2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/213951A system reservoir model, where the associated reservoir is modulated by an external colored random force, is proposed to study the transport of an overdamped Brownian particle in a periodic potential. We then derive the analytical expression for the average velocity, mobility, and diffusion rate. The bistable kinetics and escape rate from a metastable state in the overdamped region are studied consequently. By numerical simulation we then demonstrate that our analytical escape rate is in good agreement with that of numerical result.10 pages, 2 figures, RevTex4, minor correctionsSoft Condensed MatterStatistical Mechanicstext