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The longstanding problem of Brownian transport in a heterogeneous quasi one-dimensional medium with space-dependent self-diffusion coefficient is addressed in the overdamped(zero mass) limit.A satisfactory mesoscopic description is obtained in the Langevin equation formalism by introducing an appropriate drift term,which depends on the system macroscopic observables,namely the diffuser concentration and current.The drift term is related to the microscopic properties of the medium.The paradoxical existence of a finite drift at zero current suggests the possibility of designing a Maxwell demon operating between two equilibrium reservoirs at the same temperature.