Melting at a critical hopping rate: an equilibrium barrier-crossing perspective
Bibliographic record
Abstract
Melting is a first-order transition from solid to liquid, yet its microscopic trigger remains debated. We propose a criterion based on a critical barrier-crossing (hopping) rate rather than vibration amplitude alone. By separating oscillatory (wave-like) motion from activated hopping, we argue that melting occurs when the hopping frequency exceeds a fixed fraction of the characteristic attempt frequency, thereby removing shear rigidity via non-affine relaxations. The threshold follows directly from Boltzmann and Bose–Einstein/Fermi–Dirac statistics and is consistent with equilibrium thermodynamics. It recovers classical criteria such as Lindemann's rule and the Born rigidity criterion for crystalline lattices, and it extends naturally to vortex lattices in superconductors and to quantum lattice systems (Hubbard-type models). Framing melting in terms of equilibrium barrier-crossing links activated defect kinetics to the macroscopic transition and provides a unified framework across classical and quantum settings.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".