Entropy Burst from Parabolic Potentials

The change of the energy of ground state is investigated in a thermodynamical process by using the model described by one-dimensional harmonic oscillator + two-dimensional isotropic parabolic potential barrier such as $V(x,y,z)=m\omega^2 x^2/2 -m\gamma^2 (y^2+z^2)/2$. In the process where two independent many-particle systems suddenly touch with each other, it is shown that the lowest energy after the interaction can possibly be smaller than that before the interaction and then the entropy burst can occur.