Nonequilibrium work equalities in isolated quantum systems

We briefly introduce the quantum Jarzynski and Bochkov - Kuzovlev equalities in isolated quantum Hamiltonian systems, including their origin, their derivations using a quantum Feynman - Kac formula, the quantum Crooks equality, the evolution equations governing the characteristic functions of the probability density functions for the quantum work, and recent experimental verifications. Some results are given here for the first time. We particularly emphasize the formally structural consistence between these quantum equalities and their classical counterparts, which are useful for understanding the existing equalities and pursuing new fluctuation relations in other complex quantum systems.