Modeling escape from a one-dimensional potential well at zero or very low temperatures
Bibliographic record
Abstract
The process of activation from a one-dimensional potential is systematically investigated in zero and nonzero temperature conditions. The features of the potential are traced through statistical escape from its wells, whose depths are tuned in time by a forcing term. The process is carried out for the damped pendulum system imposing specific initial conditions on the potential variable. While the escape properties can be derived from the standard Kramers theory for relatively high values of the dissipation, for very low dissipation, these deviate from this theory by being dependent on the details of the initial conditions and the time dependence of the forcing term. The observed deviations have regular dependencies on initial conditions, temperature, and loss parameter itself. It is shown that failures of the thermal activation model are originated at low temperatures and very low dissipation, by the initial conditions and intrinsic, namely, T = 0, characteristic oscillations of the potential-generated dynamical equation.
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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".