The generalized Langevin equation revisited: Analytical expressions for the persistence dynamics of a viscous fluid under a time dependent external force

•The generalized Langevin equation is solved analytically for a viscoelastic fluid.•Alternative stochastic equations are derived for a diffusing dense fluid particle.•The Fluctuation–Dissipation theorem is generalized for a fluid in an external field.•A self-contained definition of diffusion coefficient is provided.•The short time dynamics within absorbing boundaries fits the MD simulations.

The non-static generalized Langevin equation and its corresponding Fokker–Planck equation for the position of a viscous fluid particle were solved in closed form for a time dependent external force. Its solution for a constant external force was obtained analytically. The non-Markovian stochastic differential equation, associated to the dynamics of the position under a colored noise, was then applied to the description of the dynamics and persistence time of particles constrained within absorbing barriers. Comparisons with molecular dynamics were very satisfactory.