Breaking microscopic reversibility with Lévy flights

A system at equilibrium exhibits microscopic reversibility, i.e. any path in phase space is just as often traversed in one direction as that it is traversed in the opposite direction. We show how it is justified to characterize white Gaussian noise as equilibrium noise: when an overdamped particle in a potential is subjected to such noise, microscopic reversibility can be proven for most-probable-paths that lead from one potential well to another. However, when the overdamped particle is subjected to white Lévy noise, time-reversal symmetry is broken and microscopic reversibility is violated, even when the noise is symmetric. We, furthermore, derive how for an overdamped particle inside a parabolic potential microscopic reversibility is violated in the presence of Lévy white noise. Similar to Brownian vortexes, Lévy flights can be associated with the presence of Lévy vortexes in phase space.