## Problem 087 — rank:271

**Title:** Molecular-motor efficiency

**Added binding assumptions (LaTeX):**

```latex
With $D_x$ in length squared per time and $v$ in length per time, $2D_x/v^2$ has units of time. The long-time relative displacement variance is approximately $2D_x/(v^2t)$; $r_0$ is therefore a time-valued uncertainty coefficient, not noise per unit time. Require positive net chemical input and include every fuel source in the efficiency denominator.
```

**Direct edits:** 1. **Fresh external checks:** None; supplied sources retained as provenance.