Heat and work distributions for mixed Gauss-Cauchy process

We analyze energetics of a non-Gaussian process described by a stochastic differential equation of the Langevin type. The process represents a paradigmatic model of a nonequilibrium system subject to thermal fluctuations and additional external noise, with both sources of perturbations considered as additive and statistically independent forcings. We define thermodynamic quantities for trajectories of the process and analyze contributions to mechanical work and heat. As a working example we consider a particle subjected to a drag force and two independent Levy white noises with stability indices $alpha=2$ and $alpha=1$. The fluctuations of dissipated energy (heat) and distribution of work performed by the force acting on the system are addressed by examining contributions of Cauchy fluctuations to either bath or external force acting on the system.

Transport in a Levy ratchet: Group velocity and distribution spread

We consider the motion of an overdamped particle in a periodic potential lacking spatial symmetry under the influence of symmetric Levy noise, being a minimal setup for a ``Levy ratchet. Due to the non-thermal character of the Levy noise, the particle exhibits a motion with a preferred direction even in the absence of whatever additional time-dependent forces. The examination of the Levy ratchet has to be based on the characteristics of directionality which are different from typically used measures like mean current and the dispersion of particles positions, since these get inappropriate when the moments of the noise diverge. To overcome this problem, we discuss robust measures of directionality of transport like the position of the median of the particles displacements distribution characterizing the group velocity, and the interquantile distance giving the measure of the distributions width. Moreover, we analyze the behavior of splitting probabilities for leaving an interval of a given length unveiling qualitative differences between the noises with Levy indices below and above unity. Finally, we inspect the problem of the first escape from an interval of given length revealing independence of exit times on the structure of the potential.