Bibliographic record
Abstract
Principle of Local State and Thermodynamic Potentials The theory in this chapter is based on the Principle of Local State given in chapter 4. Kestin has noted that this principle implies that “the local and instantaneous gradients of the thermodynamic properties as well as their local and instantaneous rates of change do not enter into the description of the state and do not modify the equations of state.” It follows that the thermodynamic potentials are assumed to be of the same form as for an equilibrium state. The important potentials in finite deformation thermoelasticity are the Helmholtz free energy and the internal energy, since, as for linear thermoelasticity, the Helmholtz free energy at constant temperature is the isothermal strain energy and the internal energy at constant entropy is the isentropic strain energy. This indicates the relation between hyperelasticity and thermoelasticity. Application of thermoelasticity to finite deformation of idealized rubber-like materials involves the concept of entropic response and energetic response and this is discussed in this chapter. Basic Relations for Finite Deformation Thermoelasticity The theory in this section is presented in terms of the absolute temperature Θ, the specific entropy s , and the referential variables, S , the second Piola-Kirchhoff stress, and C , the right Green tensor, or E , Green's strain tensor. There are four thermodynamic potentials that are fundamental equations of state, that is, all the thermodynamic properties can be obtained from a potential by differentiation if the potential is expressed as a function of the appropriate thermodynamic properties.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.015 | 0.004 |
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".