Kac limit and thermodynamic characterization of stochastic dynamics driven by Poisson-Kac fluctuations

We analyze the thermodynamic properties of stochastic dif- ferential equations driven by smooth Poisson-Kac fluctuations, and their convergence, in the Kac limit, towards Wiener-driven Langevin equations. Using a Markovian embedding of the stochastic work vari- able, it is proved that the Kac-limit convergence implies a Stratonovich formulation of the limit Langevin equations, in accordance with the Wong-Zakai theorem. Exact moment analysis applied to the case of a purely frictional system shows the occurrence of different regimes and crossover phenomena in the parameter space.