Brans–Dicke theory and thermodynamical laws on apparent and event horizons
Bibliographic record
Abstract
In this work, we describe the Brans–Dicke (BD) theory of gravity and give a particular solution by choosing a power law form for the scalar field [Formula: see text] and constant ω. If we assume that the first law of thermodynamics and the entropy formula hold on the apparent horizon, then we recover the Friedmann equations. Next, assuming the first law of thermodynamics holds, the validity conditions of the generalized second law (GSL) on the event horizon are presented. If we impose the entropy relation on the horizon, without using the first law, then we also obtain the validity condition of the GSL on the event horizon. The validity of the GSL completely depends on the BD model scalar field solutions. We have justified that the two processes are equivalent on the apparent horizon, but on the event horizon they are not equivalent. If the first law is valid on the event horizon, then the GSL may be satisfied by the BD solution, but if the first law is not satisfied then the GSL is not satisfied by the BD solution. Therefore, the first law always favours the GSL on the event horizon. In our effective approach, the first law and the GSL are always satisfied on the apparent horizon, which does not depend on the BD theory of gravity.
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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".