  We study the quasi-stationary evolution of systems where an energetic
confinement is unable to completely retain their constituents. It is performed
an extensive numerical study of a gas whose dynamics is driven by binary
encounters and its particles are able to escape from the container when their
kinetic energies overcome a given cutou Uc .We use a parametric family of
differential cross sections in order to modify the effectiveness of this
equilibration mechanism. It is verified that when the binary encounters favor
an effective exploration of all accessible velocities, the quasi-stationary
evolution is reached when the detailed balance is imposed for all those binary
collisions which do not provoke particle evaporation. However, the weakening of
this effectiveness leads to energy distribution functions which could be very
well fitted by using a Michie-King-like profile. We perform a theoretical
analysis, in the context of Hamiltonian systems driven by a strong chaotic
dynamics and particle evaporation, in order to take into account the effect of
the nonhomogeneous character of the confining potential.
