Carnot cycle for an oscillator

In 1824 Carnot established that the efficiency of cyclic engines operating between a hot bath at absolute temperature T-hot and a bath at a lower temperature T-cold cannot exceed 1 - T-cold/T-hot. We show that linear oscillators alternately in contact with hot and cold baths obey this principle in the quantum as well as classical regime. The expression of the work performed is derived from a simple prescription. Reversible and non-reversible cycles are illustrated. The paper begins with historical considerations and is essentially self-contained.