Analogies between phase transitions in potential games and quantum phase transitions
Bibliographic record
Abstract
Abstract Potential games at population level has a very natural analogy with statistical mechanical systems. Here we show that there are clear analogies between quantum phase transitions at zero temperature and phase transitions in potential games being played by fully rational players. Such phase transitions are brought about by tuning parameters which change the payoff matrix either directly (as in classical games) or indirectly through continuous change in strategies (as in quantum games). The phase transitions take the system from one Nash equilibrium to another; these Nash equilibria (NE) are, in a sense, refined as only the ones that correspond to global maxima of the potential are selected in the thermodynamic limit (infinite number of players). We observe that the types of the phase transitions depend on the states involved in the transition process: while transitions involving two symmetric NE are discontinuous, the transitions between a symmetric and an antisymmetric NE are continuous.
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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".