  We investigate how the compositeness of a quantum system influences the
characteristic time of equilibration. We study the dynamics of open composite
quantum systems strongly coupled to the environment after a quantum
perturbation accompanied by non-equilibrium heating. We use a holographic
description of the evolution of entanglement entropy. The non-smooth character
of the evolution with holographic entanglement is a general feature of
composite systems, which demonstrate a dynamical change of topology in the bulk
space and a jump-like velocity change of entanglement entropy propagation.
Moreover, the number of jumps depends on the system configuration and
especially on the number of composite parts. The evolution of the mutual
information of two composite systems inherits these jumps. We present a
detailed study of the mutual information for two subsystems with one of them
being bipartite. We have found 5 qualitatively different types of behavior of
the mutual information dynamics and indicated the corresponding ranges of
system parameters.
