Paradoxical motion of a single Brownian particle: Absolute negative mobility

We consider a single, classical Brownian particle in a spatially symmetric periodic system far from thermal equilibrium, which can be readily realized experimentally. Upon application of an external static force F, the average particle velocity is negative for $F>\mathrm{}0\mathrm{}$ and positive for $F<\mathrm{}0\mathrm{}$ (absolute negative mobility). The various physical mechanisms responsible for such a paradoxical effect are identified, leading to analytical approximations that are in good agreement with numerical simulations.