Abstract : In this thesis, we first study Lorentz gas as a
billiard ball with elastic collision with the obstacles and a system of hard spheres in 2-dimensions. We study a numerical simulation of the dynamical system and we investigate the entropy increasing in
non-equilibrium with time under the effect of collisions and its relation to positive Lyapunov exponent. Then, we study a decay model in a quantum system which called Friedrichs model. In a work, we consider coupling of the kaons and environment with continuous energies. Then, we show that this model well adapted in order to describe oscillation, regeneration, decay and CP violation of a kaonic system. In the other work, we apply in the Friedrichs model, the time
super-operator formalize that predicts the resonance, i.e. the survival probability of the instable states.