How Do Trajectories Become Physical Observables?

Note: This is an early draft page for the executable kUPS MD tutorial series. It is intentionally hidden from site navigation while the simulations, notebooks, figures, and review artifacts mature. This post follows the trajectory-length discussion by asking how sampled configurations and velocities become physical observables with normalization, finite-size limits, and uncertainty. Corrections and replication issues should be tracked in sungsoo-ahn/kups-md-tutorials.

Introduction

A trajectory is not an observable by itself. It is a source of samples from which an observable is estimated. That distinction matters because every observable has a definition, normalization, finite-size support, and uncertainty model.

For ML researchers working with MLIPs, the failure mode is familiar: a simulation produces many frames, a plotting function produces a smooth curve, and the curve is treated as a physical result. The practical question is different. What estimator was used? Which samples enter it? What finite-size region is valid? What error bar belongs on the derived number?

This draft demonstrates the executable slice of the seventh tutorial with seeded periodic argon FCC cells. It computes radial distribution functions, coordination integrals, block uncertainties, and a velocity autocorrelation function before the final argon/kUPS trajectory diagnostic is added.

• smoke configuration
• full configuration
• observable notebook
• smoke summary
• full summary
• full provenance manifest
• self-review note

What Is Being Estimated?

The current diagnostic keeps the estimator explicit:

The small-cell RDF is not drawn beyond half the periodic box length. Those radial shells are not valid for a minimum-image RDF estimator, even if a plotting routine could produce numbers there.

What Should The Diagnostic Show?

The full run checks three things. The RDF panel shows the normalized pair estimator rather than a raw distance histogram. The coordination panel turns that curve into a first-shell integral with a block standard error. The VACF panel treats time correlation as its own observable, not as a side effect of the trajectory.

Reproduction

The current executable path is:

git clone https://github.com/sungsoo-ahn/kups-md-tutorials
cd kups-md-tutorials
uv sync
uv run kups-tutorial run 07 --profile smoke
uv run kups-tutorial verify 07 --profile smoke
uv run kups-tutorial run 07 --profile full
uv run kups-tutorial verify 07 --profile full
uv run jupyter execute notebooks/post-07-observables.ipynb --inplace

The notebook is deliberately not the implementation source. It imports the configuration loader, observable diagnostics, and figure generator from src/kups_md_tutorials/.

Current Status

This page is not the final article. The implemented pieces are:

• smoke and full controlled argon-FCC observable workflows
• committed compact RDF, VACF, and summary outputs
• executable notebook
• generated SVG/PNG figure and snapshot review
• self-review note covering code, science, notebook, and figure feedback

The missing pieces are:

• final article prose
• citations for RDF normalization, coordination integrals, finite-size effects, and time-correlation functions
• rendered desktop and mobile page snapshots
• argon/kUPS trajectory diagnostics for physical observables

The rule for this post is that an observable is a statistical object. The trajectory provides samples; the estimator, normalization, finite-size support, and uncertainty determine what can be claimed from those samples.

References

• Frenkel, D. & Smit, B. (2001). Understanding Molecular Simulation: From Algorithms to Applications. Academic Press.
• Tuckerman, M. E. (2010). Statistical Mechanics: Theory and Molecular Simulation. Oxford University Press.
• Allen, M. P. & Tildesley, D. J. (1987). Computer Simulation of Liquids. Oxford University Press.