Kinetics and energetics of reflected diffusion process with time-dependent and space-homogeneous force

Abstract

We present the exact analysis of a spatially restricted one-dimensional diffusion process with a time-dependent, spatially linear potential and a reflecting boundary. Using matching conditions together with the known solution for the unbounded diffusion in the time modulated potential, we have derived a new integral equation, whose solution yields the Green function for the restricted diffusion. Applying the general scheme, we give the numerical analysis of the diffusion in a symmetrically oscillating force field superimposed on the time-independent component. The latter component alone guarantees the approach to Gibbs equilibrium with exponential probability density. We calculate both the kinetic and the energetic characteristics of the emerging non-equilibrium isothermal process and discuss their dependence on the model parameters.