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 Poissonian shot noise. The asymmetry of the noise induces an effective nonlinearity in the potential, which in turn leads to singular features in the work distribution. On the basis of an analytic solution we find that the conventional fluctuation theorem is violated in this model, even though the distribution exhibits a large deviation form. Furthermore, we demonstrate that the interplay of the various time scales leads to critical behaviors, such as a negative fluctuation function and a divergence in the work distribution at the singularity. In a certain parameter regime large negative work fluctuations are more likely to occur than the corresponding positive ones, though the average work is always positive, in agreement with the second law.