Shannon entropies and logarithmic mean excitation energies from cusp- and asymptotic-constrained model densities
Bibliographic record
Abstract
A model correctly describing the asymptotic behavior of the charge density is used to derive an expression for the Shannon entropy in terms of the ionization potential of the system. A strong similarity is observed between this model entropy and the entropy obtained from correlated wave functions providing evidence that it is the asymptotic regions that are responsible for the behavior of the entropy. We also show via a model entropy that the behavior of the momentum space Shannon entropy is due to a correct description of the cusp behavior at the nucleus. The changes in the position and momentum space entropies as a function of a parameter are shown to be linearly related for these models. The expression for the entropy, derived from a density model that obeys the asymptotic behavior, is shown to be almost identical in nature to the general expression for entropy emanating in the stopping power formalism.
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".