  The fluctuation theorem, where the central quantity is the work distribution,
is an important characterization of nonequilibrium thermodynamics. In this
work, based on the dissipaton-equation-of-motion theory, we develop an exact
method to evaluate the work distributions in quantum impurity system-bath
mixing processes, in the presence of non-Markovian and strong couplings. Our
results not only precisely reproduce the Jarzynski equality and Crooks
relation, but also reveal rich information on large deviation. The numerical
demonstrations are carried out with a spin-boson model system.
