The first law of thermodynamics and energy partition in the presence of fields
Bibliographic record
Abstract
Abstract The first law of thermodynamics in the presence of fields is considered. The presence of fields gives rise to partition of the internal energy between field and nonfield energy forms, that are characterized as state functions. Field‐dependent components of work and heat are defined with respect to their being delivered at the boundaries, or directly, by action at a distance, to the contents of the system. Interaction energy, that accounts for effects of changes in the sources of the fields is defined. The first law of thermodynamics in the presence of fields states that the change in the sum of the field and nonfield components, of the internal energy, is equal to the change in the sum of the field and nonfield components of heat and work, delivered to the system, and the interaction energy, due to changes in the sources of the field. The equivalence between potential energy and work in conjugate frames of reference facilitates the incorporation of the interaction energy as part of the field‐dependent internal energy. In this context, the significance of the degree of coupling between the field and the contents of the system, in conjunction with their thermodynamic variables, is discussed. Intensive field‐dependent variables that maintain uniformity, at equilibrium, in the absence as well as in the presence of fields, are defined. In contrast, nonfield and field components of these intensive variables can be nonuniform, and discontinuous across interfaces, at equilibrium. The implication of the theory is illustrated by specific cases that involve electromagnetic and acceleration fields. Energy partition in acceleration fields is shown to depend on mass distribution within the system. A change in position, or in the source of the field produce changes in mass distribution and energy partition. Partition of magnetic and nonmagnetic energy forms, and field‐induced heat flow and energy storage are considered. It is shown that for linear matter, the energy per unit volume stored in the field is invariable with respect to the process and work that produce the field vectors, the balance being stored in other nonfield energy forms. Finally, expressions for field‐induced temperature and energy changes in an ideal magnetizable gas are derived. It is shown that isothermal magnetization produces a shift in the partition between the field and nonfield parts of the internal energy.
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.007 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 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".