A quantum analogue of the Jarzynski equality

A quantum analogue of the Jarzynski equality is constructed. This equality connects an ensemble average of exponentiated work with the Helmholtz free- energy difference in a nonequilibrium switching process subject to a therma l heat bath. To confirm its validity in a practical situation, we also inve stigate an open quantum system that is a spin 1/2 system with a scanning ma gnetic field interacting with a thermal heat bath. As a result: we find tha t the quantum analogue functions well.