A new method of semigrand canonical ensemble to calculate first-order phase transitions for binary mixtures
Bibliographic record
Abstract
First-order phase transitions of binary mixtures at the given pressure (P) and temperature (T) are studied by taking into account the composition fluctuations. Isothermal-isobaric semigrand canonical ensemble is adopted to find the relations among the total number of molecules, the composition fluctuations and Gibbs free energy density. By combining two identical subsystems of mixtures successively, the free energy density is transformed until being stable and its linear segments represent phase transitions. A new method is developed to calculate the phase equilibriums of binary mixtures. The method handles multiple types and number of phase equilibriums at single time and its solutions are physically justified. One example is shown for calculating the phase diagram of binary Lennard-Jones mixture. It demonstrates that the fluctuations of the total number of molecules in mixtures are fundamental behind phase transitions and the van der Waals loops in Gibbs free energy are reasonable.
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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".