Understanding mechanisms for energy dissipation from nanoparticles in contact with large samples is a central problem in describing friction microscopically. Calculation of the reduced density matrix appears to be the most suitable method to study such systems that are coupled to a large environment. In this paper, the time evolution of the reduced density matrix has been evaluated for an arbitrary system coupled to a heat reservoir. The formalism is then applied to study the vibrational relaxation following the stick-slip motion of an asperity on a surface. The frequency and temperature dependence of the relaxation time is also determined. Predictions of the reduced density matrix are compared with those obtained by using the Golden Rule approach.