>[!warning] >This content has not been peer reviewed. # Variational principles — Code Script: `rst_variational_cost_vs_mu.py`. ## Purpose Illustrates a simple **cost vs fidelity** trade-off: a one-parameter family of paths with different "costs" \(S\) (proxy for action) and corresponding effective signal-to-noise ratios, and compares this with the **RST fidelity** \(\mu(\eta, n)\). Paths with lower cost correspond to higher \(\mu\). ## Engine Imports from `rst_engine`: `mu_rst` and `DEFAULT_N`. This application lives under **foundation/** so the workspace root is **three** levels up (`..`, `..`, `..`). ## Parameters | Parameter | Value | Meaning | |:---|:---|:---| | \(S\) | lin-spaced, 0.1 to 10 | Proxy for action / path cost. | | \(\eta\) | decreasing function of \(S\) | Proxy for signal-to-noise ratio. | ## Output - **Figure:** `variational_cost_vs_mu.png` — plots cost \(S\) vs RST fidelity \(\mu(\eta(S), n)\), highlighting that lower-cost paths correspond to higher fidelity. Saved in the same subfolder. ## Links - **Foundation:** [[Variational principles (RST)]] - **Roadmap:** [[../../Applications Roadmap]]