Quench hot metal fast and it freezes full of stress, stuck in the first shape it fell into. Heat it and cool it SLOWLY — annealing — and the atoms get enough jiggle to climb out of bad arrangements and settle into the true lowest-energy order. The same trick solves hard problems: let the search run hot, then cool, and it escapes the traps a greedy search falls into. Slide from a fast quench to a slow anneal.
Annealing tempers a system to its ground state by adding thermal energy and removing it SLOWLY: at high temperature the system accepts uphill moves (Boltzmann probability e^(−ΔE/kT)) and so hops OUT of local minima; as T is lowered gradually it settles into a deep, low-energy configuration a fast quench would miss. Simulated annealing (Kirkpatrick 1983) applies this to optimisation. The instrument runs a rugged 1-D landscape: a greedy quench sticks in the nearest dip, a slow anneal reaches a far lower one. A fail-loud self-check throws unless the annealed final energy is ≤ the greedy result. ◆ real statistical physics / optimisation, node-verified.
A fixed-seed anneal vs greedy on a toy multi-well landscape (deterministic here so it reproduces); real annealing needs a slow-enough schedule to guarantee the global minimum — the accept-uphill-when-hot escape mechanism is the exact core.