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 $\mathrm{\Delta }t$ between the sample points and on the stability index, $\alpha$, 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 $\alpha$ of the underlying noise.

• Received 30 November 2020
• Revised 6 April 2021
• Accepted 14 June 2021

DOI:https://doi.org/10.1103/PhysRevE.104.014119