Edwards entropy and compactivity in a model of granular matter
Why this work is in the frame
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Bibliographic record
Abstract
Formulating a statistical mechanics for granular matter remains a significant challenge, in part due to the difficulty associated with a complete characterization of the systems under study. We present a fully characterized model of a granular material consisting of N two-dimensional, frictionless hard disks, confined between hard walls, including a complete enumeration of all possible jammed structures. We show that the properties of the jammed packings are independent of the distribution of defects within the system and that all the packings are isostatic. This suggests that the assumption of equal probability for states of equal volume, which provides one possible way of constructing the equivalent of a microcanonical ensemble, is likely to be valid for our model. An application of the second law of thermodynamics involving two subsystems in contact shows that the expected spontaneous equilibration of defects between the two is accompanied by an increase in entropy and that the equilibrium, obtained by entropy maximization, is characterized by the equality of compactivities. Finally, we explore the properties of the equivalent to the canonical ensemble for this system.
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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) | 0.000 | 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 it