Counterintuitive asymmetry of transition times in the Brownian asymmetric simple exclusion process

Driven diffusion of hard spheres (rods) in a one-dimensional cosine potential under a static bias should reflect properties of the asymmetric simple exclusion process (ASEP) on a lattice, if the amplitude of the cosine potential is considered to be large compared to the particles’ thermal energy. For this Brownian asymmetric exclusion process (BASEP) [1], we study transition times of a tagged particle between potential wells against and along the bias direction in non-equilibrium steady states. These transition times exhibit a counterintuitive asymmetry: While one may expect that the mean transition time in bias direction is shorter, the opposite is true. We relate this surprising asymmetry to the collective motion of the particles. Differences in the distributions of the times in and against bias direction depend sensitively on the filling factor (number of particles per potential well) and the rod length. Our analysis sheds light on the transport behavior of the model, which, compared to the ASEP, shows richer properties due to the additional length scale given by the rod length.

[1] D. Lips, A. Ryabov, P. Maass, Phys. Rev. Lett. 121, 160601 (2018)