Quantum Otto Engine

This simulator visualises the smallest possible heat engine allowed by quantum mechanics: a single two-level system cycling between a hot and a cold reservoir. A cloud of independent instances of the same qubit is rendered as particles hopping between a ground-state level and an excited-state level whose spacing Δ(t) is swept up and down; two of the four strokes move the levels apart with the populations frozen (quantum-adiabatic, no heat exchanged), and two hold the levels fixed while the populations relax toward the Gibbs distribution of whichever bath is currently coupled (isochoric heat exchange). Live readouts track the net work extracted, the heat absorbed from the hot bath, and the resulting efficiency for the most recently completed cycle, alongside the ideal 1 − Δc/Δh limit — and pushing the cycle speed control past the qubit's thermal relaxation time shows, in real time, how running a quantum engine faster trades away efficiency.