  We study the static and dynamical properties of isolated many-body quantum
systems and compare them with the results for full random matrices. In doing
so, we link concepts from quantum information theory with those from quantum
chaos. In particular, we relate the von Neumann entanglement entropy with the
Shannon information entropy and discuss their relevance for the analysis of the
degree of complexity of the eigenstates, the behavior of the system at
different time scales and the conditions for thermalization. A main advantage
of full random matrices is that they enable the derivation of analytical
expressions that agree extremely well with the numerics and provide bounds for
realistic many-body quantum systems.
