Metastability & Phase Transitions
Systems can persist in states that are only locally stable, until they can't
Schematic toy model: temperature runs in arbitrary units from 0 to 100. Drag the slider, or the axis on the canvas.
Energy Landscape
Local minimum ≠ global minimum. Metastable states persist until a perturbation pushes the system over the energy barrier.
Critical Threshold
Near the critical point, small parameter changes produce dramatic system-wide reorganization. Wallace's stability boundary sits at ατ = 0.368: below it a system absorbs shocks; above it, oscillations amplify.
The Flip
Complex systems don't degrade gradually. They persist, persist, persist, then transition suddenly to a new state.
Physical
Ice → Water → Steam
Biological
DNA melting
Social
Institutional collapse
Cognitive
Paradigm shifts
Complex systems don't degrade gradually; they flip suddenly.
Wallace's threshold sits at ατ = 0.368: approach it, then phase transition.