Folding Funnel 2D: Free-Energy Landscape

This 2D simulator computes the same energy-landscape-theory physics as the 3D funnel visualizer, but from an explicit free-energy functional G(Q) = enthalpy − T·entropy rather than a flattened 3D scene. An ensemble of conformations undergoes overdamped Langevin dynamics along the reaction coordinate Q (fraction of native contacts), diffusing under thermal noise while being pulled downhill by the funnel's enthalpic bias −D·Q and pushed back toward the unfolded state by an explicit configurational-entropy term −T·S0·(1−Q) — the actual thermodynamic driver of the folding/unfolding transition. Because the two terms are separated, the model predicts a real folding transition temperature Tf = D/S0, shown live and verifiable: lower the funnel steepness or raise the entropy scale and Tf drops, and pushing T past it flips the ensemble from reliably folding to staying unfolded. A small free-energy-vs-Q plot beneath the funnel diagram shows the live G(Q) curve so you can watch the landscape's shape change directly as you move each slider.