Analytical results for the reactivity of a single-file system.

We derive analytical expressions for the reactivity of a single-file system with fast diffusion and particles entering and leaving the system at one end. If the conversion reaction is fast, then the reactivity depends only very weakly on the system size, and the conversion is about 100%. If the reaction is slow, then the reactivity becomes proportional to the system size, the loading, and the reaction rate constant. If the system size increases the reactivity goes to the geometric mean of the reaction rate constant and the rate of particles entering and leaving the system. For large systems, the number of unconverted particles decreases exponentially with distance from the open end.