Stochastic approach and fluctuation theorem for ion transport

We present a stochastic approach for ion transport at the mesoscopic level. The description takes into account the self-consistent electric field generated by the fixed and mobile charges as well as the discrete nature of these latter. As an application we study the noise in the ion transport process, including the effect of the displacement current generated by the fluctuating electric field. The fluctuation theorem is shown to hold for the electric current with and without the displacement current.