Fluctuation properties of an effective nonlinear system subject to Poisson noise

We study the work fluctuations of a particle, confined to a moving harmonic potential, under the influence of friction and external asymmetric Poissonian shot noise. This type of noise generalizes the usual Gaussian noise and induces an effective interaction between the noise and the potential, leading to an effectively nonlinear system with singular features. On the basis of an analytic solution we investigate the roles of time scales, symmetries, and singularities in the context of nonequilibrium fluctuations. Our results highlight the nonuniversality of the steady-state fluctuation theorem in stochastic systems.

Figure 1

The harmonic potential (full and dotted lines) changes due to the PSN into an effective potential (full and dashed lines). The dashed line, starting at the cutoff point $y^{*}$, represents physically an effective infinite barrier for the particle. The black dot indicates the particle at its mean position $⟨y⟩$ for $v>0$.

Figure 2

(Color online) The fluctuation function $f\left(p\right)$ of Eq. (23) for various $p^{*}$ values and $v>0$. The approach to $f\left(p^{*}\right)$ is with a vertical slope, while $f\left(p^{*}\right)$ itself remains finite (thin dashed line). For $p^{*}>2$, $f\left(p\right)$ becomes negative in the interval $p∊[p_{+},p^{*}]$. We observe a pronounced linear regime for small $p$ values, which is a general consequence of the large deviation form of ${\Pi }_{\tau }\left(p\right)$ [18]. In the Gaussian limit, where $p^{*}\to \infty$, the SSFT is recovered.