Quantum Otto Cycle Heat Engine

A quantum heat engine trades the piston-and-gas of a classical Otto cycle for a discrete energy ladder whose spacing ω is compressed and expanded unitarily, alternated with brief contacts to hot and cold thermal baths. This simulator animates that ladder directly: watch the level spacing tighten and widen during the unitary strokes (no heat crosses the system boundary, only work), and watch the occupation bars relax toward each bath's Gibbs distribution during the isochoric strokes (no work is done, only heat). The right-hand loop plots mean energy against level spacing exactly like a p-V diagram — its enclosed area is the net work extracted per cycle. Efficiency depends only on the ratio ω_cold/ω_hot, and the simulator computes it live alongside the Carnot bound set by the bath temperatures, so you can see exactly how far a real quantum engine sits from the reversible limit.