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Résumé : An approach to correlated dynamics of quantum nuclei and electrons both in dynamical interaction with external environments is presented. This stochastic quantum molecular dynamics rests on a theorem that establishes a one-to-one correspondence between the total ensemble-averaged current density of interacting nuclei and electrons and a given external vector potential. The theory allows for a first-principles description of phenomena previously inaccessible via standard quantum molecular dynamics such as electronic and nuclear relaxation in photochemistry, dissipative correlated electron-ion dynamics in intense laser fields, nuclear dephasing, etc. As a demonstration of the approach, we discuss the rotational relaxation of 4-(N,N-dimethylamino)benzonitrile in a uniform bath in the limit of classical nuclei.