Eddington's mass-luminosity relation and the laws of thermodynamics
Bibliographic record
Abstract
Ever since its formulation by A. S. Eddington, the mass-luminosity relation has been viewed as a triumph for theoretical astronomy and astrophysics. The idea that the luminosity of the stars could be controlled solely by their mass was indeed a revolutionary concept. The proof involved two central aspects: (1) the belief that stars could be treated as ideal gases in hydrostatic equilibrium, and (2) that the opacity of Capella could be used as a reference mark applicable to other stars. Yet, when the mass-luminosity relation was advanced, no thought was given to the need for thermodynamic balance. Within thermodynamic expressions, not only must the dimensions (hence units) be consistent on each side of the equals sign, but the extensive nature of the properties must also balance. Namely, thermodynamic expressions must be balanced by properties which are extensive to the same degree. In this regard, mass is an extensive thermodynamic property and can be represented by a homogenous function of degree 1. Conversely, the luminosity of a star is neither extensive nor intensive, but rather can be represented by a homogenous function of degree 2/3. Consequently, the mass-luminosity expression is thermodynamically unbalanced and stands in violation of the laws of thermodynamics.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.010 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".