The Friedrichs model of an unstable particle provides us with a non-trivial example of a dynamical system with a continuous spectrum. The non-unitary transformation operator which leads in our approach to a semi-group description of the time evolution of the system has been constructed in earlier papers. It is used here to evaluate the Liapounov function which plays the role of a microscopic entropy. The results, obtained without any recourse to perturbation expansions, validate resummation procedures introduced previously in a perturbative treatment. Various types of initial conditions are considered. It is shown explicitly why the distinction between pure states and mixtures is lost in the asymptotic time limit. The result is of relevance for the discussion of the quantum mechanical measurement problem.
