Link Between Continuous and Discrete Descriptions of Noise in Nonlinear Resistive Electrical Components
Bibliographic record
Abstract
We consider the modeling of noise in a nonlinear, classical, resistive electrical component using two models: (i) a continuous description based on a stochastic differential equation with a white thermal Gaussian noise; (ii) a discrete, shot noise model based on a Markovian master equation. We show that thermodynamics imposes in (i) the use of the Hänggi–Klimontovich (HK) prescription when the noise depends on bias voltage, and implies a generalized Johnson–Nyquist relation for the noise where the conductance is replaced by the ratio mean current over voltage. In (ii) we show that the discrete description compatible with thermodynamics leads to the continuous one of (i) with again the HK prescription. Here the generalized Johnson–Nyquist relation for noise is recovered only at low voltage, when the continuous description is valid.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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".