  A non-ergodic quantum state of a many body system is in general random as
well as multi-parametric, former due to a lack of exact information due to
complexity and latter reflecting its varied behavior in different parts of the
Hilbert space. An appropriate representation for the reduced density matrix of
such a state is a generalized, multi-parametric Wishart ensemble with unit
trace. Our theoretical analysis of these ensembles not only resolves the
controversy about the growth rates of the average information entropies of the
generic states but also leads to new insights in their entanglement dynamics.
While the state itself is multi-parametric, we find that the growth of the
average measures can be described in terms of an information-theoretic
function, referred as the complexity parameter. The latter in turn leads to a
common mathematical formulation of the measures for a wide range of states; it
could also act as a possible tool for hierarchical arrangement of the entangled
states of different systems.
