[lance-lii]

Summary

Part of #597.

• Fix: VelocityAutoCorrelation averaged over all atoms in the state, so systems in a batched SimState were mixed into one VACF. It now averages over the atoms of each system (using system_idx) and vacf has shape (n_systems, window_size) for batched input. Single-system input keeps the old (window_size,) shape.
• The running average now starts from the first window instead of the zero placeholder, so the batched shape works with use_running_average=True.
• Added a regression test checking that a batched state gives the same VACF per system as running each system on its own.

This only covers the calculator side. The pattern in the original report (ts.integrate with one trajectory file per system, where the reporter passes each split system to the calculator separately) still mixes systems, and I'd leave that for a follow-up PR so this one stays small.

Tests: pytest tests/test_correlations.py passes (14 tests), and ruff check / ruff format --check pass on the changed files.

AI disclosure: I used an AI coding assistant (Claude Code) to help write the fix and test. I reviewed the changes and ran the tests myself.

Checklist

Before a pull request can be merged, the following items must be checked:

• Doc strings have been added in the Google docstring format.
• Run ruff on your code.
• Tests have been added for any new functionality or bug fixes.

[CompRhys]

thanks!