Non-Arrhenius relaxation effects in collections of two-level subsystems
Bibliographic record
Abstract
We present numerical simulations of relaxation isotherms for an ensemble of thermally activated, two-level subsystems, with double-well free energy profiles, and with a distribution of dissipation barriers and level splittings. The field history imitates a typical experimental viscosity protocol, and consists of saturation in a large positive field, followed by recoil to a negative holding field, and then by the thermally driven decay of the moment towards equilibrium at fixed temperature and fixed field. The numerical simulations show that systems whose relaxation dynamics are governed explicitly by the Arrhenius law of thermal activation, can exhibit relaxation effects which are apparently ``non-Arrhenius'' in origin. In particular, the maximum value of the relaxation rate $S\ensuremath{\equiv}\ensuremath{-}\ensuremath{\partial}M(t)∕\ensuremath{\partial}\mathrm{ln}\phantom{\rule{0.2em}{0ex}}t$ extracted from model viscosity isotherms over a typical experimental time window $100\phantom{\rule{0.3em}{0ex}}\mathrm{s}\ensuremath{\leqslant}t\ensuremath{\leqslant}{10}^{4}\phantom{\rule{0.3em}{0ex}}\mathrm{s}$, and the thermal viscosity field ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}}_{\mathrm{f}}(T)$ extracted, over the same time window, from the field dependence of the logarithm of the time at which the moment reverses direction as it relaxes towards equilibrium, both exhibit variations with temperature which are highly nonlinear, and which are characterized by coincident maxima, very similar to those observed experimentally in a variety of particulate systems.
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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 | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".