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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
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