  Thermalization in open systems coupled to macroscopic environments is usually
analyzed from the perspective of relaxation of the reduced state of the system
to the equilibrium state. Less emphasis is given to the change of the state of
the bath. However, as previously shown for some specific models, during the
thermalization the environment may undergo a nontrivial dynamics, indicated by
the the change of its von Neumann entropy, at time scales even longer than the
relaxation time of the system; here such a behavior is nicknamed as
post-thermalization. We provide a more detailed analysis of this phenomenon by
simulating the full dynamics of a variety of systems together with their
environment. In particular, the post-thermalization is qualitatively explained
as a result of reconversion of the initially built up correlation between the
system and the bath into the correlation between the degrees of freedom in the
environment. We also present exemplary systems in which such a reconversion is
suppressed due to non-Markovian dynamics or the presence of interactions.
