Universality classes for thermal transport in one-dimensional oscillator systems
Bibliographic record
Abstract
Two universality classes for thermal transport in one-dimensional oscillator systems are proposed. In class A the asymptotic behavior of the frequency dependent thermal conductivity is $\ensuremath{\kappa}(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\omega}}^{\ensuremath{-}1/2}$, whereas the bulk viscosity is finite. In class B the asymptotic behavior of the thermal conductivity is $\ensuremath{\kappa}\ensuremath{\sim}{\ensuremath{\omega}}^{\ensuremath{-}\ensuremath{\alpha}}$, where $\ensuremath{\alpha}<0.4$, and the frequency dependent bulk viscosity has the same asymptotic behavior as the thermal conductivity. It is further proposed that the criterion for membership in class A is that the ratio of specific heat capacities $\ensuremath{\gamma}\ensuremath{\equiv}{c}_{P}/{c}_{V}=1$. A one-dimensional cubic-plus-quartic coupled oscillator is examined at conditions for which $\ensuremath{\gamma}=1$ but $P\ensuremath{\ne}0$. It is found that the system belongs to class A, in agreement with the proposed criterion. Additionally, it is proposed that examination of whether a system has a well-defined bulk Prandtl number is a more reliable way of determining whether a system is in class A or class B.
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How this classification was reachedexpand
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 | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".