  We study the convergence towards the equilibrium for a dissipative and
stochastic time-dependent oval billiard. The dynamics of the system is
described by using a generic four dimensional nonlinear map for the variables:
the angular position of the particle, the angle formed by the trajectory of the
article with the tangent line at the position of the collision, the absolute
velocity of the particle, and the instant of the hit with the boundary. The
dynamics of the stationary state as well as the dynamical evolution towards the
equilibrium is made by using an ensemble of non interacting particles. Finally,
we make a connection with the thermodynamic by using the energy equipartition
theorem.
