the energy gap Eg. For that reaction, the product of the electron density n and hole density p is given by np∝exp(−Eg/kBT), where kB is the Boltzmann constant and T is absolute temperature.11. C. D. Thurmond, J. Electrochem. Soc. 122, 1133 (1975). https://doi.org/10.1149/1.2134410 At the high temperatures on the left side of the graph, the semiconductor is nearly intrinsic, so n≈p∝exp(−Eg/2kBT), which is where the factor of two in the denominator of the slope originates.The caption states that the “factor of two in the denominator arises because electrons obey Fermi–Dirac statistics rather than classical Boltzmann distribution.” But at such high temperatures, Fermi–Dirac statistics approximates the Boltzmann distribution, so it cannot be the reason for the factor of two as the caption states. A similar explanation applies to the ionization of neutral donors.22. R. W. Christy, Am. J. Phys. 40, 40 (1972). https://doi.org/10.1119/1.1986444ReferencesSection:ChooseTop of pageReferences <<1. C. D. Thurmond, J. Electrochem. Soc. 122, 1133 (1975). https://doi.org/10.1149/1.2134410, Google ScholarCrossref2. R. W. Christy, Am. J. Phys. 40, 40 (1972). https://doi.org/10.1119/1.1986444, Google ScholarCrossref, ISI© 2021 American Institute of Physics.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.025 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.004 |
| Bibliometrics | 0.005 | 0.006 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.005 | 0.017 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.004 | 0.010 |
| Insufficient payload (model declined to judge) | 0.079 | 0.024 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".