Phase transitions in fluctuations and their role in two-step nucleation
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Bibliographic record
Abstract
We consider the thermodynamic behavior of local fluctuations occurring in a stable or metastable bulk phase. For a system with three or more phases, we present a simple analysis based on classical nucleation theory that predicts thermodynamic conditions at which small fluctuations resemble the phase having the lowest surface tension with the surrounding bulk phase, even if this phase does not have a lower chemical potential. We also identify the conditions at which a fluctuation may convert to a different phase as its size increases, referred to here as a "fluctuation phase transition" (FPT). We demonstrate these phenomena in simulations of a two dimensional lattice model by evaluating the free energy surface that describes the thermodynamic properties of a fluctuation as a function of its size and phase composition. We show that a FPT can occur in the fluctuations of either a stable or metastable bulk phase and that the transition is first-order. We also find that the FPT is bracketed by well-defined spinodals, which place limits on the size of fluctuations of distinct phases. Furthermore, when the FPT occurs in a metastable bulk phase, we show that the superposition of the FPT on the nucleation process results in two-step nucleation (TSN). We identify distinct regimes of TSN based on the nucleation pathway in the free energy surface and correlate these regimes to the phase diagram of the bulk system. Our results clarify the origin of TSN and elucidate a wide variety of phenomena associated with TSN, including the Ostwald step rule.
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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