The unsteady Boltzmann kinetic equation and non-equilibrium thermodynamics of an electron gas for the Rayleigh flow problem
Bibliographic record
Abstract
In the framework of irreversible thermodynamics, the characteristics of the Rayleigh flow problem of a rarified electron gas extracted from neutral atoms is examined and proved to obey the entropic behavior for gas systems. A model kinetic equation of the BGK (Bhatnager–Gross–Krook) type is solved, using the method of moments with a two-sided distribution function. Various macroscopic properties of the electron gas, such as the mean velocity, the shear stress, and the viscosity coefficient, together with the induced electric and magnetic fields, are investigated with respect to both distance and time. The distinction between the perturbed velocity distribution functions and the equilibrium velocity distribution function at different time values is illustrated. We restrict our study to the domain of irreversible thermodynamics processes with small deviation from the equilibrium state to estimate the entropy, entropy production, entropy flux, thermodynamic force, and kinetic coefficient and verify the celebrated Boltzmann H-theorem for non-equilibrium thermodynamic properties of the system. The ratios between the different contributions of the internal energy changes, based upon the total derivatives of the extensive parameters, are predicted via Gibbs’ equation for both diamagnetic and paramagnetic plasmas. The results are applied to a typical model of laboratory argon plasma.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".