Breaking of time-reversal symmetry for a particle in a parabolic potential that is subjected to Lévy noise: Theory and an application to solar flare data.

The noise in nonequilibrium systems commonly contains more outliers as compared to equilibrium systems and is often best described with a Lévy distribution. Many systems in which there are fluctuations around a steady-state throughput can be modeled as a Lévy-noise-subjected particle in a parabolic potential. We consider an overdamped particle in a parabolic potential that is subjected to noise. Microscopic reversibility and time-reversal symmetry apply if the particle is subject to Gaussian distributed noise, but are violated if the noise is Lévy. A parameter to detect this violation is formulated. We, furthermore, develop an understanding for how the time-reversal asymmetry depends on the time Δt between the sample points and on the stability index, α, of the Lévy noise. With solar flare data it is shown how the time-reversal asymmetry parameter of a signal can be used to obtain the α of the underlying noise.