Dissipated work in driven harmonic diffusive systems: General solution and application to stretching Rouse polymers

We study n-dimensional diffusive motion in an externally driven harmonic potential. For these systems the probability distribution of the applied work is a Gaussian. We give explicit expressions for its mean and variance, which are determined by a non-local integral kernel relating the time-derivatives of the applied forces. As illustrations, we specialize our results to dragging a colloidal particle through a viscous fluid and to stretching a Rouse polymer with different protocols.