Time evolution and thermodynamics for a nonequilibrium system in phase-space
Bibliographic record
Abstract
The integrable system is constrained strictly by the conservation law during the time evolution, and the prethermal state from the nearly integrable system is also constrained by the conserved parameters (the constants of motion) with the corresponding generalized Gibbs ensemble (GGE), which is indubitably a powerful tool in the prediction of the relaxation dynamics. For stochastic evolution dynamics with considerable noise, the two-point correlation of local operators (like the density of kinks or transverse magnetization correlators), which do not exhibit the thermal features, display the behaviors of nonthermalization and an asymptotic GGE. In fact it is an asymptotic quasi-steady state with an infinite temperature, therefore the required distance to the nonthermal steady state is in an infinite time average. In this paper, we unambiguously investigate the relaxation of a nonequilibrium system in a canonical ensemble for integrable and nonintegrable systems. Temporal behavior of the many-body quantum system and the corresponding linear-coupling between the harmonic oscillators are discussed. The matrix-method in entropy ensemble is utilized to discuss the boundary and the diagonalization algebraically. The approximation results for nonintegrable system under the considerable perturbations are also presented.
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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".