Extended Reversible and Irreversible Thermodynamics: A Hamiltonian Approach with Application to Heat Waves
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Bibliographic record
Abstract
Abstract A new version of extended irreversible thermodynamics (EIT) satisfying a Hamiltonian structure is proposed. For pedagogical purpose, the simple problem of linear heat conduction in a rigid body is investigated to illustrate the general framework. In contrast with earlier versions of EIT wherein the heat flux was upgraded to the status of state variables, we select here its conjugate dual and higher order fluxes as new independent variables. Their time–evolution equations are formed of reversible and irreversible terms but they cannot take any arbitrary form. Restrictions are placed on the reversible terms by imposing a Hamiltonian structure while the irreversible contribution is subject to the requirement to satisfy the second law of thermodynamics. Explicit expressions of the temperature and heat flux waves are also derived.
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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) | 0.001 | 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