Configurational and residual entropies of nonergodic crystals and the entropy’s behavior on glass formation
Bibliographic record
Abstract
We use thermodynamics of lattice vacancies to test the merits of the view that (i) statistical entropy, k(B) ln Omega, vanishes on vitrification of a liquid and hence there is no residual entropy and (ii) k(B) ln Omega of a nonergodic state would increase with time t as its structure relaxes. We argue that this view conflicts with the precepts of the configurational entropy of a crystal, -R[x ln x+(1-x)ln(1-x)], where x is the fractional population of vacancies, and with the observed decrease in x with t on structural relaxation. The issue of whether the entropy of a kinetically arrested crystal state is equal to k(B) ln Omega or equal to -R[x ln x+(1-x)ln(1-x)] can be resolved by measuring the vapor pressure, the emf of an electrolytic cell, and by scanning calorimetry. We also consider how the energy landscapes of a crystal and liquid differ, and point out that since crystals are in a nonequilibrium state, their thermodynamic data are inappropriate for testing the validity of the third law.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".