How a Nonequilibrium Bath and a Potential Well Lead to Broken Time-Reversal Symmetry-First-Order Corrections on Fluctuation-Dissipation Relations

The noise that is associated with nonequilibrium processes commonly features more outliers and is therefore often taken to be Levy noise. For a Langevin particle that is subjected to Levy noise, the kicksizes are drawn not from a Gaussian distribution, but from an alpha-stable distribution. For a Gaussian-noise-subjected particle in a potential well, microscopic reversibility applies. However, it appears that the time-reversal-symmetry is broken for a Levy-noise-subjected particle in a potential well. Major obstacles in the analysis of Langevin equations with Levy noise are the lack of simple analytic formulae and the infinite variance of the alpha-stable distribution. We propose a measure for the violation of time-reversal symmetry, and we present a procedure in which this measure is central to a controlled imposing of time-reversal asymmetry. The procedure leads to behavior that mimics much of the effects of Levy noise. Our imposing of such nonequilibrium leads to concise analytic formulae and does not yield any divergent variances. Most importantly, the theory leads to simple corrections on the Fluctuation-Dissipation Relation.

Automated summary

The noise associated with nonequilibrium processes is often referred to as Levy noise, which features more outliers. For Langevin particles subjected to Levy noise, the kicksizes are drawn from an alpha-stable distribution instead of a Gaussian distribution. Unlike Gaussian noise, Levy noise breaks the time-reversal symmetry for particles in a potential well. Analyzing Langevin equations with Levy noise is challenging due to the lack of simple analytic formulas and the infinite variance of the alpha-stable distribution. In our study, we propose a measure to quantify the violation of time-reversal symmetry and present a procedure that utilizes this measure to induce controlled time-reversal asymmetry. This procedure mimics the effects of Levy noise and yields concise analytic formulas without divergent variances. Importantly, our theory provides simple corrections on the Fluctuation-Dissipation Relation.