When is a quantity additive, and when is it extensive? ∗
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Bibliographic record
Abstract
The difference between the terms additivity and extensivity, as well as their respective negations, is critically analyzed and illustrated with a few examples. The concepts of subadditivity, pseudo-additivity, and pseudo-extensivity are also defined. To say that a given quantity (physical or mathematical) is additive and to say that a quantity is extensive are two different affirmations which, unfortunately, appear too often as undifferentiated in the physics literature. The assimilation of the two terms is especially present in studies related to the entropy measure of Tsallis [1], and to the so-called field of non-extensive thermostatistics or Tsallis ’ statistics which is based on this measure of entropy [2]. In these studies, it is not uncommon to see the words additivity and extensivity being used as synonymous, and to read sentences such as “...the appropriate framework to describe non-extensive behavior is Tsallis ’ statistics, because of the non-additivity property of Tsallis ’ entropy. ” But, how exactly is the non-additivity property of Tsallis ’ entropy related to non-extensivity? Are these concepts linked together simply because they are thought to mean the same thing? These questions are raised not with the intention of criticizing the results related to nonextensive statistics; what is more important is the fact that they point to a somewhat misleading and careless usage of scientific jargon. That this carelessness persists would not by itself be so problematic, were it not for the fact that the difference between additivity and extensivity is at the very root of the issues raised by non-extensive statistics. For this reason, it seems more than advisable to rehabilitate the proper meaning of these two terms by reviewing their Contribution to the Proceedings of the International School and Conference on Non-Extensive Thermodynamics
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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 | 0.000 | 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) | 0.026 | 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