An approach, differing from the two commonly used methods (the stochastic Schrodinger equation and a master equation) but entrenched in the traditional formulation of a density matrix, is developed in a semi-clasical setting, so as to go from the solutions of the time dependent Schrodinger equations to decohering and thermalized states. This is achieved by utilizing the time-ergodicity, rather than the sampling- (or ensemble-) ergodicity of physical systems. A model of minimal (two-parameter) complexity and comprising a classical oscillator in interaction with a spin doublet is shown to exhibit both qualitatively and quantitatively many features of state decohorence and equilibration. Furthermore, we show that equilibration may  be achieved even for adiabatically protected spin states (i.e., spin's Zeeman energy much larger than the oscillator frequency), provided the coupling to the environment is sufficiently large.

Thermalization involves the back-reaction fof the spin-system on the environment's temporal excursions.

Extensions of the method are underway for interacting spin-systems.