Locality and thermalization in closed quantum systems
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Bibliographic record
Abstract
We derive a necessary and sufficient condition for the thermalization of a local observable in a closed quantum system which offers an alternative explanation, independent of the eigenstate thermalization hypothesis, for the thermalization process. We also show that this approach is useful to investigate thermalization based on a finite-size scaling of numerical data. The condition follows from an exact representation of the observable as the sum of a projection onto the local conserved charges of the system and a projection onto the nonlocal ones. We show that thermalization requires that the time average of the latter part vanishes in the thermodynamic limit while time and statistical averages for the first part are identical. As an example, we use this thermalization condition to analyze exact diagonalization data for a one-dimensional spin model. We find that local correlators do thermalize in the thermodynamic limit, although we find no indications that the eigenstate thermalization hypothesis applies.
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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