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Existence and uniqueness of a nonequilibrium stationary state(NESS)for classical many body systems is a main theme of research by mathematical physicists in statistical mechanics for decades [1].Answering this question for quantum many‐body systems poses a major challenge for the present.Research into whether closed quantum systems can come to equilibrium and thermalize has seen a spur of recent activities [2],same for transport in constrained open spin systems [3].Our research program has a more modest goal: A)While mathematical proofs of theorems for these basic issues are of great importance it would be helpful to see how these systems evolve.For this we derive the quantum stochastic equations(master,Langevin,Fokker‐Planck)for prototypical quantum open systems(e.g.,for two oscillators in contact with two heat baths and extension to chains and networks) so one can follow their dynamics explicitly,to examine whether NESS exist at late times,prove the energy flux relations,etc.B)The effects of nonlinearity in quantum transport,equilibration,noise and fluctuation theorems(e.g.quantum anharmonic oscillators and oscillators coupled nonlinearly,each with its own heat bath,FPU models,Fourier law,etc).In this talk we give a sketch of our methodology involving the use of coarse‐grained effective action for the derivation of stochastic equations the reduced density matrix,calculation of the covariance matrix and the use of functional perturbative methods for weakly nonlinear systems.