Behavior of a bipartite system in a cavity

We study the time evolution of a superposition of product states of two dressed atoms in a spherical cavity in the situations of an arbitrarily large cavity (free space) and of a small one. In the large-cavity case, the system dissipates, whereas, for the small cavity, the system evolves in an oscillating way and never completely decays. We verify that the von Neumann entropy for such a system does not depend on time, nor on the size of the cavity