Kullback-Leibler entropy in the electron distribution shape relaxation for electron-atom thermalization
Bibliographic record
Abstract
We study the thermalization of energetic electrons dilutely dispersed in inert gas atomic moderators, with and without the presence of an external electric field. We investigate the shape relaxation of the electron distribution function relative to the steady-state distribution by means of the Kullback-Leibler entropy. The departure of the distribution function from a local Maxwellian parametrized by the temperature of the electrons is also considered with a functional analogous to the Kullback-Leibler entropy. For neon and argon as moderators, we found no evidence for the formation of a local Maxwellian followed by a slower relaxation to equilibrium. The momentum-transfer cross section for e-Ne collisions is almost constant with energy, whereas the e-Ar momentum-transfer cross section has a deep Ramsauer-Townsend minimum and a strong energy dependence. The role of the Ramsauer minimum in the relaxation processes is investigated. The time-dependent Lorentz-Fokker-Planck equation is solved for the speed distribution of the electrons with a finite difference method. A pseudospectral method is also used to investigate the spectral properties of the Fokker-Planck operator. In spite of the multi-exponential time dependence of the speed distribution function, we show that a single average relaxation time can be defined to characterize the relaxation to equilibrium.
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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".