  We briefly introduce the quantum Jarzynski and Bochkov-Kuzovlev equalities in
isolated quantum Hamiltonian systems, which includes the origin of the
equalities, 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, the recent
experimental verifications. Some results are given here first time. We
particularly emphasize the formally structural consistence between these
quantum equalities and their classical counterparts, which shall be useful in
understanding the existing equalities and pursuing new fluctuation relations in
other complex quantum systems.

Statistical Mechanics