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A generalized macroscopic Fick's first diffusion law is derived which describes steady-state particle flow between two baths explicitly as a function of the concentration gradient, acting as the thermodynamic driving force, times a functional of the first passage time. The latter is shown to be the ratio of the number of particles trapped between the baths and the first passage time. Particle trapping is shown to be a powerful mechanism by which flow can be enhanced. This is analyzed for two examples: a potential and an entropy trap

Stationary flow, first passage times, and macroscopic Fick’s first diffusion law: Application to flow enhancement by particle trapping