  We present a unifying framework to the understanding of when and how quantum
mechanical systems become independent of their initial conditions and adapt
macroscopic properties (like temperature) of the environment.By viewing this
problem from an quantum information theory perspective, we are able to simplify
it in a very natural and easy way. We first show that for any interaction
between the system and the environment, and almost all initial states of the
system, the question of how long the system retains memory of its initial
conditions can be answered by studying the temporal evolution of just one
special initial state. This special state thereby depends only on our knowledge
of macroscopic parameters of the system. We provide a simple entropic
inequality for this state that can be used to determine whether mosts states of
the system have, or have not become independent of their initial conditions
after time $t$. We discuss applications of our entropic criterion to
thermalization times in systems with an effective light-cone and to quantum
memories suffering depolarizing noise. We make a similar statement for almost
all initial states of the environment, and finally provide a sufficient
condition for which a system never thermalizes, but remains close to its
initial state for all times.
