Relationships between Jaynes entropy of the one-particle density matrix and Shannon entropy of the electron densities
Bibliographic record
Abstract
Relationships between the Jaynes and Shannon information entropies, both of which are related to the correlation energy, are given and the physical implications are explored. Evidence is provided from a study of the Be and Ne isoelectronic sequences that the Shannon entropy is more sensitive to the effects of the nuclear charge than is the Jaynes entropy. It is shown that the Jaynes entropy may be considered as the difference between the mean orbital Shannon entropy per electron and the mean orbital Shannon entropy of one electron. These mean orbital entropies display the same functional behavior as the total Shannon entropy throughout the isoelectronic sequence. We demonstrate that the Jaynes entropy may be considered as the sum of the Kullback–Leibler distance entropies occurring between natural spin orbital densities and a reference point whose occupation number is one. The large Z asymptotic behavior of the Jaynes and Shannon entropies is discussed. From a study of a Ne isonuclear sequence, it is shown that both Shannon and Jaynes entropies increase with the number of electrons, illustrating that these quantities are sensitive to the amount of electronic interactions present in the system. Relationships for the changes in the Shannon and Jaynes entropies with respect to the number of electrons for an isonuclear sequence are obtained, which depend on the electron affinity, first and second ionization potentials, and the hardness and chemical potential of the system.
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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 | 0.002 | 0.014 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".