Stiff Spring Approximation Revisited: Inertial Effects in Nonequilibrium Trajectories
Bibliographic record
Abstract
Use of harmonic guiding potentials is the most commonly adopted method for implementing steered molecular dynamics (SMD) simulations, performed to obtain potentials of mean force (PMFs) using Jarzynski's equality and other nonequilibrium work (NEW) theorems. The stiff spring approximation (SSA) of Schulten and co-workers enables calculation of the PMF by using the work performed along many SMD trajectories in NEW theorems. We discuss and demonstrate how a high spring constant, k, required for the validity of the SSA can violate another requirement of SSA, the validity of Brownian dynamics in the system under study. These result in skewed work distributions with their width increasing with k. The skew and broadening of work distributions result in biased estimation (through invoking NEW theorems) of the PMF. Remarkably, the skewness and the broadening of work distributions are independent of the average drift velocity and physical asymmetries and can only be attributed to using too-stiff springs. We discuss the proper upper limit for k such that the inertial effects are minimized. In the presence of inertial effects, using the peak value (rather than the statistical mean) of the work distributions vastly reduces the bias in the calculated PMFs and improves the accuracy.
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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".