Bibliographic record
Abstract
In classical hydrodynamics, the mass flux is universally chosen to be the momentum field. In extended hydrodynamics, the mass flux acquires different terms. The extended hydrodynamics introduced and investigated in this paper uses a one-particle distribution function as the extra state variable chosen to characterize the microstructure. We prove that the extended hydrodynamics is fully autonomous in the sense that it is compatible with thermodynamics (i.e., the entropy does not decrease during the time evolution) and with mechanics (i.e., the part of the time evolution that leaves the entropy unchanged is Hamiltonian). Subsequently, we investigate its possible reductions. In some situations the emerging reduced dynamical theory is the classical hydrodynamics that is fully autonomous (i.e., all the structure that makes the extended theory fully autonomous is kept in the reduced theory). In other situations (for example, when the fluids under investigation have large density gradients) the reduced theories are not fully autonomous. In such a case the reduced theories constitute a family of mutually related dynamical theories (each of them involving a different amount of detail) that we consider to be a mathematical formulation of multiscale (or multilevel) hydrodynamics. It is in the reduced theories belonging to the multiscale hydrodynamics where the terms that emerge in the mass flux take the form of self-diffusion.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".