The dynamics of the image potential states n = 3 and n = 4 at the Cu(100) surface are studied. We solve the Liouville-von Neumann equation for an open system and treat the dissipation within the Lindblad formalism. We compute the two-photon photoemission spectrum (2PPE) using first order perturbation theory and study the populations of the image potential states and the two-photon photoemission spectrum as functions of the lifetimes and dephasings of the image potential states. The computed two-photon photoemission spectrum is compared with the measured spectrum obtained by Hofer et al. [Appl. Phys. B 68, 383 (1999); Science 277, 1480 (1997)].