Fluctuation theory of single-file diffusion

In a one-dimensional suspension of Brownian particles, which cannot pass each other, the mean square displacement of a selected particle grows at long times with the square root of time, rather than linearly. It is shown that the coefficient of the square root, the so-called single-file mobility, can be derived from fluctuation theory, involving the velocity time scale and the fluctuation-dissipation theorem. The single-file mobility is expressed in terms of the collective diffusion coefficient and the isothermal osmotic compressibility, in agreement with the result derived earlier by Kollmann on the basis of the generalized Smoluchowski equation [M. Kollmann, Phys. Rev. Lett. 90, 180602 (2003)].